Properties

Label 6023.2.a.b.1.1
Level 6023
Weight 2
Character 6023.1
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.79086 q^{2}\) \(-1.66708 q^{3}\) \(+5.78891 q^{4}\) \(+1.47477 q^{5}\) \(+4.65258 q^{6}\) \(-1.60538 q^{7}\) \(-10.5743 q^{8}\) \(-0.220852 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.79086 q^{2}\) \(-1.66708 q^{3}\) \(+5.78891 q^{4}\) \(+1.47477 q^{5}\) \(+4.65258 q^{6}\) \(-1.60538 q^{7}\) \(-10.5743 q^{8}\) \(-0.220852 q^{9}\) \(-4.11587 q^{10}\) \(+1.76231 q^{11}\) \(-9.65056 q^{12}\) \(+3.00110 q^{13}\) \(+4.48040 q^{14}\) \(-2.45855 q^{15}\) \(+17.9336 q^{16}\) \(-0.637489 q^{17}\) \(+0.616367 q^{18}\) \(-1.00000 q^{19}\) \(+8.53728 q^{20}\) \(+2.67630 q^{21}\) \(-4.91836 q^{22}\) \(-6.91710 q^{23}\) \(+17.6282 q^{24}\) \(-2.82507 q^{25}\) \(-8.37564 q^{26}\) \(+5.36941 q^{27}\) \(-9.29341 q^{28}\) \(+7.56995 q^{29}\) \(+6.86147 q^{30}\) \(+4.71855 q^{31}\) \(-28.9017 q^{32}\) \(-2.93791 q^{33}\) \(+1.77914 q^{34}\) \(-2.36756 q^{35}\) \(-1.27849 q^{36}\) \(-7.76535 q^{37}\) \(+2.79086 q^{38}\) \(-5.00306 q^{39}\) \(-15.5946 q^{40}\) \(+2.91992 q^{41}\) \(-7.46918 q^{42}\) \(-11.8373 q^{43}\) \(+10.2018 q^{44}\) \(-0.325705 q^{45}\) \(+19.3047 q^{46}\) \(+10.5942 q^{47}\) \(-29.8968 q^{48}\) \(-4.42275 q^{49}\) \(+7.88437 q^{50}\) \(+1.06274 q^{51}\) \(+17.3731 q^{52}\) \(+8.67812 q^{53}\) \(-14.9853 q^{54}\) \(+2.59899 q^{55}\) \(+16.9758 q^{56}\) \(+1.66708 q^{57}\) \(-21.1267 q^{58}\) \(-9.03653 q^{59}\) \(-14.2323 q^{60}\) \(-0.869732 q^{61}\) \(-13.1688 q^{62}\) \(+0.354552 q^{63}\) \(+44.7932 q^{64}\) \(+4.42591 q^{65}\) \(+8.19929 q^{66}\) \(+5.37380 q^{67}\) \(-3.69037 q^{68}\) \(+11.5313 q^{69}\) \(+6.60754 q^{70}\) \(+11.9269 q^{71}\) \(+2.33536 q^{72}\) \(-8.83344 q^{73}\) \(+21.6720 q^{74}\) \(+4.70960 q^{75}\) \(-5.78891 q^{76}\) \(-2.82918 q^{77}\) \(+13.9628 q^{78}\) \(+8.24783 q^{79}\) \(+26.4479 q^{80}\) \(-8.28867 q^{81}\) \(-8.14910 q^{82}\) \(+13.0316 q^{83}\) \(+15.4928 q^{84}\) \(-0.940147 q^{85}\) \(+33.0362 q^{86}\) \(-12.6197 q^{87}\) \(-18.6352 q^{88}\) \(-4.35438 q^{89}\) \(+0.908997 q^{90}\) \(-4.81791 q^{91}\) \(-40.0424 q^{92}\) \(-7.86619 q^{93}\) \(-29.5669 q^{94}\) \(-1.47477 q^{95}\) \(+48.1813 q^{96}\) \(-7.99494 q^{97}\) \(+12.3433 q^{98}\) \(-0.389209 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.79086 −1.97344 −0.986719 0.162439i \(-0.948064\pi\)
−0.986719 + 0.162439i \(0.948064\pi\)
\(3\) −1.66708 −0.962488 −0.481244 0.876587i \(-0.659815\pi\)
−0.481244 + 0.876587i \(0.659815\pi\)
\(4\) 5.78891 2.89445
\(5\) 1.47477 0.659535 0.329768 0.944062i \(-0.393030\pi\)
0.329768 + 0.944062i \(0.393030\pi\)
\(6\) 4.65258 1.89941
\(7\) −1.60538 −0.606778 −0.303389 0.952867i \(-0.598118\pi\)
−0.303389 + 0.952867i \(0.598118\pi\)
\(8\) −10.5743 −3.73859
\(9\) −0.220852 −0.0736173
\(10\) −4.11587 −1.30155
\(11\) 1.76231 0.531356 0.265678 0.964062i \(-0.414404\pi\)
0.265678 + 0.964062i \(0.414404\pi\)
\(12\) −9.65056 −2.78588
\(13\) 3.00110 0.832354 0.416177 0.909284i \(-0.363370\pi\)
0.416177 + 0.909284i \(0.363370\pi\)
\(14\) 4.48040 1.19744
\(15\) −2.45855 −0.634795
\(16\) 17.9336 4.48341
\(17\) −0.637489 −0.154614 −0.0773069 0.997007i \(-0.524632\pi\)
−0.0773069 + 0.997007i \(0.524632\pi\)
\(18\) 0.616367 0.145279
\(19\) −1.00000 −0.229416
\(20\) 8.53728 1.90899
\(21\) 2.67630 0.584016
\(22\) −4.91836 −1.04860
\(23\) −6.91710 −1.44231 −0.721157 0.692771i \(-0.756390\pi\)
−0.721157 + 0.692771i \(0.756390\pi\)
\(24\) 17.6282 3.59834
\(25\) −2.82507 −0.565013
\(26\) −8.37564 −1.64260
\(27\) 5.36941 1.03334
\(28\) −9.29341 −1.75629
\(29\) 7.56995 1.40570 0.702852 0.711336i \(-0.251910\pi\)
0.702852 + 0.711336i \(0.251910\pi\)
\(30\) 6.86147 1.25273
\(31\) 4.71855 0.847477 0.423738 0.905785i \(-0.360718\pi\)
0.423738 + 0.905785i \(0.360718\pi\)
\(32\) −28.9017 −5.10914
\(33\) −2.93791 −0.511424
\(34\) 1.77914 0.305121
\(35\) −2.36756 −0.400191
\(36\) −1.27849 −0.213082
\(37\) −7.76535 −1.27662 −0.638308 0.769781i \(-0.720365\pi\)
−0.638308 + 0.769781i \(0.720365\pi\)
\(38\) 2.79086 0.452738
\(39\) −5.00306 −0.801131
\(40\) −15.5946 −2.46573
\(41\) 2.91992 0.456015 0.228008 0.973659i \(-0.426779\pi\)
0.228008 + 0.973659i \(0.426779\pi\)
\(42\) −7.46918 −1.15252
\(43\) −11.8373 −1.80517 −0.902585 0.430511i \(-0.858333\pi\)
−0.902585 + 0.430511i \(0.858333\pi\)
\(44\) 10.2018 1.53799
\(45\) −0.325705 −0.0485532
\(46\) 19.3047 2.84632
\(47\) 10.5942 1.54532 0.772659 0.634821i \(-0.218926\pi\)
0.772659 + 0.634821i \(0.218926\pi\)
\(48\) −29.8968 −4.31523
\(49\) −4.42275 −0.631821
\(50\) 7.88437 1.11502
\(51\) 1.06274 0.148814
\(52\) 17.3731 2.40921
\(53\) 8.67812 1.19203 0.596016 0.802973i \(-0.296750\pi\)
0.596016 + 0.802973i \(0.296750\pi\)
\(54\) −14.9853 −2.03924
\(55\) 2.59899 0.350448
\(56\) 16.9758 2.26849
\(57\) 1.66708 0.220810
\(58\) −21.1267 −2.77407
\(59\) −9.03653 −1.17646 −0.588228 0.808695i \(-0.700174\pi\)
−0.588228 + 0.808695i \(0.700174\pi\)
\(60\) −14.2323 −1.83738
\(61\) −0.869732 −0.111358 −0.0556789 0.998449i \(-0.517732\pi\)
−0.0556789 + 0.998449i \(0.517732\pi\)
\(62\) −13.1688 −1.67244
\(63\) 0.354552 0.0446693
\(64\) 44.7932 5.59916
\(65\) 4.42591 0.548967
\(66\) 8.19929 1.00926
\(67\) 5.37380 0.656515 0.328257 0.944588i \(-0.393539\pi\)
0.328257 + 0.944588i \(0.393539\pi\)
\(68\) −3.69037 −0.447523
\(69\) 11.5313 1.38821
\(70\) 6.60754 0.789752
\(71\) 11.9269 1.41546 0.707732 0.706481i \(-0.249719\pi\)
0.707732 + 0.706481i \(0.249719\pi\)
\(72\) 2.33536 0.275224
\(73\) −8.83344 −1.03388 −0.516938 0.856023i \(-0.672928\pi\)
−0.516938 + 0.856023i \(0.672928\pi\)
\(74\) 21.6720 2.51932
\(75\) 4.70960 0.543818
\(76\) −5.78891 −0.664033
\(77\) −2.82918 −0.322415
\(78\) 13.9628 1.58098
\(79\) 8.24783 0.927954 0.463977 0.885847i \(-0.346422\pi\)
0.463977 + 0.885847i \(0.346422\pi\)
\(80\) 26.4479 2.95697
\(81\) −8.28867 −0.920963
\(82\) −8.14910 −0.899918
\(83\) 13.0316 1.43041 0.715204 0.698916i \(-0.246334\pi\)
0.715204 + 0.698916i \(0.246334\pi\)
\(84\) 15.4928 1.69041
\(85\) −0.940147 −0.101973
\(86\) 33.0362 3.56239
\(87\) −12.6197 −1.35297
\(88\) −18.6352 −1.98652
\(89\) −4.35438 −0.461563 −0.230782 0.973006i \(-0.574128\pi\)
−0.230782 + 0.973006i \(0.574128\pi\)
\(90\) 0.908997 0.0958167
\(91\) −4.81791 −0.505054
\(92\) −40.0424 −4.17471
\(93\) −7.86619 −0.815686
\(94\) −29.5669 −3.04959
\(95\) −1.47477 −0.151308
\(96\) 48.1813 4.91748
\(97\) −7.99494 −0.811763 −0.405882 0.913926i \(-0.633036\pi\)
−0.405882 + 0.913926i \(0.633036\pi\)
\(98\) 12.3433 1.24686
\(99\) −0.389209 −0.0391170
\(100\) −16.3540 −1.63540
\(101\) −11.1419 −1.10866 −0.554331 0.832296i \(-0.687026\pi\)
−0.554331 + 0.832296i \(0.687026\pi\)
\(102\) −2.96597 −0.293675
\(103\) −3.87795 −0.382105 −0.191053 0.981580i \(-0.561190\pi\)
−0.191053 + 0.981580i \(0.561190\pi\)
\(104\) −31.7345 −3.11183
\(105\) 3.94691 0.385179
\(106\) −24.2194 −2.35240
\(107\) 6.81402 0.658736 0.329368 0.944202i \(-0.393164\pi\)
0.329368 + 0.944202i \(0.393164\pi\)
\(108\) 31.0830 2.99096
\(109\) 12.3137 1.17944 0.589718 0.807609i \(-0.299239\pi\)
0.589718 + 0.807609i \(0.299239\pi\)
\(110\) −7.25343 −0.691587
\(111\) 12.9454 1.22873
\(112\) −28.7903 −2.72043
\(113\) −15.4757 −1.45583 −0.727914 0.685669i \(-0.759510\pi\)
−0.727914 + 0.685669i \(0.759510\pi\)
\(114\) −4.65258 −0.435754
\(115\) −10.2011 −0.951258
\(116\) 43.8217 4.06874
\(117\) −0.662797 −0.0612756
\(118\) 25.2197 2.32166
\(119\) 1.02341 0.0938162
\(120\) 25.9975 2.37323
\(121\) −7.89427 −0.717661
\(122\) 2.42730 0.219758
\(123\) −4.86774 −0.438909
\(124\) 27.3153 2.45298
\(125\) −11.5401 −1.03218
\(126\) −0.989504 −0.0881521
\(127\) −5.13538 −0.455691 −0.227846 0.973697i \(-0.573168\pi\)
−0.227846 + 0.973697i \(0.573168\pi\)
\(128\) −67.2084 −5.94044
\(129\) 19.7337 1.73745
\(130\) −12.3521 −1.08335
\(131\) 13.8666 1.21153 0.605765 0.795644i \(-0.292867\pi\)
0.605765 + 0.795644i \(0.292867\pi\)
\(132\) −17.0073 −1.48029
\(133\) 1.60538 0.139204
\(134\) −14.9975 −1.29559
\(135\) 7.91862 0.681527
\(136\) 6.74101 0.578037
\(137\) −2.61873 −0.223733 −0.111866 0.993723i \(-0.535683\pi\)
−0.111866 + 0.993723i \(0.535683\pi\)
\(138\) −32.1824 −2.73955
\(139\) −13.9434 −1.18267 −0.591333 0.806427i \(-0.701398\pi\)
−0.591333 + 0.806427i \(0.701398\pi\)
\(140\) −13.7056 −1.15833
\(141\) −17.6613 −1.48735
\(142\) −33.2863 −2.79333
\(143\) 5.28886 0.442276
\(144\) −3.96068 −0.330056
\(145\) 11.1639 0.927111
\(146\) 24.6529 2.04029
\(147\) 7.37306 0.608120
\(148\) −44.9529 −3.69511
\(149\) −16.2748 −1.33329 −0.666643 0.745377i \(-0.732270\pi\)
−0.666643 + 0.745377i \(0.732270\pi\)
\(150\) −13.1439 −1.07319
\(151\) −12.6627 −1.03047 −0.515237 0.857048i \(-0.672296\pi\)
−0.515237 + 0.857048i \(0.672296\pi\)
\(152\) 10.5743 0.857690
\(153\) 0.140791 0.0113822
\(154\) 7.89585 0.636266
\(155\) 6.95876 0.558941
\(156\) −28.9623 −2.31884
\(157\) 17.1966 1.37244 0.686218 0.727396i \(-0.259270\pi\)
0.686218 + 0.727396i \(0.259270\pi\)
\(158\) −23.0186 −1.83126
\(159\) −14.4671 −1.14732
\(160\) −42.6232 −3.36966
\(161\) 11.1046 0.875164
\(162\) 23.1325 1.81746
\(163\) 10.6954 0.837729 0.418865 0.908049i \(-0.362428\pi\)
0.418865 + 0.908049i \(0.362428\pi\)
\(164\) 16.9032 1.31992
\(165\) −4.33272 −0.337302
\(166\) −36.3695 −2.82282
\(167\) 0.00574492 0.000444555 0 0.000222278 1.00000i \(-0.499929\pi\)
0.000222278 1.00000i \(0.499929\pi\)
\(168\) −28.3000 −2.18339
\(169\) −3.99342 −0.307186
\(170\) 2.62382 0.201238
\(171\) 0.220852 0.0168890
\(172\) −68.5250 −5.22498
\(173\) 3.55506 0.270286 0.135143 0.990826i \(-0.456851\pi\)
0.135143 + 0.990826i \(0.456851\pi\)
\(174\) 35.2198 2.67001
\(175\) 4.53531 0.342837
\(176\) 31.6046 2.38229
\(177\) 15.0646 1.13232
\(178\) 12.1525 0.910866
\(179\) −4.25306 −0.317889 −0.158944 0.987288i \(-0.550809\pi\)
−0.158944 + 0.987288i \(0.550809\pi\)
\(180\) −1.88547 −0.140535
\(181\) −25.8527 −1.92162 −0.960808 0.277216i \(-0.910588\pi\)
−0.960808 + 0.277216i \(0.910588\pi\)
\(182\) 13.4461 0.996692
\(183\) 1.44991 0.107181
\(184\) 73.1436 5.39222
\(185\) −11.4521 −0.841973
\(186\) 21.9534 1.60970
\(187\) −1.12345 −0.0821550
\(188\) 61.3287 4.47285
\(189\) −8.61996 −0.627010
\(190\) 4.11587 0.298596
\(191\) 22.8318 1.65205 0.826025 0.563633i \(-0.190597\pi\)
0.826025 + 0.563633i \(0.190597\pi\)
\(192\) −74.6738 −5.38912
\(193\) 9.98216 0.718532 0.359266 0.933235i \(-0.383027\pi\)
0.359266 + 0.933235i \(0.383027\pi\)
\(194\) 22.3128 1.60196
\(195\) −7.37834 −0.528374
\(196\) −25.6029 −1.82878
\(197\) −12.1823 −0.867951 −0.433976 0.900925i \(-0.642890\pi\)
−0.433976 + 0.900925i \(0.642890\pi\)
\(198\) 1.08623 0.0771949
\(199\) 19.7516 1.40015 0.700077 0.714068i \(-0.253149\pi\)
0.700077 + 0.714068i \(0.253149\pi\)
\(200\) 29.8731 2.11235
\(201\) −8.95855 −0.631887
\(202\) 31.0955 2.18787
\(203\) −12.1527 −0.852949
\(204\) 6.15213 0.430735
\(205\) 4.30620 0.300758
\(206\) 10.8228 0.754061
\(207\) 1.52765 0.106179
\(208\) 53.8206 3.73178
\(209\) −1.76231 −0.121901
\(210\) −11.0153 −0.760127
\(211\) 21.0500 1.44914 0.724571 0.689200i \(-0.242038\pi\)
0.724571 + 0.689200i \(0.242038\pi\)
\(212\) 50.2368 3.45028
\(213\) −19.8831 −1.36237
\(214\) −19.0170 −1.29997
\(215\) −17.4572 −1.19057
\(216\) −56.7778 −3.86324
\(217\) −7.57508 −0.514230
\(218\) −34.3657 −2.32754
\(219\) 14.7260 0.995093
\(220\) 15.0453 1.01436
\(221\) −1.91317 −0.128693
\(222\) −36.1289 −2.42482
\(223\) −8.20113 −0.549188 −0.274594 0.961560i \(-0.588543\pi\)
−0.274594 + 0.961560i \(0.588543\pi\)
\(224\) 46.3982 3.10011
\(225\) 0.623921 0.0415947
\(226\) 43.1904 2.87298
\(227\) −12.8116 −0.850336 −0.425168 0.905114i \(-0.639785\pi\)
−0.425168 + 0.905114i \(0.639785\pi\)
\(228\) 9.65056 0.639124
\(229\) −19.9771 −1.32013 −0.660063 0.751210i \(-0.729471\pi\)
−0.660063 + 0.751210i \(0.729471\pi\)
\(230\) 28.4699 1.87725
\(231\) 4.71646 0.310320
\(232\) −80.0470 −5.25534
\(233\) 11.6928 0.766021 0.383010 0.923744i \(-0.374887\pi\)
0.383010 + 0.923744i \(0.374887\pi\)
\(234\) 1.84978 0.120924
\(235\) 15.6239 1.01919
\(236\) −52.3116 −3.40520
\(237\) −13.7498 −0.893144
\(238\) −2.85621 −0.185140
\(239\) −7.63505 −0.493870 −0.246935 0.969032i \(-0.579423\pi\)
−0.246935 + 0.969032i \(0.579423\pi\)
\(240\) −44.0907 −2.84604
\(241\) 17.7372 1.14256 0.571278 0.820757i \(-0.306448\pi\)
0.571278 + 0.820757i \(0.306448\pi\)
\(242\) 22.0318 1.41626
\(243\) −2.29038 −0.146928
\(244\) −5.03480 −0.322320
\(245\) −6.52252 −0.416708
\(246\) 13.5852 0.866160
\(247\) −3.00110 −0.190955
\(248\) −49.8954 −3.16836
\(249\) −21.7247 −1.37675
\(250\) 32.2069 2.03695
\(251\) 14.1950 0.895982 0.447991 0.894038i \(-0.352140\pi\)
0.447991 + 0.894038i \(0.352140\pi\)
\(252\) 2.05247 0.129293
\(253\) −12.1901 −0.766383
\(254\) 14.3321 0.899277
\(255\) 1.56730 0.0981480
\(256\) 97.9829 6.12393
\(257\) 18.8713 1.17716 0.588580 0.808439i \(-0.299687\pi\)
0.588580 + 0.808439i \(0.299687\pi\)
\(258\) −55.0740 −3.42876
\(259\) 12.4664 0.774622
\(260\) 25.6212 1.58896
\(261\) −1.67184 −0.103484
\(262\) −38.6997 −2.39088
\(263\) −8.04943 −0.496349 −0.248175 0.968715i \(-0.579831\pi\)
−0.248175 + 0.968715i \(0.579831\pi\)
\(264\) 31.0663 1.91200
\(265\) 12.7982 0.786187
\(266\) −4.48040 −0.274711
\(267\) 7.25909 0.444249
\(268\) 31.1084 1.90025
\(269\) 26.1179 1.59243 0.796217 0.605011i \(-0.206831\pi\)
0.796217 + 0.605011i \(0.206831\pi\)
\(270\) −22.0998 −1.34495
\(271\) −13.6713 −0.830471 −0.415235 0.909714i \(-0.636301\pi\)
−0.415235 + 0.909714i \(0.636301\pi\)
\(272\) −11.4325 −0.693197
\(273\) 8.03182 0.486108
\(274\) 7.30850 0.441523
\(275\) −4.97864 −0.300223
\(276\) 66.7539 4.01811
\(277\) −11.4839 −0.689998 −0.344999 0.938603i \(-0.612121\pi\)
−0.344999 + 0.938603i \(0.612121\pi\)
\(278\) 38.9142 2.33392
\(279\) −1.04210 −0.0623889
\(280\) 25.0354 1.49615
\(281\) −0.834965 −0.0498099 −0.0249049 0.999690i \(-0.507928\pi\)
−0.0249049 + 0.999690i \(0.507928\pi\)
\(282\) 49.2902 2.93519
\(283\) 28.2891 1.68161 0.840807 0.541336i \(-0.182081\pi\)
0.840807 + 0.541336i \(0.182081\pi\)
\(284\) 69.0438 4.09699
\(285\) 2.45855 0.145632
\(286\) −14.7605 −0.872805
\(287\) −4.68759 −0.276700
\(288\) 6.38298 0.376121
\(289\) −16.5936 −0.976095
\(290\) −31.1569 −1.82960
\(291\) 13.3282 0.781312
\(292\) −51.1360 −2.99251
\(293\) 3.94594 0.230524 0.115262 0.993335i \(-0.463229\pi\)
0.115262 + 0.993335i \(0.463229\pi\)
\(294\) −20.5772 −1.20009
\(295\) −13.3268 −0.775915
\(296\) 82.1133 4.77274
\(297\) 9.46256 0.549073
\(298\) 45.4208 2.63116
\(299\) −20.7589 −1.20052
\(300\) 27.2635 1.57406
\(301\) 19.0034 1.09534
\(302\) 35.3398 2.03357
\(303\) 18.5744 1.06707
\(304\) −17.9336 −1.02856
\(305\) −1.28265 −0.0734444
\(306\) −0.392927 −0.0224622
\(307\) −7.77529 −0.443759 −0.221880 0.975074i \(-0.571219\pi\)
−0.221880 + 0.975074i \(0.571219\pi\)
\(308\) −16.3779 −0.933215
\(309\) 6.46484 0.367772
\(310\) −19.4209 −1.10303
\(311\) 13.1183 0.743872 0.371936 0.928258i \(-0.378694\pi\)
0.371936 + 0.928258i \(0.378694\pi\)
\(312\) 52.9039 2.99510
\(313\) −16.6411 −0.940613 −0.470306 0.882503i \(-0.655857\pi\)
−0.470306 + 0.882503i \(0.655857\pi\)
\(314\) −47.9933 −2.70842
\(315\) 0.522881 0.0294610
\(316\) 47.7459 2.68592
\(317\) −1.00000 −0.0561656
\(318\) 40.3757 2.26416
\(319\) 13.3406 0.746929
\(320\) 66.0596 3.69284
\(321\) −11.3595 −0.634026
\(322\) −30.9914 −1.72708
\(323\) 0.637489 0.0354708
\(324\) −47.9823 −2.66569
\(325\) −8.47829 −0.470291
\(326\) −29.8494 −1.65321
\(327\) −20.5278 −1.13519
\(328\) −30.8762 −1.70485
\(329\) −17.0077 −0.937664
\(330\) 12.0920 0.665644
\(331\) −14.3389 −0.788135 −0.394067 0.919082i \(-0.628932\pi\)
−0.394067 + 0.919082i \(0.628932\pi\)
\(332\) 75.4389 4.14025
\(333\) 1.71499 0.0939810
\(334\) −0.0160333 −0.000877302 0
\(335\) 7.92510 0.432995
\(336\) 47.9957 2.61838
\(337\) 4.76806 0.259733 0.129866 0.991532i \(-0.458545\pi\)
0.129866 + 0.991532i \(0.458545\pi\)
\(338\) 11.1451 0.606213
\(339\) 25.7991 1.40122
\(340\) −5.44243 −0.295157
\(341\) 8.31554 0.450312
\(342\) −0.616367 −0.0333293
\(343\) 18.3379 0.990152
\(344\) 125.171 6.74878
\(345\) 17.0060 0.915574
\(346\) −9.92167 −0.533392
\(347\) 32.1588 1.72638 0.863189 0.504882i \(-0.168464\pi\)
0.863189 + 0.504882i \(0.168464\pi\)
\(348\) −73.0542 −3.91612
\(349\) 8.42544 0.451003 0.225502 0.974243i \(-0.427598\pi\)
0.225502 + 0.974243i \(0.427598\pi\)
\(350\) −12.6574 −0.676568
\(351\) 16.1141 0.860108
\(352\) −50.9336 −2.71477
\(353\) −29.6599 −1.57864 −0.789320 0.613982i \(-0.789567\pi\)
−0.789320 + 0.613982i \(0.789567\pi\)
\(354\) −42.0432 −2.23457
\(355\) 17.5894 0.933548
\(356\) −25.2071 −1.33597
\(357\) −1.70611 −0.0902970
\(358\) 11.8697 0.627333
\(359\) 17.1516 0.905229 0.452614 0.891706i \(-0.350491\pi\)
0.452614 + 0.891706i \(0.350491\pi\)
\(360\) 3.44410 0.181520
\(361\) 1.00000 0.0526316
\(362\) 72.1513 3.79219
\(363\) 13.1604 0.690740
\(364\) −27.8904 −1.46185
\(365\) −13.0273 −0.681878
\(366\) −4.04650 −0.211514
\(367\) 8.06530 0.421005 0.210503 0.977593i \(-0.432490\pi\)
0.210503 + 0.977593i \(0.432490\pi\)
\(368\) −124.049 −6.46649
\(369\) −0.644870 −0.0335706
\(370\) 31.9612 1.66158
\(371\) −13.9317 −0.723298
\(372\) −45.5367 −2.36097
\(373\) 3.27675 0.169663 0.0848317 0.996395i \(-0.472965\pi\)
0.0848317 + 0.996395i \(0.472965\pi\)
\(374\) 3.13540 0.162128
\(375\) 19.2383 0.993462
\(376\) −112.026 −5.77730
\(377\) 22.7181 1.17004
\(378\) 24.0571 1.23736
\(379\) 10.5128 0.540009 0.270004 0.962859i \(-0.412975\pi\)
0.270004 + 0.962859i \(0.412975\pi\)
\(380\) −8.53728 −0.437953
\(381\) 8.56107 0.438597
\(382\) −63.7204 −3.26022
\(383\) −18.9950 −0.970600 −0.485300 0.874348i \(-0.661290\pi\)
−0.485300 + 0.874348i \(0.661290\pi\)
\(384\) 112.042 5.71760
\(385\) −4.17238 −0.212644
\(386\) −27.8588 −1.41798
\(387\) 2.61429 0.132892
\(388\) −46.2820 −2.34961
\(389\) −9.47760 −0.480534 −0.240267 0.970707i \(-0.577235\pi\)
−0.240267 + 0.970707i \(0.577235\pi\)
\(390\) 20.5919 1.04271
\(391\) 4.40958 0.223002
\(392\) 46.7675 2.36212
\(393\) −23.1167 −1.16608
\(394\) 33.9990 1.71285
\(395\) 12.1636 0.612018
\(396\) −2.25310 −0.113222
\(397\) −34.5485 −1.73394 −0.866971 0.498359i \(-0.833936\pi\)
−0.866971 + 0.498359i \(0.833936\pi\)
\(398\) −55.1240 −2.76311
\(399\) −2.67630 −0.133982
\(400\) −50.6637 −2.53318
\(401\) 25.8235 1.28956 0.644782 0.764367i \(-0.276948\pi\)
0.644782 + 0.764367i \(0.276948\pi\)
\(402\) 25.0021 1.24699
\(403\) 14.1608 0.705401
\(404\) −64.4995 −3.20897
\(405\) −12.2238 −0.607408
\(406\) 33.9164 1.68324
\(407\) −13.6849 −0.678338
\(408\) −11.2378 −0.556354
\(409\) 35.7879 1.76960 0.884798 0.465974i \(-0.154296\pi\)
0.884798 + 0.465974i \(0.154296\pi\)
\(410\) −12.0180 −0.593528
\(411\) 4.36562 0.215340
\(412\) −22.4491 −1.10599
\(413\) 14.5071 0.713847
\(414\) −4.26347 −0.209538
\(415\) 19.2186 0.943404
\(416\) −86.7366 −4.25261
\(417\) 23.2448 1.13830
\(418\) 4.91836 0.240565
\(419\) −37.6689 −1.84025 −0.920124 0.391627i \(-0.871912\pi\)
−0.920124 + 0.391627i \(0.871912\pi\)
\(420\) 22.8483 1.11488
\(421\) −4.57550 −0.222996 −0.111498 0.993765i \(-0.535565\pi\)
−0.111498 + 0.993765i \(0.535565\pi\)
\(422\) −58.7476 −2.85979
\(423\) −2.33974 −0.113762
\(424\) −91.7652 −4.45651
\(425\) 1.80095 0.0873589
\(426\) 55.4909 2.68854
\(427\) 1.39625 0.0675694
\(428\) 39.4457 1.90668
\(429\) −8.81694 −0.425686
\(430\) 48.7207 2.34952
\(431\) −26.3981 −1.27155 −0.635775 0.771874i \(-0.719319\pi\)
−0.635775 + 0.771874i \(0.719319\pi\)
\(432\) 96.2930 4.63290
\(433\) −20.7339 −0.996410 −0.498205 0.867059i \(-0.666007\pi\)
−0.498205 + 0.867059i \(0.666007\pi\)
\(434\) 21.1410 1.01480
\(435\) −18.6111 −0.892333
\(436\) 71.2827 3.41382
\(437\) 6.91710 0.330890
\(438\) −41.0983 −1.96375
\(439\) −7.01026 −0.334581 −0.167291 0.985908i \(-0.553502\pi\)
−0.167291 + 0.985908i \(0.553502\pi\)
\(440\) −27.4826 −1.31018
\(441\) 0.976772 0.0465129
\(442\) 5.33938 0.253968
\(443\) −8.86017 −0.420959 −0.210480 0.977598i \(-0.567503\pi\)
−0.210480 + 0.977598i \(0.567503\pi\)
\(444\) 74.9400 3.55649
\(445\) −6.42169 −0.304417
\(446\) 22.8882 1.08379
\(447\) 27.1314 1.28327
\(448\) −71.9103 −3.39744
\(449\) 18.0063 0.849769 0.424885 0.905248i \(-0.360315\pi\)
0.424885 + 0.905248i \(0.360315\pi\)
\(450\) −1.74128 −0.0820846
\(451\) 5.14581 0.242307
\(452\) −89.5871 −4.21382
\(453\) 21.1097 0.991818
\(454\) 35.7554 1.67809
\(455\) −7.10528 −0.333101
\(456\) −17.6282 −0.825516
\(457\) 25.4252 1.18934 0.594671 0.803969i \(-0.297282\pi\)
0.594671 + 0.803969i \(0.297282\pi\)
\(458\) 55.7534 2.60519
\(459\) −3.42294 −0.159769
\(460\) −59.0532 −2.75337
\(461\) −31.7667 −1.47952 −0.739762 0.672869i \(-0.765062\pi\)
−0.739762 + 0.672869i \(0.765062\pi\)
\(462\) −13.1630 −0.612398
\(463\) −33.6176 −1.56234 −0.781172 0.624316i \(-0.785378\pi\)
−0.781172 + 0.624316i \(0.785378\pi\)
\(464\) 135.757 6.30234
\(465\) −11.6008 −0.537974
\(466\) −32.6330 −1.51169
\(467\) 16.8467 0.779574 0.389787 0.920905i \(-0.372549\pi\)
0.389787 + 0.920905i \(0.372549\pi\)
\(468\) −3.83687 −0.177360
\(469\) −8.62701 −0.398358
\(470\) −43.6042 −2.01131
\(471\) −28.6680 −1.32095
\(472\) 95.5551 4.39828
\(473\) −20.8610 −0.959188
\(474\) 38.3737 1.76256
\(475\) 2.82507 0.129623
\(476\) 5.92445 0.271547
\(477\) −1.91658 −0.0877541
\(478\) 21.3084 0.974622
\(479\) 21.6908 0.991079 0.495539 0.868585i \(-0.334970\pi\)
0.495539 + 0.868585i \(0.334970\pi\)
\(480\) 71.0561 3.24325
\(481\) −23.3046 −1.06260
\(482\) −49.5022 −2.25476
\(483\) −18.5122 −0.842335
\(484\) −45.6992 −2.07724
\(485\) −11.7907 −0.535387
\(486\) 6.39212 0.289952
\(487\) −35.9859 −1.63068 −0.815338 0.578986i \(-0.803449\pi\)
−0.815338 + 0.578986i \(0.803449\pi\)
\(488\) 9.19682 0.416321
\(489\) −17.8301 −0.806304
\(490\) 18.2034 0.822348
\(491\) −24.6591 −1.11285 −0.556426 0.830897i \(-0.687828\pi\)
−0.556426 + 0.830897i \(0.687828\pi\)
\(492\) −28.1789 −1.27040
\(493\) −4.82576 −0.217341
\(494\) 8.37564 0.376838
\(495\) −0.573992 −0.0257990
\(496\) 84.6208 3.79958
\(497\) −19.1472 −0.858871
\(498\) 60.6307 2.71693
\(499\) −22.2571 −0.996363 −0.498181 0.867073i \(-0.665999\pi\)
−0.498181 + 0.867073i \(0.665999\pi\)
\(500\) −66.8048 −2.98760
\(501\) −0.00957723 −0.000427879 0
\(502\) −39.6163 −1.76816
\(503\) −4.03338 −0.179840 −0.0899199 0.995949i \(-0.528661\pi\)
−0.0899199 + 0.995949i \(0.528661\pi\)
\(504\) −3.74914 −0.167000
\(505\) −16.4317 −0.731201
\(506\) 34.0208 1.51241
\(507\) 6.65735 0.295663
\(508\) −29.7282 −1.31898
\(509\) −38.4965 −1.70633 −0.853163 0.521644i \(-0.825319\pi\)
−0.853163 + 0.521644i \(0.825319\pi\)
\(510\) −4.37411 −0.193689
\(511\) 14.1811 0.627333
\(512\) −139.040 −6.14475
\(513\) −5.36941 −0.237065
\(514\) −52.6672 −2.32305
\(515\) −5.71906 −0.252012
\(516\) 114.237 5.02898
\(517\) 18.6702 0.821114
\(518\) −34.7919 −1.52867
\(519\) −5.92656 −0.260147
\(520\) −46.8010 −2.05236
\(521\) 44.2293 1.93772 0.968860 0.247608i \(-0.0796444\pi\)
0.968860 + 0.247608i \(0.0796444\pi\)
\(522\) 4.66586 0.204219
\(523\) −26.5160 −1.15947 −0.579733 0.814807i \(-0.696843\pi\)
−0.579733 + 0.814807i \(0.696843\pi\)
\(524\) 80.2724 3.50671
\(525\) −7.56072 −0.329977
\(526\) 22.4648 0.979514
\(527\) −3.00803 −0.131032
\(528\) −52.6873 −2.29292
\(529\) 24.8463 1.08027
\(530\) −35.7180 −1.55149
\(531\) 1.99573 0.0866075
\(532\) 9.29341 0.402920
\(533\) 8.76297 0.379566
\(534\) −20.2591 −0.876698
\(535\) 10.0491 0.434460
\(536\) −56.8243 −2.45444
\(537\) 7.09018 0.305964
\(538\) −72.8913 −3.14257
\(539\) −7.79425 −0.335722
\(540\) 45.8402 1.97265
\(541\) −33.1555 −1.42547 −0.712734 0.701435i \(-0.752543\pi\)
−0.712734 + 0.701435i \(0.752543\pi\)
\(542\) 38.1546 1.63888
\(543\) 43.0984 1.84953
\(544\) 18.4245 0.789944
\(545\) 18.1598 0.777879
\(546\) −22.4157 −0.959304
\(547\) 13.5577 0.579687 0.289843 0.957074i \(-0.406397\pi\)
0.289843 + 0.957074i \(0.406397\pi\)
\(548\) −15.1596 −0.647585
\(549\) 0.192082 0.00819786
\(550\) 13.8947 0.592472
\(551\) −7.56995 −0.322491
\(552\) −121.936 −5.18994
\(553\) −13.2409 −0.563061
\(554\) 32.0499 1.36167
\(555\) 19.0915 0.810389
\(556\) −80.7172 −3.42317
\(557\) −19.2303 −0.814814 −0.407407 0.913247i \(-0.633567\pi\)
−0.407407 + 0.913247i \(0.633567\pi\)
\(558\) 2.90836 0.123121
\(559\) −35.5249 −1.50254
\(560\) −42.4590 −1.79422
\(561\) 1.87288 0.0790732
\(562\) 2.33027 0.0982966
\(563\) −29.7936 −1.25565 −0.627825 0.778354i \(-0.716055\pi\)
−0.627825 + 0.778354i \(0.716055\pi\)
\(564\) −102.240 −4.30507
\(565\) −22.8230 −0.960169
\(566\) −78.9510 −3.31856
\(567\) 13.3065 0.558820
\(568\) −126.119 −5.29183
\(569\) −0.302431 −0.0126786 −0.00633928 0.999980i \(-0.502018\pi\)
−0.00633928 + 0.999980i \(0.502018\pi\)
\(570\) −6.86147 −0.287395
\(571\) 8.20964 0.343563 0.171781 0.985135i \(-0.445048\pi\)
0.171781 + 0.985135i \(0.445048\pi\)
\(572\) 30.6167 1.28015
\(573\) −38.0624 −1.59008
\(574\) 13.0824 0.546050
\(575\) 19.5413 0.814927
\(576\) −9.89267 −0.412195
\(577\) 32.4061 1.34908 0.674542 0.738236i \(-0.264341\pi\)
0.674542 + 0.738236i \(0.264341\pi\)
\(578\) 46.3105 1.92626
\(579\) −16.6410 −0.691578
\(580\) 64.6268 2.68348
\(581\) −20.9207 −0.867939
\(582\) −37.1971 −1.54187
\(583\) 15.2935 0.633393
\(584\) 93.4076 3.86523
\(585\) −0.977471 −0.0404135
\(586\) −11.0126 −0.454925
\(587\) 34.9183 1.44123 0.720617 0.693333i \(-0.243859\pi\)
0.720617 + 0.693333i \(0.243859\pi\)
\(588\) 42.6820 1.76018
\(589\) −4.71855 −0.194425
\(590\) 37.1932 1.53122
\(591\) 20.3088 0.835392
\(592\) −139.261 −5.72359
\(593\) 33.1001 1.35926 0.679630 0.733555i \(-0.262140\pi\)
0.679630 + 0.733555i \(0.262140\pi\)
\(594\) −26.4087 −1.08356
\(595\) 1.50930 0.0618751
\(596\) −94.2135 −3.85914
\(597\) −32.9274 −1.34763
\(598\) 57.9351 2.36914
\(599\) −48.0981 −1.96523 −0.982617 0.185642i \(-0.940563\pi\)
−0.982617 + 0.185642i \(0.940563\pi\)
\(600\) −49.8008 −2.03311
\(601\) −28.7990 −1.17473 −0.587367 0.809320i \(-0.699836\pi\)
−0.587367 + 0.809320i \(0.699836\pi\)
\(602\) −53.0358 −2.16158
\(603\) −1.18681 −0.0483308
\(604\) −73.3030 −2.98266
\(605\) −11.6422 −0.473323
\(606\) −51.8387 −2.10580
\(607\) −30.0228 −1.21859 −0.609294 0.792945i \(-0.708547\pi\)
−0.609294 + 0.792945i \(0.708547\pi\)
\(608\) 28.9017 1.17212
\(609\) 20.2594 0.820953
\(610\) 3.57970 0.144938
\(611\) 31.7941 1.28625
\(612\) 0.815024 0.0329454
\(613\) −39.5554 −1.59763 −0.798814 0.601579i \(-0.794539\pi\)
−0.798814 + 0.601579i \(0.794539\pi\)
\(614\) 21.6998 0.875731
\(615\) −7.17878 −0.289476
\(616\) 29.9166 1.20538
\(617\) 8.56120 0.344661 0.172331 0.985039i \(-0.444870\pi\)
0.172331 + 0.985039i \(0.444870\pi\)
\(618\) −18.0425 −0.725774
\(619\) −11.0026 −0.442231 −0.221116 0.975248i \(-0.570970\pi\)
−0.221116 + 0.975248i \(0.570970\pi\)
\(620\) 40.2836 1.61783
\(621\) −37.1407 −1.49041
\(622\) −36.6114 −1.46799
\(623\) 6.99045 0.280066
\(624\) −89.7230 −3.59180
\(625\) −2.89368 −0.115747
\(626\) 46.4431 1.85624
\(627\) 2.93791 0.117329
\(628\) 99.5494 3.97245
\(629\) 4.95033 0.197383
\(630\) −1.45929 −0.0581394
\(631\) 11.3136 0.450387 0.225194 0.974314i \(-0.427698\pi\)
0.225194 + 0.974314i \(0.427698\pi\)
\(632\) −87.2152 −3.46923
\(633\) −35.0920 −1.39478
\(634\) 2.79086 0.110839
\(635\) −7.57348 −0.300544
\(636\) −83.7487 −3.32085
\(637\) −13.2731 −0.525899
\(638\) −37.2317 −1.47402
\(639\) −2.63408 −0.104203
\(640\) −99.1167 −3.91793
\(641\) −3.43862 −0.135817 −0.0679087 0.997692i \(-0.521633\pi\)
−0.0679087 + 0.997692i \(0.521633\pi\)
\(642\) 31.7028 1.25121
\(643\) −3.44233 −0.135752 −0.0678762 0.997694i \(-0.521622\pi\)
−0.0678762 + 0.997694i \(0.521622\pi\)
\(644\) 64.2834 2.53312
\(645\) 29.1026 1.14591
\(646\) −1.77914 −0.0699995
\(647\) −14.6929 −0.577639 −0.288820 0.957384i \(-0.593263\pi\)
−0.288820 + 0.957384i \(0.593263\pi\)
\(648\) 87.6470 3.44310
\(649\) −15.9252 −0.625117
\(650\) 23.6617 0.928090
\(651\) 12.6282 0.494940
\(652\) 61.9148 2.42477
\(653\) 15.6734 0.613346 0.306673 0.951815i \(-0.400784\pi\)
0.306673 + 0.951815i \(0.400784\pi\)
\(654\) 57.2904 2.24023
\(655\) 20.4500 0.799046
\(656\) 52.3648 2.04450
\(657\) 1.95088 0.0761111
\(658\) 47.4661 1.85042
\(659\) −33.1709 −1.29215 −0.646077 0.763272i \(-0.723591\pi\)
−0.646077 + 0.763272i \(0.723591\pi\)
\(660\) −25.0817 −0.976305
\(661\) −6.98589 −0.271719 −0.135860 0.990728i \(-0.543380\pi\)
−0.135860 + 0.990728i \(0.543380\pi\)
\(662\) 40.0177 1.55533
\(663\) 3.18940 0.123866
\(664\) −137.801 −5.34770
\(665\) 2.36756 0.0918102
\(666\) −4.78631 −0.185466
\(667\) −52.3621 −2.02747
\(668\) 0.0332568 0.00128674
\(669\) 13.6719 0.528587
\(670\) −22.1179 −0.854487
\(671\) −1.53274 −0.0591707
\(672\) −77.3494 −2.98382
\(673\) 27.2023 1.04857 0.524285 0.851543i \(-0.324333\pi\)
0.524285 + 0.851543i \(0.324333\pi\)
\(674\) −13.3070 −0.512566
\(675\) −15.1689 −0.583853
\(676\) −23.1176 −0.889137
\(677\) 5.00982 0.192543 0.0962716 0.995355i \(-0.469308\pi\)
0.0962716 + 0.995355i \(0.469308\pi\)
\(678\) −72.0018 −2.76521
\(679\) 12.8349 0.492560
\(680\) 9.94141 0.381236
\(681\) 21.3580 0.818438
\(682\) −23.2075 −0.888662
\(683\) −0.454863 −0.0174048 −0.00870242 0.999962i \(-0.502770\pi\)
−0.00870242 + 0.999962i \(0.502770\pi\)
\(684\) 1.27849 0.0488843
\(685\) −3.86201 −0.147560
\(686\) −51.1785 −1.95400
\(687\) 33.3034 1.27061
\(688\) −212.286 −8.09332
\(689\) 26.0439 0.992193
\(690\) −47.4615 −1.80683
\(691\) 16.3220 0.620916 0.310458 0.950587i \(-0.399518\pi\)
0.310458 + 0.950587i \(0.399518\pi\)
\(692\) 20.5799 0.782330
\(693\) 0.624829 0.0237353
\(694\) −89.7509 −3.40690
\(695\) −20.5633 −0.780010
\(696\) 133.445 5.05820
\(697\) −1.86142 −0.0705063
\(698\) −23.5142 −0.890027
\(699\) −19.4928 −0.737286
\(700\) 26.2545 0.992327
\(701\) 4.38283 0.165537 0.0827687 0.996569i \(-0.473624\pi\)
0.0827687 + 0.996569i \(0.473624\pi\)
\(702\) −44.9723 −1.69737
\(703\) 7.76535 0.292876
\(704\) 78.9395 2.97515
\(705\) −26.0463 −0.980960
\(706\) 82.7768 3.11535
\(707\) 17.8870 0.672711
\(708\) 87.2076 3.27746
\(709\) −26.2711 −0.986632 −0.493316 0.869850i \(-0.664215\pi\)
−0.493316 + 0.869850i \(0.664215\pi\)
\(710\) −49.0896 −1.84230
\(711\) −1.82155 −0.0683134
\(712\) 46.0446 1.72559
\(713\) −32.6387 −1.22233
\(714\) 4.76152 0.178195
\(715\) 7.79983 0.291697
\(716\) −24.6206 −0.920114
\(717\) 12.7282 0.475344
\(718\) −47.8678 −1.78641
\(719\) −39.4160 −1.46997 −0.734985 0.678083i \(-0.762811\pi\)
−0.734985 + 0.678083i \(0.762811\pi\)
\(720\) −5.84107 −0.217684
\(721\) 6.22559 0.231853
\(722\) −2.79086 −0.103865
\(723\) −29.5693 −1.09970
\(724\) −149.659 −5.56203
\(725\) −21.3856 −0.794241
\(726\) −36.7287 −1.36313
\(727\) −9.70602 −0.359976 −0.179988 0.983669i \(-0.557606\pi\)
−0.179988 + 0.983669i \(0.557606\pi\)
\(728\) 50.9461 1.88819
\(729\) 28.6842 1.06238
\(730\) 36.3573 1.34564
\(731\) 7.54615 0.279104
\(732\) 8.39340 0.310229
\(733\) −25.1275 −0.928106 −0.464053 0.885808i \(-0.653605\pi\)
−0.464053 + 0.885808i \(0.653605\pi\)
\(734\) −22.5091 −0.830827
\(735\) 10.8735 0.401077
\(736\) 199.916 7.36899
\(737\) 9.47030 0.348843
\(738\) 1.79974 0.0662495
\(739\) −4.66784 −0.171709 −0.0858546 0.996308i \(-0.527362\pi\)
−0.0858546 + 0.996308i \(0.527362\pi\)
\(740\) −66.2950 −2.43705
\(741\) 5.00306 0.183792
\(742\) 38.8815 1.42738
\(743\) 4.75426 0.174417 0.0872085 0.996190i \(-0.472205\pi\)
0.0872085 + 0.996190i \(0.472205\pi\)
\(744\) 83.1796 3.04951
\(745\) −24.0016 −0.879350
\(746\) −9.14494 −0.334820
\(747\) −2.87806 −0.105303
\(748\) −6.50356 −0.237794
\(749\) −10.9391 −0.399706
\(750\) −53.6915 −1.96053
\(751\) 4.10506 0.149796 0.0748979 0.997191i \(-0.476137\pi\)
0.0748979 + 0.997191i \(0.476137\pi\)
\(752\) 189.992 6.92829
\(753\) −23.6642 −0.862371
\(754\) −63.4032 −2.30901
\(755\) −18.6745 −0.679634
\(756\) −49.9001 −1.81485
\(757\) 16.6814 0.606296 0.303148 0.952943i \(-0.401962\pi\)
0.303148 + 0.952943i \(0.401962\pi\)
\(758\) −29.3399 −1.06567
\(759\) 20.3218 0.737634
\(760\) 15.5946 0.565677
\(761\) −40.2784 −1.46009 −0.730046 0.683398i \(-0.760501\pi\)
−0.730046 + 0.683398i \(0.760501\pi\)
\(762\) −23.8928 −0.865544
\(763\) −19.7681 −0.715655
\(764\) 132.171 4.78178
\(765\) 0.207633 0.00750699
\(766\) 53.0125 1.91542
\(767\) −27.1195 −0.979228
\(768\) −163.345 −5.89421
\(769\) 12.8078 0.461862 0.230931 0.972970i \(-0.425823\pi\)
0.230931 + 0.972970i \(0.425823\pi\)
\(770\) 11.6445 0.419640
\(771\) −31.4600 −1.13300
\(772\) 57.7858 2.07976
\(773\) −2.57445 −0.0925966 −0.0462983 0.998928i \(-0.514742\pi\)
−0.0462983 + 0.998928i \(0.514742\pi\)
\(774\) −7.29612 −0.262253
\(775\) −13.3302 −0.478836
\(776\) 84.5410 3.03485
\(777\) −20.7824 −0.745564
\(778\) 26.4507 0.948303
\(779\) −2.91992 −0.104617
\(780\) −42.7125 −1.52935
\(781\) 21.0189 0.752115
\(782\) −12.3065 −0.440080
\(783\) 40.6461 1.45257
\(784\) −79.3159 −2.83271
\(785\) 25.3609 0.905170
\(786\) 64.5154 2.30119
\(787\) −41.2312 −1.46973 −0.734866 0.678212i \(-0.762755\pi\)
−0.734866 + 0.678212i \(0.762755\pi\)
\(788\) −70.5220 −2.51224
\(789\) 13.4190 0.477730
\(790\) −33.9470 −1.20778
\(791\) 24.8443 0.883363
\(792\) 4.11562 0.146242
\(793\) −2.61015 −0.0926891
\(794\) 96.4202 3.42182
\(795\) −21.3356 −0.756695
\(796\) 114.340 4.05268
\(797\) −20.5250 −0.727034 −0.363517 0.931588i \(-0.618424\pi\)
−0.363517 + 0.931588i \(0.618424\pi\)
\(798\) 7.46918 0.264406
\(799\) −6.75367 −0.238928
\(800\) 81.6491 2.88673
\(801\) 0.961673 0.0339790
\(802\) −72.0698 −2.54487
\(803\) −15.5673 −0.549356
\(804\) −51.8602 −1.82897
\(805\) 16.3767 0.577202
\(806\) −39.5209 −1.39206
\(807\) −43.5405 −1.53270
\(808\) 117.818 4.14483
\(809\) −22.1283 −0.777990 −0.388995 0.921240i \(-0.627178\pi\)
−0.388995 + 0.921240i \(0.627178\pi\)
\(810\) 34.1151 1.19868
\(811\) 33.8533 1.18875 0.594375 0.804188i \(-0.297399\pi\)
0.594375 + 0.804188i \(0.297399\pi\)
\(812\) −70.3506 −2.46882
\(813\) 22.7911 0.799318
\(814\) 38.1928 1.33866
\(815\) 15.7732 0.552512
\(816\) 19.0589 0.667194
\(817\) 11.8373 0.414135
\(818\) −99.8790 −3.49219
\(819\) 1.06404 0.0371807
\(820\) 24.9282 0.870531
\(821\) 19.7718 0.690042 0.345021 0.938595i \(-0.387872\pi\)
0.345021 + 0.938595i \(0.387872\pi\)
\(822\) −12.1838 −0.424960
\(823\) 22.2353 0.775075 0.387537 0.921854i \(-0.373326\pi\)
0.387537 + 0.921854i \(0.373326\pi\)
\(824\) 41.0066 1.42853
\(825\) 8.29978 0.288961
\(826\) −40.4873 −1.40873
\(827\) 49.9926 1.73841 0.869206 0.494450i \(-0.164631\pi\)
0.869206 + 0.494450i \(0.164631\pi\)
\(828\) 8.84345 0.307331
\(829\) −33.0179 −1.14676 −0.573379 0.819290i \(-0.694368\pi\)
−0.573379 + 0.819290i \(0.694368\pi\)
\(830\) −53.6365 −1.86175
\(831\) 19.1445 0.664115
\(832\) 134.429 4.66048
\(833\) 2.81945 0.0976883
\(834\) −64.8730 −2.24637
\(835\) 0.00847241 0.000293200 0
\(836\) −10.2018 −0.352838
\(837\) 25.3358 0.875735
\(838\) 105.129 3.63161
\(839\) 22.3431 0.771369 0.385684 0.922631i \(-0.373965\pi\)
0.385684 + 0.922631i \(0.373965\pi\)
\(840\) −41.7359 −1.44003
\(841\) 28.3041 0.976002
\(842\) 12.7696 0.440069
\(843\) 1.39195 0.0479414
\(844\) 121.856 4.19447
\(845\) −5.88937 −0.202600
\(846\) 6.52989 0.224502
\(847\) 12.6733 0.435460
\(848\) 155.630 5.34437
\(849\) −47.1602 −1.61853
\(850\) −5.02620 −0.172397
\(851\) 53.7137 1.84128
\(852\) −115.101 −3.94331
\(853\) 16.1099 0.551592 0.275796 0.961216i \(-0.411059\pi\)
0.275796 + 0.961216i \(0.411059\pi\)
\(854\) −3.89675 −0.133344
\(855\) 0.325705 0.0111389
\(856\) −72.0536 −2.46274
\(857\) −49.2768 −1.68326 −0.841631 0.540053i \(-0.818404\pi\)
−0.841631 + 0.540053i \(0.818404\pi\)
\(858\) 24.6068 0.840064
\(859\) −38.3647 −1.30899 −0.654494 0.756067i \(-0.727118\pi\)
−0.654494 + 0.756067i \(0.727118\pi\)
\(860\) −101.058 −3.44606
\(861\) 7.81458 0.266320
\(862\) 73.6734 2.50932
\(863\) 4.61485 0.157091 0.0785456 0.996911i \(-0.474972\pi\)
0.0785456 + 0.996911i \(0.474972\pi\)
\(864\) −155.185 −5.27950
\(865\) 5.24288 0.178263
\(866\) 57.8656 1.96635
\(867\) 27.6628 0.939479
\(868\) −43.8514 −1.48841
\(869\) 14.5352 0.493074
\(870\) 51.9410 1.76096
\(871\) 16.1273 0.546453
\(872\) −130.209 −4.40942
\(873\) 1.76570 0.0597598
\(874\) −19.3047 −0.652990
\(875\) 18.5263 0.626305
\(876\) 85.2476 2.88025
\(877\) −3.22479 −0.108894 −0.0544468 0.998517i \(-0.517340\pi\)
−0.0544468 + 0.998517i \(0.517340\pi\)
\(878\) 19.5647 0.660275
\(879\) −6.57819 −0.221877
\(880\) 46.6094 1.57120
\(881\) −0.585620 −0.0197300 −0.00986502 0.999951i \(-0.503140\pi\)
−0.00986502 + 0.999951i \(0.503140\pi\)
\(882\) −2.72603 −0.0917904
\(883\) −41.6107 −1.40031 −0.700155 0.713991i \(-0.746886\pi\)
−0.700155 + 0.713991i \(0.746886\pi\)
\(884\) −11.0751 −0.372497
\(885\) 22.2168 0.746808
\(886\) 24.7275 0.830737
\(887\) 17.3700 0.583228 0.291614 0.956536i \(-0.405808\pi\)
0.291614 + 0.956536i \(0.405808\pi\)
\(888\) −136.889 −4.59370
\(889\) 8.24424 0.276503
\(890\) 17.9221 0.600749
\(891\) −14.6072 −0.489359
\(892\) −47.4756 −1.58960
\(893\) −10.5942 −0.354520
\(894\) −75.7200 −2.53246
\(895\) −6.27227 −0.209659
\(896\) 107.895 3.60453
\(897\) 34.6067 1.15548
\(898\) −50.2530 −1.67697
\(899\) 35.7192 1.19130
\(900\) 3.61182 0.120394
\(901\) −5.53221 −0.184305
\(902\) −14.3612 −0.478177
\(903\) −31.6801 −1.05425
\(904\) 163.644 5.44273
\(905\) −38.1267 −1.26737
\(906\) −58.9141 −1.95729
\(907\) −32.5385 −1.08042 −0.540211 0.841530i \(-0.681656\pi\)
−0.540211 + 0.841530i \(0.681656\pi\)
\(908\) −74.1652 −2.46126
\(909\) 2.46071 0.0816166
\(910\) 19.8299 0.657354
\(911\) −32.8722 −1.08910 −0.544552 0.838727i \(-0.683300\pi\)
−0.544552 + 0.838727i \(0.683300\pi\)
\(912\) 29.8968 0.989981
\(913\) 22.9658 0.760056
\(914\) −70.9583 −2.34709
\(915\) 2.13828 0.0706893
\(916\) −115.646 −3.82104
\(917\) −22.2612 −0.735129
\(918\) 9.55295 0.315294
\(919\) 58.0395 1.91455 0.957274 0.289182i \(-0.0933834\pi\)
0.957274 + 0.289182i \(0.0933834\pi\)
\(920\) 107.870 3.55636
\(921\) 12.9620 0.427113
\(922\) 88.6565 2.91975
\(923\) 35.7938 1.17817
\(924\) 27.3032 0.898208
\(925\) 21.9376 0.721305
\(926\) 93.8222 3.08319
\(927\) 0.856451 0.0281295
\(928\) −218.784 −7.18193
\(929\) −32.0482 −1.05147 −0.525734 0.850649i \(-0.676209\pi\)
−0.525734 + 0.850649i \(0.676209\pi\)
\(930\) 32.3762 1.06166
\(931\) 4.42275 0.144950
\(932\) 67.6885 2.21721
\(933\) −21.8693 −0.715968
\(934\) −47.0169 −1.53844
\(935\) −1.65683 −0.0541841
\(936\) 7.00863 0.229084
\(937\) 4.59366 0.150068 0.0750342 0.997181i \(-0.476093\pi\)
0.0750342 + 0.997181i \(0.476093\pi\)
\(938\) 24.0768 0.786135
\(939\) 27.7421 0.905328
\(940\) 90.4454 2.95000
\(941\) −7.13058 −0.232450 −0.116225 0.993223i \(-0.537079\pi\)
−0.116225 + 0.993223i \(0.537079\pi\)
\(942\) 80.0085 2.60682
\(943\) −20.1974 −0.657718
\(944\) −162.058 −5.27453
\(945\) −12.7124 −0.413535
\(946\) 58.2201 1.89290
\(947\) −11.0836 −0.360169 −0.180084 0.983651i \(-0.557637\pi\)
−0.180084 + 0.983651i \(0.557637\pi\)
\(948\) −79.5962 −2.58516
\(949\) −26.5100 −0.860551
\(950\) −7.88437 −0.255803
\(951\) 1.66708 0.0540587
\(952\) −10.8219 −0.350740
\(953\) −17.2942 −0.560214 −0.280107 0.959969i \(-0.590370\pi\)
−0.280107 + 0.959969i \(0.590370\pi\)
\(954\) 5.34891 0.173177
\(955\) 33.6715 1.08959
\(956\) −44.1986 −1.42949
\(957\) −22.2398 −0.718910
\(958\) −60.5361 −1.95583
\(959\) 4.20406 0.135756
\(960\) −110.126 −3.55431
\(961\) −8.73528 −0.281783
\(962\) 65.0398 2.09697
\(963\) −1.50489 −0.0484944
\(964\) 102.679 3.30707
\(965\) 14.7213 0.473897
\(966\) 51.6650 1.66229
\(967\) −30.6001 −0.984031 −0.492016 0.870586i \(-0.663740\pi\)
−0.492016 + 0.870586i \(0.663740\pi\)
\(968\) 83.4765 2.68304
\(969\) −1.06274 −0.0341403
\(970\) 32.9061 1.05655
\(971\) −54.1496 −1.73774 −0.868872 0.495036i \(-0.835155\pi\)
−0.868872 + 0.495036i \(0.835155\pi\)
\(972\) −13.2588 −0.425275
\(973\) 22.3845 0.717616
\(974\) 100.432 3.21803
\(975\) 14.1340 0.452649
\(976\) −15.5975 −0.499263
\(977\) 9.65440 0.308872 0.154436 0.988003i \(-0.450644\pi\)
0.154436 + 0.988003i \(0.450644\pi\)
\(978\) 49.7613 1.59119
\(979\) −7.67376 −0.245255
\(980\) −37.7582 −1.20614
\(981\) −2.71950 −0.0868268
\(982\) 68.8202 2.19614
\(983\) 33.3082 1.06237 0.531183 0.847257i \(-0.321748\pi\)
0.531183 + 0.847257i \(0.321748\pi\)
\(984\) 51.4730 1.64090
\(985\) −17.9660 −0.572444
\(986\) 13.4680 0.428909
\(987\) 28.3531 0.902491
\(988\) −17.3731 −0.552711
\(989\) 81.8797 2.60362
\(990\) 1.60193 0.0509128
\(991\) 25.0874 0.796929 0.398464 0.917184i \(-0.369543\pi\)
0.398464 + 0.917184i \(0.369543\pi\)
\(992\) −136.374 −4.32988
\(993\) 23.9040 0.758570
\(994\) 53.4373 1.69493
\(995\) 29.1290 0.923451
\(996\) −125.763 −3.98494
\(997\) −26.4911 −0.838982 −0.419491 0.907760i \(-0.637791\pi\)
−0.419491 + 0.907760i \(0.637791\pi\)
\(998\) 62.1164 1.96626
\(999\) −41.6954 −1.31918
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 \(a_p\))