Properties

Label 6034.2.a.n.1.15
Level 6034
Weight 2
Character 6034.1
Self dual Yes
Analytic conductor 48.182
Analytic rank 0
Dimension 24
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 6034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.20386 q^{3}\) \(+1.00000 q^{4}\) \(-2.97794 q^{5}\) \(-1.20386 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-1.55072 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.20386 q^{3}\) \(+1.00000 q^{4}\) \(-2.97794 q^{5}\) \(-1.20386 q^{6}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(-1.55072 q^{9}\) \(+2.97794 q^{10}\) \(+4.89942 q^{11}\) \(+1.20386 q^{12}\) \(+0.849112 q^{13}\) \(+1.00000 q^{14}\) \(-3.58501 q^{15}\) \(+1.00000 q^{16}\) \(+0.911913 q^{17}\) \(+1.55072 q^{18}\) \(-0.375237 q^{19}\) \(-2.97794 q^{20}\) \(-1.20386 q^{21}\) \(-4.89942 q^{22}\) \(-0.153613 q^{23}\) \(-1.20386 q^{24}\) \(+3.86810 q^{25}\) \(-0.849112 q^{26}\) \(-5.47843 q^{27}\) \(-1.00000 q^{28}\) \(+6.12429 q^{29}\) \(+3.58501 q^{30}\) \(+5.66260 q^{31}\) \(-1.00000 q^{32}\) \(+5.89821 q^{33}\) \(-0.911913 q^{34}\) \(+2.97794 q^{35}\) \(-1.55072 q^{36}\) \(-11.1147 q^{37}\) \(+0.375237 q^{38}\) \(+1.02221 q^{39}\) \(+2.97794 q^{40}\) \(-3.62198 q^{41}\) \(+1.20386 q^{42}\) \(-0.855256 q^{43}\) \(+4.89942 q^{44}\) \(+4.61796 q^{45}\) \(+0.153613 q^{46}\) \(-8.00473 q^{47}\) \(+1.20386 q^{48}\) \(+1.00000 q^{49}\) \(-3.86810 q^{50}\) \(+1.09781 q^{51}\) \(+0.849112 q^{52}\) \(-3.06278 q^{53}\) \(+5.47843 q^{54}\) \(-14.5902 q^{55}\) \(+1.00000 q^{56}\) \(-0.451732 q^{57}\) \(-6.12429 q^{58}\) \(+9.27497 q^{59}\) \(-3.58501 q^{60}\) \(+6.50346 q^{61}\) \(-5.66260 q^{62}\) \(+1.55072 q^{63}\) \(+1.00000 q^{64}\) \(-2.52860 q^{65}\) \(-5.89821 q^{66}\) \(-4.31228 q^{67}\) \(+0.911913 q^{68}\) \(-0.184928 q^{69}\) \(-2.97794 q^{70}\) \(-0.739152 q^{71}\) \(+1.55072 q^{72}\) \(-8.19489 q^{73}\) \(+11.1147 q^{74}\) \(+4.65665 q^{75}\) \(-0.375237 q^{76}\) \(-4.89942 q^{77}\) \(-1.02221 q^{78}\) \(+17.0294 q^{79}\) \(-2.97794 q^{80}\) \(-1.94308 q^{81}\) \(+3.62198 q^{82}\) \(+6.32734 q^{83}\) \(-1.20386 q^{84}\) \(-2.71562 q^{85}\) \(+0.855256 q^{86}\) \(+7.37278 q^{87}\) \(-4.89942 q^{88}\) \(+0.101939 q^{89}\) \(-4.61796 q^{90}\) \(-0.849112 q^{91}\) \(-0.153613 q^{92}\) \(+6.81696 q^{93}\) \(+8.00473 q^{94}\) \(+1.11743 q^{95}\) \(-1.20386 q^{96}\) \(+4.01210 q^{97}\) \(-1.00000 q^{98}\) \(-7.59766 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut -\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 15q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 24q^{14} \) \(\mathstrut +\mathstrut 13q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 19q^{18} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 7q^{21} \) \(\mathstrut -\mathstrut 15q^{22} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut -\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 12q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut +\mathstrut 22q^{27} \) \(\mathstrut -\mathstrut 24q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 13q^{30} \) \(\mathstrut +\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut +\mathstrut 19q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 7q^{42} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 41q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut +\mathstrut 35q^{47} \) \(\mathstrut +\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 24q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 31q^{51} \) \(\mathstrut -\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 14q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 5q^{58} \) \(\mathstrut +\mathstrut 35q^{59} \) \(\mathstrut +\mathstrut 13q^{60} \) \(\mathstrut -\mathstrut 7q^{61} \) \(\mathstrut -\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 58q^{71} \) \(\mathstrut -\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 9q^{73} \) \(\mathstrut -\mathstrut 2q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 6q^{76} \) \(\mathstrut -\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 16q^{81} \) \(\mathstrut -\mathstrut 25q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 15q^{86} \) \(\mathstrut +\mathstrut 30q^{87} \) \(\mathstrut -\mathstrut 15q^{88} \) \(\mathstrut +\mathstrut 45q^{89} \) \(\mathstrut -\mathstrut 41q^{90} \) \(\mathstrut +\mathstrut 7q^{91} \) \(\mathstrut +\mathstrut 3q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut -\mathstrut 35q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 9q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 64q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.20386 0.695048 0.347524 0.937671i \(-0.387023\pi\)
0.347524 + 0.937671i \(0.387023\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.97794 −1.33177 −0.665887 0.746053i \(-0.731947\pi\)
−0.665887 + 0.746053i \(0.731947\pi\)
\(6\) −1.20386 −0.491473
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) −1.55072 −0.516908
\(10\) 2.97794 0.941706
\(11\) 4.89942 1.47723 0.738616 0.674127i \(-0.235480\pi\)
0.738616 + 0.674127i \(0.235480\pi\)
\(12\) 1.20386 0.347524
\(13\) 0.849112 0.235501 0.117751 0.993043i \(-0.462432\pi\)
0.117751 + 0.993043i \(0.462432\pi\)
\(14\) 1.00000 0.267261
\(15\) −3.58501 −0.925647
\(16\) 1.00000 0.250000
\(17\) 0.911913 0.221171 0.110586 0.993867i \(-0.464727\pi\)
0.110586 + 0.993867i \(0.464727\pi\)
\(18\) 1.55072 0.365509
\(19\) −0.375237 −0.0860852 −0.0430426 0.999073i \(-0.513705\pi\)
−0.0430426 + 0.999073i \(0.513705\pi\)
\(20\) −2.97794 −0.665887
\(21\) −1.20386 −0.262703
\(22\) −4.89942 −1.04456
\(23\) −0.153613 −0.0320304 −0.0160152 0.999872i \(-0.505098\pi\)
−0.0160152 + 0.999872i \(0.505098\pi\)
\(24\) −1.20386 −0.245737
\(25\) 3.86810 0.773621
\(26\) −0.849112 −0.166525
\(27\) −5.47843 −1.05432
\(28\) −1.00000 −0.188982
\(29\) 6.12429 1.13725 0.568626 0.822596i \(-0.307475\pi\)
0.568626 + 0.822596i \(0.307475\pi\)
\(30\) 3.58501 0.654531
\(31\) 5.66260 1.01703 0.508516 0.861052i \(-0.330194\pi\)
0.508516 + 0.861052i \(0.330194\pi\)
\(32\) −1.00000 −0.176777
\(33\) 5.89821 1.02675
\(34\) −0.911913 −0.156392
\(35\) 2.97794 0.503363
\(36\) −1.55072 −0.258454
\(37\) −11.1147 −1.82725 −0.913626 0.406557i \(-0.866729\pi\)
−0.913626 + 0.406557i \(0.866729\pi\)
\(38\) 0.375237 0.0608715
\(39\) 1.02221 0.163685
\(40\) 2.97794 0.470853
\(41\) −3.62198 −0.565658 −0.282829 0.959170i \(-0.591273\pi\)
−0.282829 + 0.959170i \(0.591273\pi\)
\(42\) 1.20386 0.185759
\(43\) −0.855256 −0.130425 −0.0652127 0.997871i \(-0.520773\pi\)
−0.0652127 + 0.997871i \(0.520773\pi\)
\(44\) 4.89942 0.738616
\(45\) 4.61796 0.688405
\(46\) 0.153613 0.0226489
\(47\) −8.00473 −1.16761 −0.583805 0.811894i \(-0.698437\pi\)
−0.583805 + 0.811894i \(0.698437\pi\)
\(48\) 1.20386 0.173762
\(49\) 1.00000 0.142857
\(50\) −3.86810 −0.547033
\(51\) 1.09781 0.153725
\(52\) 0.849112 0.117751
\(53\) −3.06278 −0.420705 −0.210353 0.977626i \(-0.567461\pi\)
−0.210353 + 0.977626i \(0.567461\pi\)
\(54\) 5.47843 0.745520
\(55\) −14.5902 −1.96734
\(56\) 1.00000 0.133631
\(57\) −0.451732 −0.0598334
\(58\) −6.12429 −0.804159
\(59\) 9.27497 1.20750 0.603749 0.797174i \(-0.293673\pi\)
0.603749 + 0.797174i \(0.293673\pi\)
\(60\) −3.58501 −0.462823
\(61\) 6.50346 0.832683 0.416341 0.909208i \(-0.363312\pi\)
0.416341 + 0.909208i \(0.363312\pi\)
\(62\) −5.66260 −0.719150
\(63\) 1.55072 0.195373
\(64\) 1.00000 0.125000
\(65\) −2.52860 −0.313635
\(66\) −5.89821 −0.726020
\(67\) −4.31228 −0.526829 −0.263415 0.964683i \(-0.584849\pi\)
−0.263415 + 0.964683i \(0.584849\pi\)
\(68\) 0.911913 0.110586
\(69\) −0.184928 −0.0222627
\(70\) −2.97794 −0.355931
\(71\) −0.739152 −0.0877212 −0.0438606 0.999038i \(-0.513966\pi\)
−0.0438606 + 0.999038i \(0.513966\pi\)
\(72\) 1.55072 0.182755
\(73\) −8.19489 −0.959139 −0.479570 0.877504i \(-0.659207\pi\)
−0.479570 + 0.877504i \(0.659207\pi\)
\(74\) 11.1147 1.29206
\(75\) 4.65665 0.537704
\(76\) −0.375237 −0.0430426
\(77\) −4.89942 −0.558341
\(78\) −1.02221 −0.115743
\(79\) 17.0294 1.91596 0.957980 0.286836i \(-0.0926035\pi\)
0.957980 + 0.286836i \(0.0926035\pi\)
\(80\) −2.97794 −0.332943
\(81\) −1.94308 −0.215898
\(82\) 3.62198 0.399980
\(83\) 6.32734 0.694516 0.347258 0.937770i \(-0.387113\pi\)
0.347258 + 0.937770i \(0.387113\pi\)
\(84\) −1.20386 −0.131352
\(85\) −2.71562 −0.294550
\(86\) 0.855256 0.0922246
\(87\) 7.37278 0.790445
\(88\) −4.89942 −0.522280
\(89\) 0.101939 0.0108055 0.00540276 0.999985i \(-0.498280\pi\)
0.00540276 + 0.999985i \(0.498280\pi\)
\(90\) −4.61796 −0.486776
\(91\) −0.849112 −0.0890112
\(92\) −0.153613 −0.0160152
\(93\) 6.81696 0.706886
\(94\) 8.00473 0.825625
\(95\) 1.11743 0.114646
\(96\) −1.20386 −0.122868
\(97\) 4.01210 0.407367 0.203683 0.979037i \(-0.434709\pi\)
0.203683 + 0.979037i \(0.434709\pi\)
\(98\) −1.00000 −0.101015
\(99\) −7.59766 −0.763593
\(100\) 3.86810 0.386810
\(101\) −3.91128 −0.389187 −0.194594 0.980884i \(-0.562339\pi\)
−0.194594 + 0.980884i \(0.562339\pi\)
\(102\) −1.09781 −0.108700
\(103\) 6.58489 0.648829 0.324414 0.945915i \(-0.394833\pi\)
0.324414 + 0.945915i \(0.394833\pi\)
\(104\) −0.849112 −0.0832623
\(105\) 3.58501 0.349862
\(106\) 3.06278 0.297484
\(107\) −19.3066 −1.86644 −0.933219 0.359307i \(-0.883013\pi\)
−0.933219 + 0.359307i \(0.883013\pi\)
\(108\) −5.47843 −0.527162
\(109\) 17.7165 1.69693 0.848464 0.529252i \(-0.177528\pi\)
0.848464 + 0.529252i \(0.177528\pi\)
\(110\) 14.5902 1.39112
\(111\) −13.3806 −1.27003
\(112\) −1.00000 −0.0944911
\(113\) −8.03226 −0.755611 −0.377806 0.925885i \(-0.623321\pi\)
−0.377806 + 0.925885i \(0.623321\pi\)
\(114\) 0.451732 0.0423086
\(115\) 0.457448 0.0426573
\(116\) 6.12429 0.568626
\(117\) −1.31674 −0.121733
\(118\) −9.27497 −0.853830
\(119\) −0.911913 −0.0835949
\(120\) 3.58501 0.327266
\(121\) 13.0043 1.18221
\(122\) −6.50346 −0.588796
\(123\) −4.36035 −0.393159
\(124\) 5.66260 0.508516
\(125\) 3.37071 0.301486
\(126\) −1.55072 −0.138150
\(127\) −17.3063 −1.53569 −0.767843 0.640638i \(-0.778670\pi\)
−0.767843 + 0.640638i \(0.778670\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −1.02961 −0.0906519
\(130\) 2.52860 0.221773
\(131\) 5.19930 0.454265 0.227132 0.973864i \(-0.427065\pi\)
0.227132 + 0.973864i \(0.427065\pi\)
\(132\) 5.89821 0.513373
\(133\) 0.375237 0.0325372
\(134\) 4.31228 0.372524
\(135\) 16.3144 1.40412
\(136\) −0.911913 −0.0781959
\(137\) 1.31183 0.112077 0.0560384 0.998429i \(-0.482153\pi\)
0.0560384 + 0.998429i \(0.482153\pi\)
\(138\) 0.184928 0.0157421
\(139\) −6.40785 −0.543507 −0.271753 0.962367i \(-0.587603\pi\)
−0.271753 + 0.962367i \(0.587603\pi\)
\(140\) 2.97794 0.251682
\(141\) −9.63656 −0.811545
\(142\) 0.739152 0.0620282
\(143\) 4.16016 0.347890
\(144\) −1.55072 −0.129227
\(145\) −18.2378 −1.51456
\(146\) 8.19489 0.678214
\(147\) 1.20386 0.0992926
\(148\) −11.1147 −0.913626
\(149\) 14.5607 1.19286 0.596431 0.802665i \(-0.296585\pi\)
0.596431 + 0.802665i \(0.296585\pi\)
\(150\) −4.65665 −0.380214
\(151\) 1.41094 0.114821 0.0574104 0.998351i \(-0.481716\pi\)
0.0574104 + 0.998351i \(0.481716\pi\)
\(152\) 0.375237 0.0304357
\(153\) −1.41413 −0.114325
\(154\) 4.89942 0.394807
\(155\) −16.8629 −1.35446
\(156\) 1.02221 0.0818424
\(157\) 11.7978 0.941565 0.470782 0.882249i \(-0.343972\pi\)
0.470782 + 0.882249i \(0.343972\pi\)
\(158\) −17.0294 −1.35479
\(159\) −3.68716 −0.292410
\(160\) 2.97794 0.235427
\(161\) 0.153613 0.0121064
\(162\) 1.94308 0.152663
\(163\) −4.07480 −0.319163 −0.159581 0.987185i \(-0.551014\pi\)
−0.159581 + 0.987185i \(0.551014\pi\)
\(164\) −3.62198 −0.282829
\(165\) −17.5645 −1.36739
\(166\) −6.32734 −0.491097
\(167\) 21.6489 1.67525 0.837623 0.546249i \(-0.183945\pi\)
0.837623 + 0.546249i \(0.183945\pi\)
\(168\) 1.20386 0.0928797
\(169\) −12.2790 −0.944539
\(170\) 2.71562 0.208278
\(171\) 0.581889 0.0444982
\(172\) −0.855256 −0.0652127
\(173\) −0.175422 −0.0133371 −0.00666856 0.999978i \(-0.502123\pi\)
−0.00666856 + 0.999978i \(0.502123\pi\)
\(174\) −7.37278 −0.558929
\(175\) −3.86810 −0.292401
\(176\) 4.89942 0.369308
\(177\) 11.1657 0.839269
\(178\) −0.101939 −0.00764066
\(179\) 25.9266 1.93785 0.968923 0.247362i \(-0.0795637\pi\)
0.968923 + 0.247362i \(0.0795637\pi\)
\(180\) 4.61796 0.344202
\(181\) −13.8892 −1.03238 −0.516188 0.856475i \(-0.672649\pi\)
−0.516188 + 0.856475i \(0.672649\pi\)
\(182\) 0.849112 0.0629404
\(183\) 7.82925 0.578755
\(184\) 0.153613 0.0113245
\(185\) 33.0990 2.43348
\(186\) −6.81696 −0.499844
\(187\) 4.46785 0.326721
\(188\) −8.00473 −0.583805
\(189\) 5.47843 0.398497
\(190\) −1.11743 −0.0810670
\(191\) −2.88488 −0.208742 −0.104371 0.994538i \(-0.533283\pi\)
−0.104371 + 0.994538i \(0.533283\pi\)
\(192\) 1.20386 0.0868810
\(193\) −17.1765 −1.23639 −0.618195 0.786025i \(-0.712136\pi\)
−0.618195 + 0.786025i \(0.712136\pi\)
\(194\) −4.01210 −0.288052
\(195\) −3.04408 −0.217991
\(196\) 1.00000 0.0714286
\(197\) 23.8850 1.70174 0.850869 0.525377i \(-0.176076\pi\)
0.850869 + 0.525377i \(0.176076\pi\)
\(198\) 7.59766 0.539942
\(199\) 21.2542 1.50667 0.753336 0.657636i \(-0.228444\pi\)
0.753336 + 0.657636i \(0.228444\pi\)
\(200\) −3.86810 −0.273516
\(201\) −5.19138 −0.366171
\(202\) 3.91128 0.275197
\(203\) −6.12429 −0.429841
\(204\) 1.09781 0.0768624
\(205\) 10.7860 0.753328
\(206\) −6.58489 −0.458791
\(207\) 0.238211 0.0165568
\(208\) 0.849112 0.0588754
\(209\) −1.83844 −0.127168
\(210\) −3.58501 −0.247389
\(211\) 3.44404 0.237097 0.118549 0.992948i \(-0.462176\pi\)
0.118549 + 0.992948i \(0.462176\pi\)
\(212\) −3.06278 −0.210353
\(213\) −0.889834 −0.0609704
\(214\) 19.3066 1.31977
\(215\) 2.54690 0.173697
\(216\) 5.47843 0.372760
\(217\) −5.66260 −0.384402
\(218\) −17.7165 −1.19991
\(219\) −9.86549 −0.666648
\(220\) −14.5902 −0.983669
\(221\) 0.774317 0.0520862
\(222\) 13.3806 0.898045
\(223\) 9.70779 0.650081 0.325041 0.945700i \(-0.394622\pi\)
0.325041 + 0.945700i \(0.394622\pi\)
\(224\) 1.00000 0.0668153
\(225\) −5.99837 −0.399891
\(226\) 8.03226 0.534298
\(227\) −0.123312 −0.00818453 −0.00409226 0.999992i \(-0.501303\pi\)
−0.00409226 + 0.999992i \(0.501303\pi\)
\(228\) −0.451732 −0.0299167
\(229\) 23.6533 1.56306 0.781528 0.623870i \(-0.214440\pi\)
0.781528 + 0.623870i \(0.214440\pi\)
\(230\) −0.457448 −0.0301632
\(231\) −5.89821 −0.388074
\(232\) −6.12429 −0.402080
\(233\) 17.7608 1.16355 0.581773 0.813351i \(-0.302359\pi\)
0.581773 + 0.813351i \(0.302359\pi\)
\(234\) 1.31674 0.0860780
\(235\) 23.8376 1.55499
\(236\) 9.27497 0.603749
\(237\) 20.5010 1.33168
\(238\) 0.911913 0.0591105
\(239\) 18.0820 1.16963 0.584813 0.811168i \(-0.301168\pi\)
0.584813 + 0.811168i \(0.301168\pi\)
\(240\) −3.58501 −0.231412
\(241\) 24.4403 1.57434 0.787170 0.616736i \(-0.211545\pi\)
0.787170 + 0.616736i \(0.211545\pi\)
\(242\) −13.0043 −0.835951
\(243\) 14.0961 0.904265
\(244\) 6.50346 0.416341
\(245\) −2.97794 −0.190253
\(246\) 4.36035 0.278006
\(247\) −0.318618 −0.0202732
\(248\) −5.66260 −0.359575
\(249\) 7.61722 0.482722
\(250\) −3.37071 −0.213183
\(251\) −13.5545 −0.855554 −0.427777 0.903884i \(-0.640703\pi\)
−0.427777 + 0.903884i \(0.640703\pi\)
\(252\) 1.55072 0.0976865
\(253\) −0.752613 −0.0473164
\(254\) 17.3063 1.08589
\(255\) −3.26922 −0.204727
\(256\) 1.00000 0.0625000
\(257\) 17.4714 1.08984 0.544919 0.838489i \(-0.316560\pi\)
0.544919 + 0.838489i \(0.316560\pi\)
\(258\) 1.02961 0.0641006
\(259\) 11.1147 0.690636
\(260\) −2.52860 −0.156817
\(261\) −9.49709 −0.587855
\(262\) −5.19930 −0.321214
\(263\) 5.31907 0.327988 0.163994 0.986461i \(-0.447562\pi\)
0.163994 + 0.986461i \(0.447562\pi\)
\(264\) −5.89821 −0.363010
\(265\) 9.12077 0.560284
\(266\) −0.375237 −0.0230072
\(267\) 0.122720 0.00751036
\(268\) −4.31228 −0.263415
\(269\) 22.4922 1.37137 0.685687 0.727896i \(-0.259502\pi\)
0.685687 + 0.727896i \(0.259502\pi\)
\(270\) −16.3144 −0.992863
\(271\) −9.76482 −0.593170 −0.296585 0.955006i \(-0.595848\pi\)
−0.296585 + 0.955006i \(0.595848\pi\)
\(272\) 0.911913 0.0552928
\(273\) −1.02221 −0.0618670
\(274\) −1.31183 −0.0792503
\(275\) 18.9515 1.14282
\(276\) −0.184928 −0.0111313
\(277\) −5.29525 −0.318161 −0.159080 0.987266i \(-0.550853\pi\)
−0.159080 + 0.987266i \(0.550853\pi\)
\(278\) 6.40785 0.384317
\(279\) −8.78113 −0.525712
\(280\) −2.97794 −0.177966
\(281\) 24.7062 1.47385 0.736924 0.675976i \(-0.236278\pi\)
0.736924 + 0.675976i \(0.236278\pi\)
\(282\) 9.63656 0.573849
\(283\) −6.29861 −0.374413 −0.187207 0.982321i \(-0.559943\pi\)
−0.187207 + 0.982321i \(0.559943\pi\)
\(284\) −0.739152 −0.0438606
\(285\) 1.34523 0.0796845
\(286\) −4.16016 −0.245995
\(287\) 3.62198 0.213799
\(288\) 1.55072 0.0913773
\(289\) −16.1684 −0.951083
\(290\) 18.2378 1.07096
\(291\) 4.83000 0.283140
\(292\) −8.19489 −0.479570
\(293\) 17.8681 1.04387 0.521933 0.852987i \(-0.325211\pi\)
0.521933 + 0.852987i \(0.325211\pi\)
\(294\) −1.20386 −0.0702105
\(295\) −27.6203 −1.60811
\(296\) 11.1147 0.646031
\(297\) −26.8411 −1.55748
\(298\) −14.5607 −0.843480
\(299\) −0.130434 −0.00754321
\(300\) 4.65665 0.268852
\(301\) 0.855256 0.0492961
\(302\) −1.41094 −0.0811905
\(303\) −4.70863 −0.270504
\(304\) −0.375237 −0.0215213
\(305\) −19.3669 −1.10895
\(306\) 1.41413 0.0808402
\(307\) 7.20156 0.411015 0.205507 0.978656i \(-0.434116\pi\)
0.205507 + 0.978656i \(0.434116\pi\)
\(308\) −4.89942 −0.279171
\(309\) 7.92728 0.450967
\(310\) 16.8629 0.957746
\(311\) −10.2189 −0.579459 −0.289729 0.957109i \(-0.593565\pi\)
−0.289729 + 0.957109i \(0.593565\pi\)
\(312\) −1.02221 −0.0578713
\(313\) 18.4553 1.04316 0.521579 0.853203i \(-0.325343\pi\)
0.521579 + 0.853203i \(0.325343\pi\)
\(314\) −11.7978 −0.665787
\(315\) −4.61796 −0.260193
\(316\) 17.0294 0.957980
\(317\) 35.1777 1.97577 0.987887 0.155173i \(-0.0495935\pi\)
0.987887 + 0.155173i \(0.0495935\pi\)
\(318\) 3.68716 0.206765
\(319\) 30.0055 1.67999
\(320\) −2.97794 −0.166472
\(321\) −23.2424 −1.29726
\(322\) −0.153613 −0.00856049
\(323\) −0.342183 −0.0190396
\(324\) −1.94308 −0.107949
\(325\) 3.28446 0.182189
\(326\) 4.07480 0.225682
\(327\) 21.3281 1.17945
\(328\) 3.62198 0.199990
\(329\) 8.00473 0.441315
\(330\) 17.5645 0.966894
\(331\) −33.0006 −1.81388 −0.906939 0.421261i \(-0.861588\pi\)
−0.906939 + 0.421261i \(0.861588\pi\)
\(332\) 6.32734 0.347258
\(333\) 17.2359 0.944521
\(334\) −21.6489 −1.18458
\(335\) 12.8417 0.701617
\(336\) −1.20386 −0.0656759
\(337\) −4.26202 −0.232167 −0.116083 0.993239i \(-0.537034\pi\)
−0.116083 + 0.993239i \(0.537034\pi\)
\(338\) 12.2790 0.667890
\(339\) −9.66970 −0.525186
\(340\) −2.71562 −0.147275
\(341\) 27.7435 1.50239
\(342\) −0.581889 −0.0314650
\(343\) −1.00000 −0.0539949
\(344\) 0.855256 0.0461123
\(345\) 0.550703 0.0296489
\(346\) 0.175422 0.00943077
\(347\) 21.0191 1.12836 0.564181 0.825651i \(-0.309192\pi\)
0.564181 + 0.825651i \(0.309192\pi\)
\(348\) 7.37278 0.395223
\(349\) −6.89685 −0.369180 −0.184590 0.982816i \(-0.559096\pi\)
−0.184590 + 0.982816i \(0.559096\pi\)
\(350\) 3.86810 0.206759
\(351\) −4.65180 −0.248295
\(352\) −4.89942 −0.261140
\(353\) 1.22121 0.0649982 0.0324991 0.999472i \(-0.489653\pi\)
0.0324991 + 0.999472i \(0.489653\pi\)
\(354\) −11.1657 −0.593453
\(355\) 2.20115 0.116825
\(356\) 0.101939 0.00540276
\(357\) −1.09781 −0.0581025
\(358\) −25.9266 −1.37026
\(359\) 10.3281 0.545099 0.272549 0.962142i \(-0.412133\pi\)
0.272549 + 0.962142i \(0.412133\pi\)
\(360\) −4.61796 −0.243388
\(361\) −18.8592 −0.992589
\(362\) 13.8892 0.730000
\(363\) 15.6554 0.821695
\(364\) −0.849112 −0.0445056
\(365\) 24.4039 1.27736
\(366\) −7.82925 −0.409241
\(367\) −16.0744 −0.839078 −0.419539 0.907737i \(-0.637808\pi\)
−0.419539 + 0.907737i \(0.637808\pi\)
\(368\) −0.153613 −0.00800761
\(369\) 5.61669 0.292393
\(370\) −33.0990 −1.72073
\(371\) 3.06278 0.159012
\(372\) 6.81696 0.353443
\(373\) −21.6027 −1.11854 −0.559272 0.828984i \(-0.688919\pi\)
−0.559272 + 0.828984i \(0.688919\pi\)
\(374\) −4.46785 −0.231027
\(375\) 4.05786 0.209547
\(376\) 8.00473 0.412812
\(377\) 5.20021 0.267825
\(378\) −5.47843 −0.281780
\(379\) −33.3433 −1.71273 −0.856365 0.516370i \(-0.827283\pi\)
−0.856365 + 0.516370i \(0.827283\pi\)
\(380\) 1.11743 0.0573230
\(381\) −20.8343 −1.06738
\(382\) 2.88488 0.147603
\(383\) 2.61129 0.133431 0.0667153 0.997772i \(-0.478748\pi\)
0.0667153 + 0.997772i \(0.478748\pi\)
\(384\) −1.20386 −0.0614341
\(385\) 14.5902 0.743584
\(386\) 17.1765 0.874259
\(387\) 1.32627 0.0674179
\(388\) 4.01210 0.203683
\(389\) 7.59768 0.385218 0.192609 0.981276i \(-0.438305\pi\)
0.192609 + 0.981276i \(0.438305\pi\)
\(390\) 3.04408 0.154143
\(391\) −0.140081 −0.00708421
\(392\) −1.00000 −0.0505076
\(393\) 6.25922 0.315736
\(394\) −23.8850 −1.20331
\(395\) −50.7125 −2.55162
\(396\) −7.59766 −0.381797
\(397\) 29.3810 1.47459 0.737295 0.675571i \(-0.236103\pi\)
0.737295 + 0.675571i \(0.236103\pi\)
\(398\) −21.2542 −1.06538
\(399\) 0.451732 0.0226149
\(400\) 3.86810 0.193405
\(401\) 0.873498 0.0436204 0.0218102 0.999762i \(-0.493057\pi\)
0.0218102 + 0.999762i \(0.493057\pi\)
\(402\) 5.19138 0.258922
\(403\) 4.80818 0.239513
\(404\) −3.91128 −0.194594
\(405\) 5.78637 0.287527
\(406\) 6.12429 0.303944
\(407\) −54.4558 −2.69927
\(408\) −1.09781 −0.0543499
\(409\) −14.1825 −0.701277 −0.350639 0.936511i \(-0.614035\pi\)
−0.350639 + 0.936511i \(0.614035\pi\)
\(410\) −10.7860 −0.532683
\(411\) 1.57925 0.0778988
\(412\) 6.58489 0.324414
\(413\) −9.27497 −0.456391
\(414\) −0.238211 −0.0117074
\(415\) −18.8424 −0.924938
\(416\) −0.849112 −0.0416312
\(417\) −7.71414 −0.377763
\(418\) 1.83844 0.0899212
\(419\) −15.3410 −0.749458 −0.374729 0.927134i \(-0.622264\pi\)
−0.374729 + 0.927134i \(0.622264\pi\)
\(420\) 3.58501 0.174931
\(421\) 10.6330 0.518223 0.259112 0.965847i \(-0.416570\pi\)
0.259112 + 0.965847i \(0.416570\pi\)
\(422\) −3.44404 −0.167653
\(423\) 12.4131 0.603547
\(424\) 3.06278 0.148742
\(425\) 3.52737 0.171103
\(426\) 0.889834 0.0431126
\(427\) −6.50346 −0.314725
\(428\) −19.3066 −0.933219
\(429\) 5.00825 0.241800
\(430\) −2.54690 −0.122822
\(431\) 1.00000 0.0481683
\(432\) −5.47843 −0.263581
\(433\) −12.7433 −0.612406 −0.306203 0.951966i \(-0.599059\pi\)
−0.306203 + 0.951966i \(0.599059\pi\)
\(434\) 5.66260 0.271813
\(435\) −21.9557 −1.05269
\(436\) 17.7165 0.848464
\(437\) 0.0576411 0.00275735
\(438\) 9.86549 0.471391
\(439\) 5.97985 0.285403 0.142701 0.989766i \(-0.454421\pi\)
0.142701 + 0.989766i \(0.454421\pi\)
\(440\) 14.5902 0.695559
\(441\) −1.55072 −0.0738440
\(442\) −0.774317 −0.0368305
\(443\) −20.8026 −0.988360 −0.494180 0.869360i \(-0.664532\pi\)
−0.494180 + 0.869360i \(0.664532\pi\)
\(444\) −13.3806 −0.635014
\(445\) −0.303568 −0.0143905
\(446\) −9.70779 −0.459677
\(447\) 17.5291 0.829096
\(448\) −1.00000 −0.0472456
\(449\) 13.1429 0.620249 0.310125 0.950696i \(-0.399629\pi\)
0.310125 + 0.950696i \(0.399629\pi\)
\(450\) 5.99837 0.282766
\(451\) −17.7456 −0.835607
\(452\) −8.03226 −0.377806
\(453\) 1.69857 0.0798059
\(454\) 0.123312 0.00578733
\(455\) 2.52860 0.118543
\(456\) 0.451732 0.0211543
\(457\) 33.8831 1.58499 0.792493 0.609881i \(-0.208783\pi\)
0.792493 + 0.609881i \(0.208783\pi\)
\(458\) −23.6533 −1.10525
\(459\) −4.99585 −0.233186
\(460\) 0.457448 0.0213286
\(461\) 41.3424 1.92551 0.962755 0.270376i \(-0.0871482\pi\)
0.962755 + 0.270376i \(0.0871482\pi\)
\(462\) 5.89821 0.274410
\(463\) −8.35730 −0.388397 −0.194198 0.980962i \(-0.562211\pi\)
−0.194198 + 0.980962i \(0.562211\pi\)
\(464\) 6.12429 0.284313
\(465\) −20.3005 −0.941413
\(466\) −17.7608 −0.822751
\(467\) −27.6848 −1.28110 −0.640550 0.767916i \(-0.721294\pi\)
−0.640550 + 0.767916i \(0.721294\pi\)
\(468\) −1.31674 −0.0608663
\(469\) 4.31228 0.199123
\(470\) −23.8376 −1.09954
\(471\) 14.2028 0.654433
\(472\) −9.27497 −0.426915
\(473\) −4.19026 −0.192668
\(474\) −20.5010 −0.941643
\(475\) −1.45146 −0.0665973
\(476\) −0.911913 −0.0417975
\(477\) 4.74953 0.217466
\(478\) −18.0820 −0.827050
\(479\) 29.1826 1.33339 0.666694 0.745331i \(-0.267709\pi\)
0.666694 + 0.745331i \(0.267709\pi\)
\(480\) 3.58501 0.163633
\(481\) −9.43766 −0.430320
\(482\) −24.4403 −1.11323
\(483\) 0.184928 0.00841450
\(484\) 13.0043 0.591107
\(485\) −11.9478 −0.542521
\(486\) −14.0961 −0.639412
\(487\) −17.3831 −0.787703 −0.393851 0.919174i \(-0.628858\pi\)
−0.393851 + 0.919174i \(0.628858\pi\)
\(488\) −6.50346 −0.294398
\(489\) −4.90548 −0.221834
\(490\) 2.97794 0.134529
\(491\) 12.4935 0.563825 0.281912 0.959440i \(-0.409031\pi\)
0.281912 + 0.959440i \(0.409031\pi\)
\(492\) −4.36035 −0.196580
\(493\) 5.58482 0.251528
\(494\) 0.318618 0.0143353
\(495\) 22.6253 1.01693
\(496\) 5.66260 0.254258
\(497\) 0.739152 0.0331555
\(498\) −7.61722 −0.341336
\(499\) −7.84699 −0.351280 −0.175640 0.984454i \(-0.556199\pi\)
−0.175640 + 0.984454i \(0.556199\pi\)
\(500\) 3.37071 0.150743
\(501\) 26.0623 1.16438
\(502\) 13.5545 0.604968
\(503\) −31.5109 −1.40500 −0.702501 0.711682i \(-0.747934\pi\)
−0.702501 + 0.711682i \(0.747934\pi\)
\(504\) −1.55072 −0.0690748
\(505\) 11.6475 0.518309
\(506\) 0.752613 0.0334577
\(507\) −14.7822 −0.656500
\(508\) −17.3063 −0.767843
\(509\) −10.8749 −0.482020 −0.241010 0.970523i \(-0.577479\pi\)
−0.241010 + 0.970523i \(0.577479\pi\)
\(510\) 3.26922 0.144764
\(511\) 8.19489 0.362521
\(512\) −1.00000 −0.0441942
\(513\) 2.05571 0.0907617
\(514\) −17.4714 −0.770632
\(515\) −19.6094 −0.864093
\(516\) −1.02961 −0.0453259
\(517\) −39.2185 −1.72483
\(518\) −11.1147 −0.488353
\(519\) −0.211184 −0.00926994
\(520\) 2.52860 0.110887
\(521\) −9.84742 −0.431423 −0.215712 0.976457i \(-0.569207\pi\)
−0.215712 + 0.976457i \(0.569207\pi\)
\(522\) 9.49709 0.415676
\(523\) 38.6803 1.69137 0.845685 0.533682i \(-0.179192\pi\)
0.845685 + 0.533682i \(0.179192\pi\)
\(524\) 5.19930 0.227132
\(525\) −4.65665 −0.203233
\(526\) −5.31907 −0.231923
\(527\) 5.16379 0.224938
\(528\) 5.89821 0.256687
\(529\) −22.9764 −0.998974
\(530\) −9.12077 −0.396181
\(531\) −14.3829 −0.624166
\(532\) 0.375237 0.0162686
\(533\) −3.07547 −0.133213
\(534\) −0.122720 −0.00531062
\(535\) 57.4938 2.48567
\(536\) 4.31228 0.186262
\(537\) 31.2120 1.34690
\(538\) −22.4922 −0.969709
\(539\) 4.89942 0.211033
\(540\) 16.3144 0.702060
\(541\) −14.1263 −0.607339 −0.303669 0.952778i \(-0.598212\pi\)
−0.303669 + 0.952778i \(0.598212\pi\)
\(542\) 9.76482 0.419435
\(543\) −16.7206 −0.717551
\(544\) −0.911913 −0.0390979
\(545\) −52.7585 −2.25993
\(546\) 1.02221 0.0437466
\(547\) 35.5049 1.51808 0.759040 0.651044i \(-0.225669\pi\)
0.759040 + 0.651044i \(0.225669\pi\)
\(548\) 1.31183 0.0560384
\(549\) −10.0851 −0.430421
\(550\) −18.9515 −0.808094
\(551\) −2.29806 −0.0979007
\(552\) 0.184928 0.00787105
\(553\) −17.0294 −0.724165
\(554\) 5.29525 0.224974
\(555\) 39.8465 1.69139
\(556\) −6.40785 −0.271753
\(557\) −5.55212 −0.235251 −0.117625 0.993058i \(-0.537528\pi\)
−0.117625 + 0.993058i \(0.537528\pi\)
\(558\) 8.78113 0.371735
\(559\) −0.726209 −0.0307154
\(560\) 2.97794 0.125841
\(561\) 5.37866 0.227087
\(562\) −24.7062 −1.04217
\(563\) 23.6788 0.997944 0.498972 0.866618i \(-0.333711\pi\)
0.498972 + 0.866618i \(0.333711\pi\)
\(564\) −9.63656 −0.405772
\(565\) 23.9196 1.00630
\(566\) 6.29861 0.264750
\(567\) 1.94308 0.0816017
\(568\) 0.739152 0.0310141
\(569\) −35.8502 −1.50292 −0.751459 0.659779i \(-0.770650\pi\)
−0.751459 + 0.659779i \(0.770650\pi\)
\(570\) −1.34523 −0.0563455
\(571\) 31.0243 1.29833 0.649163 0.760650i \(-0.275119\pi\)
0.649163 + 0.760650i \(0.275119\pi\)
\(572\) 4.16016 0.173945
\(573\) −3.47298 −0.145086
\(574\) −3.62198 −0.151178
\(575\) −0.594189 −0.0247794
\(576\) −1.55072 −0.0646135
\(577\) −0.533387 −0.0222052 −0.0111026 0.999938i \(-0.503534\pi\)
−0.0111026 + 0.999938i \(0.503534\pi\)
\(578\) 16.1684 0.672517
\(579\) −20.6780 −0.859350
\(580\) −18.2378 −0.757282
\(581\) −6.32734 −0.262502
\(582\) −4.83000 −0.200210
\(583\) −15.0059 −0.621479
\(584\) 8.19489 0.339107
\(585\) 3.92117 0.162120
\(586\) −17.8681 −0.738124
\(587\) 1.56328 0.0645234 0.0322617 0.999479i \(-0.489729\pi\)
0.0322617 + 0.999479i \(0.489729\pi\)
\(588\) 1.20386 0.0496463
\(589\) −2.12481 −0.0875515
\(590\) 27.6203 1.13711
\(591\) 28.7542 1.18279
\(592\) −11.1147 −0.456813
\(593\) 39.4369 1.61948 0.809740 0.586789i \(-0.199608\pi\)
0.809740 + 0.586789i \(0.199608\pi\)
\(594\) 26.8411 1.10131
\(595\) 2.71562 0.111329
\(596\) 14.5607 0.596431
\(597\) 25.5871 1.04721
\(598\) 0.130434 0.00533386
\(599\) 18.3831 0.751112 0.375556 0.926800i \(-0.377452\pi\)
0.375556 + 0.926800i \(0.377452\pi\)
\(600\) −4.65665 −0.190107
\(601\) 17.3942 0.709524 0.354762 0.934957i \(-0.384562\pi\)
0.354762 + 0.934957i \(0.384562\pi\)
\(602\) −0.855256 −0.0348576
\(603\) 6.68716 0.272322
\(604\) 1.41094 0.0574104
\(605\) −38.7261 −1.57444
\(606\) 4.70863 0.191275
\(607\) 41.3720 1.67924 0.839618 0.543177i \(-0.182779\pi\)
0.839618 + 0.543177i \(0.182779\pi\)
\(608\) 0.375237 0.0152179
\(609\) −7.37278 −0.298760
\(610\) 19.3669 0.784143
\(611\) −6.79691 −0.274974
\(612\) −1.41413 −0.0571626
\(613\) −13.7858 −0.556805 −0.278402 0.960465i \(-0.589805\pi\)
−0.278402 + 0.960465i \(0.589805\pi\)
\(614\) −7.20156 −0.290631
\(615\) 12.9848 0.523599
\(616\) 4.89942 0.197403
\(617\) 41.0153 1.65122 0.825608 0.564245i \(-0.190833\pi\)
0.825608 + 0.564245i \(0.190833\pi\)
\(618\) −7.92728 −0.318882
\(619\) −8.28944 −0.333181 −0.166590 0.986026i \(-0.553276\pi\)
−0.166590 + 0.986026i \(0.553276\pi\)
\(620\) −16.8629 −0.677228
\(621\) 0.841555 0.0337704
\(622\) 10.2189 0.409739
\(623\) −0.101939 −0.00408410
\(624\) 1.02221 0.0409212
\(625\) −29.3783 −1.17513
\(626\) −18.4553 −0.737624
\(627\) −2.21323 −0.0883878
\(628\) 11.7978 0.470782
\(629\) −10.1357 −0.404136
\(630\) 4.61796 0.183984
\(631\) −37.2337 −1.48225 −0.741124 0.671368i \(-0.765707\pi\)
−0.741124 + 0.671368i \(0.765707\pi\)
\(632\) −17.0294 −0.677394
\(633\) 4.14613 0.164794
\(634\) −35.1777 −1.39708
\(635\) 51.5371 2.04519
\(636\) −3.68716 −0.146205
\(637\) 0.849112 0.0336431
\(638\) −30.0055 −1.18793
\(639\) 1.14622 0.0453438
\(640\) 2.97794 0.117713
\(641\) 11.2760 0.445374 0.222687 0.974890i \(-0.428517\pi\)
0.222687 + 0.974890i \(0.428517\pi\)
\(642\) 23.2424 0.917305
\(643\) −39.7003 −1.56563 −0.782814 0.622256i \(-0.786216\pi\)
−0.782814 + 0.622256i \(0.786216\pi\)
\(644\) 0.153613 0.00605318
\(645\) 3.06611 0.120728
\(646\) 0.342183 0.0134630
\(647\) −6.06715 −0.238524 −0.119262 0.992863i \(-0.538053\pi\)
−0.119262 + 0.992863i \(0.538053\pi\)
\(648\) 1.94308 0.0763314
\(649\) 45.4420 1.78375
\(650\) −3.28446 −0.128827
\(651\) −6.81696 −0.267178
\(652\) −4.07480 −0.159581
\(653\) 23.3853 0.915138 0.457569 0.889174i \(-0.348720\pi\)
0.457569 + 0.889174i \(0.348720\pi\)
\(654\) −21.3281 −0.833995
\(655\) −15.4832 −0.604978
\(656\) −3.62198 −0.141414
\(657\) 12.7080 0.495787
\(658\) −8.00473 −0.312057
\(659\) −0.288809 −0.0112504 −0.00562520 0.999984i \(-0.501791\pi\)
−0.00562520 + 0.999984i \(0.501791\pi\)
\(660\) −17.5645 −0.683697
\(661\) 1.54303 0.0600168 0.0300084 0.999550i \(-0.490447\pi\)
0.0300084 + 0.999550i \(0.490447\pi\)
\(662\) 33.0006 1.28261
\(663\) 0.932168 0.0362024
\(664\) −6.32734 −0.245548
\(665\) −1.11743 −0.0433321
\(666\) −17.2359 −0.667877
\(667\) −0.940768 −0.0364267
\(668\) 21.6489 0.837623
\(669\) 11.6868 0.451838
\(670\) −12.8417 −0.496118
\(671\) 31.8632 1.23007
\(672\) 1.20386 0.0464399
\(673\) 9.80088 0.377796 0.188898 0.981997i \(-0.439508\pi\)
0.188898 + 0.981997i \(0.439508\pi\)
\(674\) 4.26202 0.164167
\(675\) −21.1911 −0.815647
\(676\) −12.2790 −0.472270
\(677\) −14.4180 −0.554131 −0.277065 0.960851i \(-0.589362\pi\)
−0.277065 + 0.960851i \(0.589362\pi\)
\(678\) 9.66970 0.371363
\(679\) −4.01210 −0.153970
\(680\) 2.71562 0.104139
\(681\) −0.148451 −0.00568864
\(682\) −27.7435 −1.06235
\(683\) 11.9966 0.459037 0.229518 0.973304i \(-0.426285\pi\)
0.229518 + 0.973304i \(0.426285\pi\)
\(684\) 0.581889 0.0222491
\(685\) −3.90653 −0.149261
\(686\) 1.00000 0.0381802
\(687\) 28.4753 1.08640
\(688\) −0.855256 −0.0326063
\(689\) −2.60065 −0.0990767
\(690\) −0.550703 −0.0209649
\(691\) −14.4858 −0.551068 −0.275534 0.961291i \(-0.588855\pi\)
−0.275534 + 0.961291i \(0.588855\pi\)
\(692\) −0.175422 −0.00666856
\(693\) 7.59766 0.288611
\(694\) −21.0191 −0.797872
\(695\) 19.0822 0.723828
\(696\) −7.37278 −0.279465
\(697\) −3.30293 −0.125107
\(698\) 6.89685 0.261049
\(699\) 21.3814 0.808720
\(700\) −3.86810 −0.146201
\(701\) 1.19892 0.0452825 0.0226413 0.999744i \(-0.492792\pi\)
0.0226413 + 0.999744i \(0.492792\pi\)
\(702\) 4.65180 0.175571
\(703\) 4.17066 0.157299
\(704\) 4.89942 0.184654
\(705\) 28.6971 1.08079
\(706\) −1.22121 −0.0459607
\(707\) 3.91128 0.147099
\(708\) 11.1657 0.419635
\(709\) −14.2392 −0.534764 −0.267382 0.963591i \(-0.586159\pi\)
−0.267382 + 0.963591i \(0.586159\pi\)
\(710\) −2.20115 −0.0826076
\(711\) −26.4079 −0.990375
\(712\) −0.101939 −0.00382033
\(713\) −0.869846 −0.0325760
\(714\) 1.09781 0.0410847
\(715\) −12.3887 −0.463311
\(716\) 25.9266 0.968923
\(717\) 21.7681 0.812946
\(718\) −10.3281 −0.385443
\(719\) 19.0688 0.711146 0.355573 0.934648i \(-0.384286\pi\)
0.355573 + 0.934648i \(0.384286\pi\)
\(720\) 4.61796 0.172101
\(721\) −6.58489 −0.245234
\(722\) 18.8592 0.701867
\(723\) 29.4227 1.09424
\(724\) −13.8892 −0.516188
\(725\) 23.6894 0.879803
\(726\) −15.6554 −0.581026
\(727\) 38.7830 1.43838 0.719192 0.694812i \(-0.244512\pi\)
0.719192 + 0.694812i \(0.244512\pi\)
\(728\) 0.849112 0.0314702
\(729\) 22.7989 0.844405
\(730\) −24.4039 −0.903227
\(731\) −0.779919 −0.0288463
\(732\) 7.82925 0.289377
\(733\) −17.5495 −0.648205 −0.324103 0.946022i \(-0.605062\pi\)
−0.324103 + 0.946022i \(0.605062\pi\)
\(734\) 16.0744 0.593318
\(735\) −3.58501 −0.132235
\(736\) 0.153613 0.00566223
\(737\) −21.1277 −0.778248
\(738\) −5.61669 −0.206753
\(739\) −40.7463 −1.49888 −0.749438 0.662075i \(-0.769676\pi\)
−0.749438 + 0.662075i \(0.769676\pi\)
\(740\) 33.0990 1.21674
\(741\) −0.383571 −0.0140908
\(742\) −3.06278 −0.112438
\(743\) −7.78704 −0.285679 −0.142839 0.989746i \(-0.545623\pi\)
−0.142839 + 0.989746i \(0.545623\pi\)
\(744\) −6.81696 −0.249922
\(745\) −43.3609 −1.58862
\(746\) 21.6027 0.790930
\(747\) −9.81196 −0.359001
\(748\) 4.46785 0.163361
\(749\) 19.3066 0.705448
\(750\) −4.05786 −0.148172
\(751\) −30.4526 −1.11123 −0.555615 0.831440i \(-0.687517\pi\)
−0.555615 + 0.831440i \(0.687517\pi\)
\(752\) −8.00473 −0.291902
\(753\) −16.3177 −0.594651
\(754\) −5.20021 −0.189381
\(755\) −4.20169 −0.152915
\(756\) 5.47843 0.199249
\(757\) 15.8007 0.574287 0.287144 0.957888i \(-0.407294\pi\)
0.287144 + 0.957888i \(0.407294\pi\)
\(758\) 33.3433 1.21108
\(759\) −0.906039 −0.0328871
\(760\) −1.11743 −0.0405335
\(761\) −11.7935 −0.427514 −0.213757 0.976887i \(-0.568570\pi\)
−0.213757 + 0.976887i \(0.568570\pi\)
\(762\) 20.8343 0.754749
\(763\) −17.7165 −0.641379
\(764\) −2.88488 −0.104371
\(765\) 4.21118 0.152255
\(766\) −2.61129 −0.0943497
\(767\) 7.87549 0.284368
\(768\) 1.20386 0.0434405
\(769\) −19.9145 −0.718135 −0.359067 0.933312i \(-0.616905\pi\)
−0.359067 + 0.933312i \(0.616905\pi\)
\(770\) −14.5902 −0.525793
\(771\) 21.0331 0.757489
\(772\) −17.1765 −0.618195
\(773\) −15.9098 −0.572237 −0.286118 0.958194i \(-0.592365\pi\)
−0.286118 + 0.958194i \(0.592365\pi\)
\(774\) −1.32627 −0.0476717
\(775\) 21.9035 0.786797
\(776\) −4.01210 −0.144026
\(777\) 13.3806 0.480025
\(778\) −7.59768 −0.272390
\(779\) 1.35910 0.0486948
\(780\) −3.04408 −0.108996
\(781\) −3.62142 −0.129584
\(782\) 0.140081 0.00500929
\(783\) −33.5515 −1.19903
\(784\) 1.00000 0.0357143
\(785\) −35.1330 −1.25395
\(786\) −6.25922 −0.223259
\(787\) 16.1022 0.573980 0.286990 0.957934i \(-0.407345\pi\)
0.286990 + 0.957934i \(0.407345\pi\)
\(788\) 23.8850 0.850869
\(789\) 6.40341 0.227968
\(790\) 50.7125 1.80427
\(791\) 8.03226 0.285594
\(792\) 7.59766 0.269971
\(793\) 5.52217 0.196098
\(794\) −29.3810 −1.04269
\(795\) 10.9801 0.389425
\(796\) 21.2542 0.753336
\(797\) −17.7679 −0.629373 −0.314686 0.949196i \(-0.601899\pi\)
−0.314686 + 0.949196i \(0.601899\pi\)
\(798\) −0.451732 −0.0159911
\(799\) −7.29961 −0.258242
\(800\) −3.86810 −0.136758
\(801\) −0.158079 −0.00558546
\(802\) −0.873498 −0.0308443
\(803\) −40.1502 −1.41687
\(804\) −5.19138 −0.183086
\(805\) −0.457448 −0.0161229
\(806\) −4.80818 −0.169361
\(807\) 27.0775 0.953171
\(808\) 3.91128 0.137598
\(809\) 27.3112 0.960212 0.480106 0.877210i \(-0.340598\pi\)
0.480106 + 0.877210i \(0.340598\pi\)
\(810\) −5.78637 −0.203312
\(811\) 40.1021 1.40818 0.704088 0.710112i \(-0.251356\pi\)
0.704088 + 0.710112i \(0.251356\pi\)
\(812\) −6.12429 −0.214921
\(813\) −11.7555 −0.412282
\(814\) 54.4558 1.90867
\(815\) 12.1345 0.425053
\(816\) 1.09781 0.0384312
\(817\) 0.320924 0.0112277
\(818\) 14.1825 0.495878
\(819\) 1.31674 0.0460106
\(820\) 10.7860 0.376664
\(821\) −26.4707 −0.923835 −0.461918 0.886923i \(-0.652838\pi\)
−0.461918 + 0.886923i \(0.652838\pi\)
\(822\) −1.57925 −0.0550828
\(823\) −28.8445 −1.00546 −0.502728 0.864444i \(-0.667670\pi\)
−0.502728 + 0.864444i \(0.667670\pi\)
\(824\) −6.58489 −0.229396
\(825\) 22.8149 0.794313
\(826\) 9.27497 0.322717
\(827\) 9.00424 0.313108 0.156554 0.987669i \(-0.449961\pi\)
0.156554 + 0.987669i \(0.449961\pi\)
\(828\) 0.238211 0.00827839
\(829\) −8.45567 −0.293678 −0.146839 0.989160i \(-0.546910\pi\)
−0.146839 + 0.989160i \(0.546910\pi\)
\(830\) 18.8424 0.654030
\(831\) −6.37473 −0.221137
\(832\) 0.849112 0.0294377
\(833\) 0.911913 0.0315959
\(834\) 7.71414 0.267119
\(835\) −64.4692 −2.23105
\(836\) −1.83844 −0.0635839
\(837\) −31.0221 −1.07228
\(838\) 15.3410 0.529947
\(839\) 5.67357 0.195874 0.0979368 0.995193i \(-0.468776\pi\)
0.0979368 + 0.995193i \(0.468776\pi\)
\(840\) −3.58501 −0.123695
\(841\) 8.50697 0.293344
\(842\) −10.6330 −0.366439
\(843\) 29.7428 1.02439
\(844\) 3.44404 0.118549
\(845\) 36.5661 1.25791
\(846\) −12.4131 −0.426772
\(847\) −13.0043 −0.446835
\(848\) −3.06278 −0.105176
\(849\) −7.58263 −0.260235
\(850\) −3.52737 −0.120988
\(851\) 1.70736 0.0585276
\(852\) −0.889834 −0.0304852
\(853\) 4.22755 0.144749 0.0723743 0.997378i \(-0.476942\pi\)
0.0723743 + 0.997378i \(0.476942\pi\)
\(854\) 6.50346 0.222544
\(855\) −1.73283 −0.0592615
\(856\) 19.3066 0.659886
\(857\) 10.4515 0.357017 0.178508 0.983938i \(-0.442873\pi\)
0.178508 + 0.983938i \(0.442873\pi\)
\(858\) −5.00825 −0.170979
\(859\) 51.3007 1.75036 0.875178 0.483801i \(-0.160744\pi\)
0.875178 + 0.483801i \(0.160744\pi\)
\(860\) 2.54690 0.0868485
\(861\) 4.36035 0.148600
\(862\) −1.00000 −0.0340601
\(863\) −30.5520 −1.04000 −0.520000 0.854166i \(-0.674068\pi\)
−0.520000 + 0.854166i \(0.674068\pi\)
\(864\) 5.47843 0.186380
\(865\) 0.522397 0.0177620
\(866\) 12.7433 0.433036
\(867\) −19.4645 −0.661049
\(868\) −5.66260 −0.192201
\(869\) 83.4343 2.83032
\(870\) 21.9557 0.744367
\(871\) −3.66161 −0.124069
\(872\) −17.7165 −0.599955
\(873\) −6.22166 −0.210571
\(874\) −0.0576411 −0.00194974
\(875\) −3.37071 −0.113951
\(876\) −9.86549 −0.333324
\(877\) −26.7214 −0.902319 −0.451160 0.892443i \(-0.648989\pi\)
−0.451160 + 0.892443i \(0.648989\pi\)
\(878\) −5.97985 −0.201810
\(879\) 21.5107 0.725537
\(880\) −14.5902 −0.491835
\(881\) 18.2124 0.613591 0.306795 0.951775i \(-0.400743\pi\)
0.306795 + 0.951775i \(0.400743\pi\)
\(882\) 1.55072 0.0522156
\(883\) 17.3310 0.583233 0.291617 0.956535i \(-0.405807\pi\)
0.291617 + 0.956535i \(0.405807\pi\)
\(884\) 0.774317 0.0260431
\(885\) −33.2509 −1.11772
\(886\) 20.8026 0.698876
\(887\) −33.0353 −1.10922 −0.554608 0.832112i \(-0.687132\pi\)
−0.554608 + 0.832112i \(0.687132\pi\)
\(888\) 13.3806 0.449022
\(889\) 17.3063 0.580435
\(890\) 0.303568 0.0101756
\(891\) −9.51997 −0.318931
\(892\) 9.70779 0.325041
\(893\) 3.00367 0.100514
\(894\) −17.5291 −0.586259
\(895\) −77.2078 −2.58077
\(896\) 1.00000 0.0334077
\(897\) −0.157024 −0.00524289
\(898\) −13.1429 −0.438583
\(899\) 34.6794 1.15662
\(900\) −5.99837 −0.199946
\(901\) −2.79299 −0.0930480
\(902\) 17.7456 0.590864
\(903\) 1.02961 0.0342632
\(904\) 8.03226 0.267149
\(905\) 41.3612 1.37489
\(906\) −1.69857 −0.0564313
\(907\) −55.8510 −1.85450 −0.927252 0.374439i \(-0.877835\pi\)
−0.927252 + 0.374439i \(0.877835\pi\)
\(908\) −0.123312 −0.00409226
\(909\) 6.06532 0.201174
\(910\) −2.52860 −0.0838224
\(911\) −5.59433 −0.185348 −0.0926741 0.995696i \(-0.529541\pi\)
−0.0926741 + 0.995696i \(0.529541\pi\)
\(912\) −0.451732 −0.0149583
\(913\) 31.0003 1.02596
\(914\) −33.8831 −1.12075
\(915\) −23.3150 −0.770770
\(916\) 23.6533 0.781528
\(917\) −5.19930 −0.171696
\(918\) 4.99585 0.164888
\(919\) −5.94745 −0.196188 −0.0980942 0.995177i \(-0.531275\pi\)
−0.0980942 + 0.995177i \(0.531275\pi\)
\(920\) −0.457448 −0.0150816
\(921\) 8.66966 0.285675
\(922\) −41.3424 −1.36154
\(923\) −0.627623 −0.0206585
\(924\) −5.89821 −0.194037
\(925\) −42.9930 −1.41360
\(926\) 8.35730 0.274638
\(927\) −10.2114 −0.335385
\(928\) −6.12429 −0.201040
\(929\) −2.45834 −0.0806554 −0.0403277 0.999187i \(-0.512840\pi\)
−0.0403277 + 0.999187i \(0.512840\pi\)
\(930\) 20.3005 0.665679
\(931\) −0.375237 −0.0122979
\(932\) 17.7608 0.581773
\(933\) −12.3021 −0.402752
\(934\) 27.6848 0.905875
\(935\) −13.3050 −0.435119
\(936\) 1.31674 0.0430390
\(937\) 18.2375 0.595794 0.297897 0.954598i \(-0.403715\pi\)
0.297897 + 0.954598i \(0.403715\pi\)
\(938\) −4.31228 −0.140801
\(939\) 22.2176 0.725045
\(940\) 23.8376 0.777496
\(941\) 36.2405 1.18141 0.590703 0.806889i \(-0.298851\pi\)
0.590703 + 0.806889i \(0.298851\pi\)
\(942\) −14.2028 −0.462754
\(943\) 0.556381 0.0181183
\(944\) 9.27497 0.301875
\(945\) −16.3144 −0.530708
\(946\) 4.19026 0.136237
\(947\) 13.6050 0.442104 0.221052 0.975262i \(-0.429051\pi\)
0.221052 + 0.975262i \(0.429051\pi\)
\(948\) 20.5010 0.665842
\(949\) −6.95838 −0.225879
\(950\) 1.45146 0.0470914
\(951\) 42.3489 1.37326
\(952\) 0.911913 0.0295553
\(953\) 26.9883 0.874235 0.437118 0.899404i \(-0.355999\pi\)
0.437118 + 0.899404i \(0.355999\pi\)
\(954\) −4.74953 −0.153772
\(955\) 8.59098 0.277997
\(956\) 18.0820 0.584813
\(957\) 36.1224 1.16767
\(958\) −29.1826 −0.942848
\(959\) −1.31183 −0.0423611
\(960\) −3.58501 −0.115706
\(961\) 1.06499 0.0343546
\(962\) 9.43766 0.304282
\(963\) 29.9392 0.964777
\(964\) 24.4403 0.787170
\(965\) 51.1504 1.64659
\(966\) −0.184928 −0.00594995
\(967\) 42.8974 1.37949 0.689744 0.724054i \(-0.257723\pi\)
0.689744 + 0.724054i \(0.257723\pi\)
\(968\) −13.0043 −0.417976
\(969\) −0.411940 −0.0132334
\(970\) 11.9478 0.383620
\(971\) −5.99974 −0.192541 −0.0962705 0.995355i \(-0.530691\pi\)
−0.0962705 + 0.995355i \(0.530691\pi\)
\(972\) 14.0961 0.452132
\(973\) 6.40785 0.205426
\(974\) 17.3831 0.556990
\(975\) 3.95402 0.126630
\(976\) 6.50346 0.208171
\(977\) −33.4513 −1.07020 −0.535102 0.844788i \(-0.679727\pi\)
−0.535102 + 0.844788i \(0.679727\pi\)
\(978\) 4.90548 0.156860
\(979\) 0.499443 0.0159623
\(980\) −2.97794 −0.0951267
\(981\) −27.4733 −0.877157
\(982\) −12.4935 −0.398684
\(983\) 16.5376 0.527467 0.263734 0.964596i \(-0.415046\pi\)
0.263734 + 0.964596i \(0.415046\pi\)
\(984\) 4.36035 0.139003
\(985\) −71.1281 −2.26633
\(986\) −5.58482 −0.177857
\(987\) 9.63656 0.306735
\(988\) −0.318618 −0.0101366
\(989\) 0.131378 0.00417758
\(990\) −22.6253 −0.719080
\(991\) −13.8339 −0.439448 −0.219724 0.975562i \(-0.570516\pi\)
−0.219724 + 0.975562i \(0.570516\pi\)
\(992\) −5.66260 −0.179788
\(993\) −39.7281 −1.26073
\(994\) −0.739152 −0.0234445
\(995\) −63.2937 −2.00655
\(996\) 7.61722 0.241361
\(997\) 22.4176 0.709974 0.354987 0.934871i \(-0.384485\pi\)
0.354987 + 0.934871i \(0.384485\pi\)
\(998\) 7.84699 0.248392
\(999\) 60.8913 1.92651
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 \(a_p\))