Properties

Label 4009.2.a.c.1.10
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4009.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0120261703\)
Analytic rank: \(1\)
Dimension: \(71\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.30773 q^{2}\) \(-2.77619 q^{3}\) \(+3.32561 q^{4}\) \(+2.46750 q^{5}\) \(+6.40670 q^{6}\) \(-0.00709873 q^{7}\) \(-3.05915 q^{8}\) \(+4.70724 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.30773 q^{2}\) \(-2.77619 q^{3}\) \(+3.32561 q^{4}\) \(+2.46750 q^{5}\) \(+6.40670 q^{6}\) \(-0.00709873 q^{7}\) \(-3.05915 q^{8}\) \(+4.70724 q^{9}\) \(-5.69433 q^{10}\) \(+0.0942316 q^{11}\) \(-9.23254 q^{12}\) \(+2.65123 q^{13}\) \(+0.0163820 q^{14}\) \(-6.85027 q^{15}\) \(+0.408469 q^{16}\) \(-0.103040 q^{17}\) \(-10.8630 q^{18}\) \(+1.00000 q^{19}\) \(+8.20596 q^{20}\) \(+0.0197074 q^{21}\) \(-0.217461 q^{22}\) \(+6.73094 q^{23}\) \(+8.49279 q^{24}\) \(+1.08858 q^{25}\) \(-6.11831 q^{26}\) \(-4.73963 q^{27}\) \(-0.0236076 q^{28}\) \(+1.19143 q^{29}\) \(+15.8086 q^{30}\) \(-3.37678 q^{31}\) \(+5.17567 q^{32}\) \(-0.261605 q^{33}\) \(+0.237788 q^{34}\) \(-0.0175162 q^{35}\) \(+15.6545 q^{36}\) \(-2.20219 q^{37}\) \(-2.30773 q^{38}\) \(-7.36031 q^{39}\) \(-7.54847 q^{40}\) \(-4.74460 q^{41}\) \(-0.0454794 q^{42}\) \(+0.284048 q^{43}\) \(+0.313378 q^{44}\) \(+11.6151 q^{45}\) \(-15.5332 q^{46}\) \(-5.74737 q^{47}\) \(-1.13399 q^{48}\) \(-6.99995 q^{49}\) \(-2.51214 q^{50}\) \(+0.286059 q^{51}\) \(+8.81694 q^{52}\) \(-8.09152 q^{53}\) \(+10.9378 q^{54}\) \(+0.232517 q^{55}\) \(+0.0217161 q^{56}\) \(-2.77619 q^{57}\) \(-2.74949 q^{58}\) \(-15.0926 q^{59}\) \(-22.7813 q^{60}\) \(+6.40394 q^{61}\) \(+7.79269 q^{62}\) \(-0.0334155 q^{63}\) \(-12.7610 q^{64}\) \(+6.54191 q^{65}\) \(+0.603713 q^{66}\) \(-12.4217 q^{67}\) \(-0.342671 q^{68}\) \(-18.6864 q^{69}\) \(+0.0404225 q^{70}\) \(+5.05126 q^{71}\) \(-14.4002 q^{72}\) \(+8.19008 q^{73}\) \(+5.08206 q^{74}\) \(-3.02210 q^{75}\) \(+3.32561 q^{76}\) \(-0.000668925 q^{77}\) \(+16.9856 q^{78}\) \(-13.2669 q^{79}\) \(+1.00790 q^{80}\) \(-0.963597 q^{81}\) \(+10.9492 q^{82}\) \(+2.51249 q^{83}\) \(+0.0655393 q^{84}\) \(-0.254252 q^{85}\) \(-0.655507 q^{86}\) \(-3.30763 q^{87}\) \(-0.288269 q^{88}\) \(-14.9772 q^{89}\) \(-26.8046 q^{90}\) \(-0.0188203 q^{91}\) \(+22.3845 q^{92}\) \(+9.37459 q^{93}\) \(+13.2634 q^{94}\) \(+2.46750 q^{95}\) \(-14.3686 q^{96}\) \(+13.5456 q^{97}\) \(+16.1540 q^{98}\) \(+0.443571 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.30773 −1.63181 −0.815905 0.578186i \(-0.803761\pi\)
−0.815905 + 0.578186i \(0.803761\pi\)
\(3\) −2.77619 −1.60284 −0.801418 0.598105i \(-0.795920\pi\)
−0.801418 + 0.598105i \(0.795920\pi\)
\(4\) 3.32561 1.66281
\(5\) 2.46750 1.10350 0.551751 0.834009i \(-0.313960\pi\)
0.551751 + 0.834009i \(0.313960\pi\)
\(6\) 6.40670 2.61552
\(7\) −0.00709873 −0.00268307 −0.00134153 0.999999i \(-0.500427\pi\)
−0.00134153 + 0.999999i \(0.500427\pi\)
\(8\) −3.05915 −1.08157
\(9\) 4.70724 1.56908
\(10\) −5.69433 −1.80071
\(11\) 0.0942316 0.0284119 0.0142059 0.999899i \(-0.495478\pi\)
0.0142059 + 0.999899i \(0.495478\pi\)
\(12\) −9.23254 −2.66520
\(13\) 2.65123 0.735318 0.367659 0.929961i \(-0.380159\pi\)
0.367659 + 0.929961i \(0.380159\pi\)
\(14\) 0.0163820 0.00437826
\(15\) −6.85027 −1.76873
\(16\) 0.408469 0.102117
\(17\) −0.103040 −0.0249909 −0.0124954 0.999922i \(-0.503978\pi\)
−0.0124954 + 0.999922i \(0.503978\pi\)
\(18\) −10.8630 −2.56044
\(19\) 1.00000 0.229416
\(20\) 8.20596 1.83491
\(21\) 0.0197074 0.00430052
\(22\) −0.217461 −0.0463628
\(23\) 6.73094 1.40350 0.701749 0.712424i \(-0.252403\pi\)
0.701749 + 0.712424i \(0.252403\pi\)
\(24\) 8.49279 1.73358
\(25\) 1.08858 0.217715
\(26\) −6.11831 −1.19990
\(27\) −4.73963 −0.912143
\(28\) −0.0236076 −0.00446142
\(29\) 1.19143 0.221242 0.110621 0.993863i \(-0.464716\pi\)
0.110621 + 0.993863i \(0.464716\pi\)
\(30\) 15.8086 2.88623
\(31\) −3.37678 −0.606488 −0.303244 0.952913i \(-0.598070\pi\)
−0.303244 + 0.952913i \(0.598070\pi\)
\(32\) 5.17567 0.914938
\(33\) −0.261605 −0.0455396
\(34\) 0.237788 0.0407804
\(35\) −0.0175162 −0.00296077
\(36\) 15.6545 2.60908
\(37\) −2.20219 −0.362038 −0.181019 0.983480i \(-0.557940\pi\)
−0.181019 + 0.983480i \(0.557940\pi\)
\(38\) −2.30773 −0.374363
\(39\) −7.36031 −1.17859
\(40\) −7.54847 −1.19352
\(41\) −4.74460 −0.740982 −0.370491 0.928836i \(-0.620811\pi\)
−0.370491 + 0.928836i \(0.620811\pi\)
\(42\) −0.0454794 −0.00701763
\(43\) 0.284048 0.0433170 0.0216585 0.999765i \(-0.493105\pi\)
0.0216585 + 0.999765i \(0.493105\pi\)
\(44\) 0.313378 0.0472435
\(45\) 11.6151 1.73148
\(46\) −15.5332 −2.29024
\(47\) −5.74737 −0.838339 −0.419170 0.907908i \(-0.637679\pi\)
−0.419170 + 0.907908i \(0.637679\pi\)
\(48\) −1.13399 −0.163677
\(49\) −6.99995 −0.999993
\(50\) −2.51214 −0.355270
\(51\) 0.286059 0.0400563
\(52\) 8.81694 1.22269
\(53\) −8.09152 −1.11146 −0.555728 0.831364i \(-0.687560\pi\)
−0.555728 + 0.831364i \(0.687560\pi\)
\(54\) 10.9378 1.48844
\(55\) 0.232517 0.0313526
\(56\) 0.0217161 0.00290194
\(57\) −2.77619 −0.367716
\(58\) −2.74949 −0.361026
\(59\) −15.0926 −1.96489 −0.982447 0.186544i \(-0.940271\pi\)
−0.982447 + 0.186544i \(0.940271\pi\)
\(60\) −22.7813 −2.94106
\(61\) 6.40394 0.819940 0.409970 0.912099i \(-0.365539\pi\)
0.409970 + 0.912099i \(0.365539\pi\)
\(62\) 7.79269 0.989673
\(63\) −0.0334155 −0.00420995
\(64\) −12.7610 −1.59512
\(65\) 6.54191 0.811424
\(66\) 0.603713 0.0743120
\(67\) −12.4217 −1.51755 −0.758777 0.651351i \(-0.774203\pi\)
−0.758777 + 0.651351i \(0.774203\pi\)
\(68\) −0.342671 −0.0415550
\(69\) −18.6864 −2.24958
\(70\) 0.0404225 0.00483142
\(71\) 5.05126 0.599474 0.299737 0.954022i \(-0.403101\pi\)
0.299737 + 0.954022i \(0.403101\pi\)
\(72\) −14.4002 −1.69708
\(73\) 8.19008 0.958576 0.479288 0.877658i \(-0.340895\pi\)
0.479288 + 0.877658i \(0.340895\pi\)
\(74\) 5.08206 0.590778
\(75\) −3.02210 −0.348962
\(76\) 3.32561 0.381474
\(77\) −0.000668925 0 −7.62311e−5 0
\(78\) 16.9856 1.92324
\(79\) −13.2669 −1.49264 −0.746322 0.665585i \(-0.768182\pi\)
−0.746322 + 0.665585i \(0.768182\pi\)
\(80\) 1.00790 0.112686
\(81\) −0.963597 −0.107066
\(82\) 10.9492 1.20914
\(83\) 2.51249 0.275782 0.137891 0.990447i \(-0.455968\pi\)
0.137891 + 0.990447i \(0.455968\pi\)
\(84\) 0.0655393 0.00715093
\(85\) −0.254252 −0.0275775
\(86\) −0.655507 −0.0706851
\(87\) −3.30763 −0.354615
\(88\) −0.288269 −0.0307295
\(89\) −14.9772 −1.58757 −0.793787 0.608195i \(-0.791894\pi\)
−0.793787 + 0.608195i \(0.791894\pi\)
\(90\) −26.8046 −2.82545
\(91\) −0.0188203 −0.00197291
\(92\) 22.3845 2.33375
\(93\) 9.37459 0.972100
\(94\) 13.2634 1.36801
\(95\) 2.46750 0.253161
\(96\) −14.3686 −1.46649
\(97\) 13.5456 1.37534 0.687672 0.726022i \(-0.258633\pi\)
0.687672 + 0.726022i \(0.258633\pi\)
\(98\) 16.1540 1.63180
\(99\) 0.443571 0.0445806
\(100\) 3.62018 0.362018
\(101\) 1.87558 0.186627 0.0933137 0.995637i \(-0.470254\pi\)
0.0933137 + 0.995637i \(0.470254\pi\)
\(102\) −0.660147 −0.0653642
\(103\) −16.9679 −1.67189 −0.835947 0.548810i \(-0.815081\pi\)
−0.835947 + 0.548810i \(0.815081\pi\)
\(104\) −8.11050 −0.795300
\(105\) 0.0486282 0.00474563
\(106\) 18.6730 1.81368
\(107\) −18.0512 −1.74507 −0.872536 0.488550i \(-0.837526\pi\)
−0.872536 + 0.488550i \(0.837526\pi\)
\(108\) −15.7622 −1.51672
\(109\) 12.1388 1.16268 0.581341 0.813660i \(-0.302528\pi\)
0.581341 + 0.813660i \(0.302528\pi\)
\(110\) −0.536586 −0.0511614
\(111\) 6.11371 0.580287
\(112\) −0.00289961 −0.000273987 0
\(113\) 10.5627 0.993652 0.496826 0.867850i \(-0.334499\pi\)
0.496826 + 0.867850i \(0.334499\pi\)
\(114\) 6.40670 0.600042
\(115\) 16.6086 1.54876
\(116\) 3.96222 0.367883
\(117\) 12.4800 1.15377
\(118\) 34.8297 3.20633
\(119\) 0.000731454 0 6.70523e−5 0
\(120\) 20.9560 1.91301
\(121\) −10.9911 −0.999193
\(122\) −14.7786 −1.33799
\(123\) 13.1719 1.18767
\(124\) −11.2299 −1.00847
\(125\) −9.65145 −0.863252
\(126\) 0.0771138 0.00686984
\(127\) 20.6097 1.82882 0.914409 0.404792i \(-0.132656\pi\)
0.914409 + 0.404792i \(0.132656\pi\)
\(128\) 19.0975 1.68800
\(129\) −0.788573 −0.0694300
\(130\) −15.0969 −1.32409
\(131\) −8.80506 −0.769302 −0.384651 0.923062i \(-0.625678\pi\)
−0.384651 + 0.923062i \(0.625678\pi\)
\(132\) −0.869997 −0.0757235
\(133\) −0.00709873 −0.000615538 0
\(134\) 28.6659 2.47636
\(135\) −11.6951 −1.00655
\(136\) 0.315215 0.0270295
\(137\) 18.4343 1.57495 0.787476 0.616345i \(-0.211387\pi\)
0.787476 + 0.616345i \(0.211387\pi\)
\(138\) 43.1231 3.67088
\(139\) 7.83167 0.664274 0.332137 0.943231i \(-0.392230\pi\)
0.332137 + 0.943231i \(0.392230\pi\)
\(140\) −0.0582519 −0.00492319
\(141\) 15.9558 1.34372
\(142\) −11.6569 −0.978229
\(143\) 0.249829 0.0208918
\(144\) 1.92276 0.160230
\(145\) 2.93985 0.244141
\(146\) −18.9005 −1.56421
\(147\) 19.4332 1.60282
\(148\) −7.32363 −0.601999
\(149\) −14.6002 −1.19609 −0.598047 0.801461i \(-0.704056\pi\)
−0.598047 + 0.801461i \(0.704056\pi\)
\(150\) 6.97418 0.569439
\(151\) −4.10746 −0.334260 −0.167130 0.985935i \(-0.553450\pi\)
−0.167130 + 0.985935i \(0.553450\pi\)
\(152\) −3.05915 −0.248130
\(153\) −0.485035 −0.0392127
\(154\) 0.00154370 0.000124395 0
\(155\) −8.33222 −0.669260
\(156\) −24.4775 −1.95977
\(157\) 13.9117 1.11027 0.555136 0.831760i \(-0.312666\pi\)
0.555136 + 0.831760i \(0.312666\pi\)
\(158\) 30.6164 2.43571
\(159\) 22.4636 1.78148
\(160\) 12.7710 1.00963
\(161\) −0.0477812 −0.00376568
\(162\) 2.22372 0.174712
\(163\) −6.72695 −0.526895 −0.263448 0.964674i \(-0.584860\pi\)
−0.263448 + 0.964674i \(0.584860\pi\)
\(164\) −15.7787 −1.23211
\(165\) −0.645511 −0.0502530
\(166\) −5.79815 −0.450023
\(167\) −11.9187 −0.922293 −0.461147 0.887324i \(-0.652562\pi\)
−0.461147 + 0.887324i \(0.652562\pi\)
\(168\) −0.0602881 −0.00465133
\(169\) −5.97101 −0.459308
\(170\) 0.586744 0.0450012
\(171\) 4.70724 0.359972
\(172\) 0.944635 0.0720277
\(173\) 3.85339 0.292968 0.146484 0.989213i \(-0.453204\pi\)
0.146484 + 0.989213i \(0.453204\pi\)
\(174\) 7.63311 0.578664
\(175\) −0.00772751 −0.000584145 0
\(176\) 0.0384906 0.00290134
\(177\) 41.9000 3.14940
\(178\) 34.5632 2.59062
\(179\) 10.2772 0.768156 0.384078 0.923301i \(-0.374519\pi\)
0.384078 + 0.923301i \(0.374519\pi\)
\(180\) 38.6274 2.87912
\(181\) 9.36529 0.696116 0.348058 0.937473i \(-0.386841\pi\)
0.348058 + 0.937473i \(0.386841\pi\)
\(182\) 0.0434322 0.00321941
\(183\) −17.7786 −1.31423
\(184\) −20.5910 −1.51799
\(185\) −5.43392 −0.399510
\(186\) −21.6340 −1.58628
\(187\) −0.00970963 −0.000710038 0
\(188\) −19.1135 −1.39400
\(189\) 0.0336454 0.00244734
\(190\) −5.69433 −0.413110
\(191\) −13.7017 −0.991423 −0.495712 0.868487i \(-0.665093\pi\)
−0.495712 + 0.868487i \(0.665093\pi\)
\(192\) 35.4269 2.55672
\(193\) −10.5585 −0.760021 −0.380010 0.924982i \(-0.624080\pi\)
−0.380010 + 0.924982i \(0.624080\pi\)
\(194\) −31.2595 −2.24430
\(195\) −18.1616 −1.30058
\(196\) −23.2791 −1.66279
\(197\) 22.7222 1.61889 0.809443 0.587198i \(-0.199769\pi\)
0.809443 + 0.587198i \(0.199769\pi\)
\(198\) −1.02364 −0.0727470
\(199\) 1.60359 0.113675 0.0568377 0.998383i \(-0.481898\pi\)
0.0568377 + 0.998383i \(0.481898\pi\)
\(200\) −3.33012 −0.235475
\(201\) 34.4851 2.43239
\(202\) −4.32833 −0.304541
\(203\) −0.00845762 −0.000593608 0
\(204\) 0.951321 0.0666058
\(205\) −11.7073 −0.817675
\(206\) 39.1572 2.72821
\(207\) 31.6842 2.20220
\(208\) 1.08294 0.0750885
\(209\) 0.0942316 0.00651814
\(210\) −0.112221 −0.00774396
\(211\) 1.00000 0.0688428
\(212\) −26.9092 −1.84813
\(213\) −14.0233 −0.960859
\(214\) 41.6572 2.84763
\(215\) 0.700891 0.0478004
\(216\) 14.4993 0.986549
\(217\) 0.0239709 0.00162725
\(218\) −28.0130 −1.89728
\(219\) −22.7372 −1.53644
\(220\) 0.773261 0.0521332
\(221\) −0.273182 −0.0183762
\(222\) −14.1088 −0.946919
\(223\) 4.01739 0.269024 0.134512 0.990912i \(-0.457053\pi\)
0.134512 + 0.990912i \(0.457053\pi\)
\(224\) −0.0367407 −0.00245484
\(225\) 5.12419 0.341613
\(226\) −24.3758 −1.62145
\(227\) −15.0161 −0.996651 −0.498326 0.866990i \(-0.666052\pi\)
−0.498326 + 0.866990i \(0.666052\pi\)
\(228\) −9.23254 −0.611440
\(229\) −5.95353 −0.393421 −0.196710 0.980462i \(-0.563026\pi\)
−0.196710 + 0.980462i \(0.563026\pi\)
\(230\) −38.3282 −2.52729
\(231\) 0.00185706 0.000122186 0
\(232\) −3.64475 −0.239290
\(233\) −17.7642 −1.16377 −0.581885 0.813271i \(-0.697685\pi\)
−0.581885 + 0.813271i \(0.697685\pi\)
\(234\) −28.8004 −1.88274
\(235\) −14.1816 −0.925109
\(236\) −50.1922 −3.26724
\(237\) 36.8315 2.39246
\(238\) −0.00168800 −0.000109417 0
\(239\) 7.79067 0.503936 0.251968 0.967736i \(-0.418922\pi\)
0.251968 + 0.967736i \(0.418922\pi\)
\(240\) −2.79812 −0.180618
\(241\) 15.4883 0.997687 0.498844 0.866692i \(-0.333758\pi\)
0.498844 + 0.866692i \(0.333758\pi\)
\(242\) 25.3645 1.63049
\(243\) 16.8940 1.08375
\(244\) 21.2970 1.36340
\(245\) −17.2724 −1.10349
\(246\) −30.3972 −1.93806
\(247\) 2.65123 0.168693
\(248\) 10.3301 0.655961
\(249\) −6.97516 −0.442033
\(250\) 22.2729 1.40866
\(251\) −30.1430 −1.90261 −0.951305 0.308253i \(-0.900256\pi\)
−0.951305 + 0.308253i \(0.900256\pi\)
\(252\) −0.111127 −0.00700033
\(253\) 0.634267 0.0398761
\(254\) −47.5617 −2.98428
\(255\) 0.705852 0.0442021
\(256\) −18.5500 −1.15937
\(257\) 13.6903 0.853975 0.426988 0.904257i \(-0.359575\pi\)
0.426988 + 0.904257i \(0.359575\pi\)
\(258\) 1.81981 0.113297
\(259\) 0.0156328 0.000971373 0
\(260\) 21.7558 1.34924
\(261\) 5.60833 0.347147
\(262\) 20.3197 1.25536
\(263\) −5.82562 −0.359223 −0.179612 0.983738i \(-0.557484\pi\)
−0.179612 + 0.983738i \(0.557484\pi\)
\(264\) 0.800289 0.0492544
\(265\) −19.9659 −1.22649
\(266\) 0.0163820 0.00100444
\(267\) 41.5795 2.54462
\(268\) −41.3098 −2.52340
\(269\) 6.07542 0.370425 0.185212 0.982699i \(-0.440703\pi\)
0.185212 + 0.982699i \(0.440703\pi\)
\(270\) 26.9890 1.64250
\(271\) 16.5306 1.00416 0.502082 0.864820i \(-0.332568\pi\)
0.502082 + 0.864820i \(0.332568\pi\)
\(272\) −0.0420886 −0.00255200
\(273\) 0.0522489 0.00316225
\(274\) −42.5415 −2.57002
\(275\) 0.102578 0.00618570
\(276\) −62.1437 −3.74061
\(277\) 3.99850 0.240247 0.120123 0.992759i \(-0.461671\pi\)
0.120123 + 0.992759i \(0.461671\pi\)
\(278\) −18.0734 −1.08397
\(279\) −15.8953 −0.951628
\(280\) 0.0535846 0.00320229
\(281\) −0.886828 −0.0529037 −0.0264519 0.999650i \(-0.508421\pi\)
−0.0264519 + 0.999650i \(0.508421\pi\)
\(282\) −36.8216 −2.19270
\(283\) 14.3953 0.855710 0.427855 0.903847i \(-0.359269\pi\)
0.427855 + 0.903847i \(0.359269\pi\)
\(284\) 16.7985 0.996809
\(285\) −6.85027 −0.405775
\(286\) −0.576538 −0.0340914
\(287\) 0.0336807 0.00198811
\(288\) 24.3631 1.43561
\(289\) −16.9894 −0.999375
\(290\) −6.78437 −0.398392
\(291\) −37.6051 −2.20445
\(292\) 27.2370 1.59393
\(293\) −0.185756 −0.0108520 −0.00542599 0.999985i \(-0.501727\pi\)
−0.00542599 + 0.999985i \(0.501727\pi\)
\(294\) −44.8466 −2.61550
\(295\) −37.2411 −2.16826
\(296\) 6.73684 0.391571
\(297\) −0.446623 −0.0259157
\(298\) 33.6932 1.95180
\(299\) 17.8452 1.03202
\(300\) −10.0503 −0.580255
\(301\) −0.00201638 −0.000116222 0
\(302\) 9.47889 0.545449
\(303\) −5.20698 −0.299133
\(304\) 0.408469 0.0234273
\(305\) 15.8017 0.904805
\(306\) 1.11933 0.0639877
\(307\) −5.93099 −0.338500 −0.169250 0.985573i \(-0.554134\pi\)
−0.169250 + 0.985573i \(0.554134\pi\)
\(308\) −0.00222458 −0.000126757 0
\(309\) 47.1061 2.67977
\(310\) 19.2285 1.09211
\(311\) 24.6039 1.39516 0.697580 0.716506i \(-0.254260\pi\)
0.697580 + 0.716506i \(0.254260\pi\)
\(312\) 22.5163 1.27473
\(313\) −17.1223 −0.967808 −0.483904 0.875121i \(-0.660782\pi\)
−0.483904 + 0.875121i \(0.660782\pi\)
\(314\) −32.1043 −1.81175
\(315\) −0.0824528 −0.00464569
\(316\) −44.1206 −2.48198
\(317\) −32.2130 −1.80926 −0.904630 0.426197i \(-0.859853\pi\)
−0.904630 + 0.426197i \(0.859853\pi\)
\(318\) −51.8399 −2.90704
\(319\) 0.112270 0.00628591
\(320\) −31.4878 −1.76022
\(321\) 50.1135 2.79706
\(322\) 0.110266 0.00614488
\(323\) −0.103040 −0.00573330
\(324\) −3.20455 −0.178030
\(325\) 2.88606 0.160090
\(326\) 15.5240 0.859793
\(327\) −33.6995 −1.86359
\(328\) 14.5144 0.801426
\(329\) 0.0407990 0.00224932
\(330\) 1.48967 0.0820034
\(331\) −20.9500 −1.15152 −0.575759 0.817619i \(-0.695293\pi\)
−0.575759 + 0.817619i \(0.695293\pi\)
\(332\) 8.35557 0.458571
\(333\) −10.3663 −0.568067
\(334\) 27.5050 1.50501
\(335\) −30.6506 −1.67462
\(336\) 0.00804987 0.000439157 0
\(337\) 17.7372 0.966205 0.483102 0.875564i \(-0.339510\pi\)
0.483102 + 0.875564i \(0.339510\pi\)
\(338\) 13.7795 0.749504
\(339\) −29.3240 −1.59266
\(340\) −0.845543 −0.0458560
\(341\) −0.318199 −0.0172315
\(342\) −10.8630 −0.587406
\(343\) 0.0993819 0.00536612
\(344\) −0.868947 −0.0468505
\(345\) −46.1087 −2.48241
\(346\) −8.89257 −0.478068
\(347\) −22.3755 −1.20118 −0.600589 0.799558i \(-0.705067\pi\)
−0.600589 + 0.799558i \(0.705067\pi\)
\(348\) −10.9999 −0.589656
\(349\) −20.4619 −1.09530 −0.547651 0.836707i \(-0.684478\pi\)
−0.547651 + 0.836707i \(0.684478\pi\)
\(350\) 0.0178330 0.000953214 0
\(351\) −12.5658 −0.670715
\(352\) 0.487711 0.0259951
\(353\) 1.97517 0.105128 0.0525640 0.998618i \(-0.483261\pi\)
0.0525640 + 0.998618i \(0.483261\pi\)
\(354\) −96.6939 −5.13922
\(355\) 12.4640 0.661521
\(356\) −49.8082 −2.63983
\(357\) −0.00203066 −0.000107474 0
\(358\) −23.7170 −1.25348
\(359\) −5.28651 −0.279011 −0.139506 0.990221i \(-0.544551\pi\)
−0.139506 + 0.990221i \(0.544551\pi\)
\(360\) −35.5325 −1.87273
\(361\) 1.00000 0.0526316
\(362\) −21.6125 −1.13593
\(363\) 30.5135 1.60154
\(364\) −0.0625891 −0.00328056
\(365\) 20.2091 1.05779
\(366\) 41.0281 2.14457
\(367\) −8.17698 −0.426835 −0.213418 0.976961i \(-0.568459\pi\)
−0.213418 + 0.976961i \(0.568459\pi\)
\(368\) 2.74938 0.143321
\(369\) −22.3340 −1.16266
\(370\) 12.5400 0.651924
\(371\) 0.0574395 0.00298211
\(372\) 31.1762 1.61641
\(373\) 32.5326 1.68447 0.842236 0.539108i \(-0.181239\pi\)
0.842236 + 0.539108i \(0.181239\pi\)
\(374\) 0.0224072 0.00115865
\(375\) 26.7943 1.38365
\(376\) 17.5821 0.906726
\(377\) 3.15874 0.162683
\(378\) −0.0776444 −0.00399360
\(379\) −21.6289 −1.11100 −0.555501 0.831516i \(-0.687473\pi\)
−0.555501 + 0.831516i \(0.687473\pi\)
\(380\) 8.20596 0.420957
\(381\) −57.2166 −2.93129
\(382\) 31.6199 1.61782
\(383\) −22.0712 −1.12779 −0.563893 0.825848i \(-0.690697\pi\)
−0.563893 + 0.825848i \(0.690697\pi\)
\(384\) −53.0184 −2.70558
\(385\) −0.00165058 −8.41211e−5 0
\(386\) 24.3663 1.24021
\(387\) 1.33709 0.0679679
\(388\) 45.0473 2.28693
\(389\) 0.268461 0.0136115 0.00680575 0.999977i \(-0.497834\pi\)
0.00680575 + 0.999977i \(0.497834\pi\)
\(390\) 41.9120 2.12230
\(391\) −0.693557 −0.0350747
\(392\) 21.4139 1.08157
\(393\) 24.4446 1.23306
\(394\) −52.4366 −2.64172
\(395\) −32.7362 −1.64713
\(396\) 1.47514 0.0741288
\(397\) 22.7082 1.13969 0.569845 0.821752i \(-0.307003\pi\)
0.569845 + 0.821752i \(0.307003\pi\)
\(398\) −3.70065 −0.185497
\(399\) 0.0197074 0.000986606 0
\(400\) 0.444649 0.0222325
\(401\) 3.20323 0.159962 0.0799808 0.996796i \(-0.474514\pi\)
0.0799808 + 0.996796i \(0.474514\pi\)
\(402\) −79.5822 −3.96920
\(403\) −8.95260 −0.445961
\(404\) 6.23746 0.310325
\(405\) −2.37768 −0.118148
\(406\) 0.0195179 0.000968656 0
\(407\) −0.207516 −0.0102862
\(408\) −0.875098 −0.0433238
\(409\) −3.19210 −0.157839 −0.0789195 0.996881i \(-0.525147\pi\)
−0.0789195 + 0.996881i \(0.525147\pi\)
\(410\) 27.0173 1.33429
\(411\) −51.1773 −2.52439
\(412\) −56.4285 −2.78003
\(413\) 0.107139 0.00527194
\(414\) −73.1185 −3.59358
\(415\) 6.19958 0.304325
\(416\) 13.7219 0.672770
\(417\) −21.7422 −1.06472
\(418\) −0.217461 −0.0106364
\(419\) −11.0482 −0.539742 −0.269871 0.962897i \(-0.586981\pi\)
−0.269871 + 0.962897i \(0.586981\pi\)
\(420\) 0.161719 0.00789106
\(421\) 19.8039 0.965185 0.482592 0.875845i \(-0.339695\pi\)
0.482592 + 0.875845i \(0.339695\pi\)
\(422\) −2.30773 −0.112338
\(423\) −27.0542 −1.31542
\(424\) 24.7532 1.20212
\(425\) −0.112167 −0.00544090
\(426\) 32.3619 1.56794
\(427\) −0.0454599 −0.00219996
\(428\) −60.0311 −2.90171
\(429\) −0.693574 −0.0334861
\(430\) −1.61747 −0.0780011
\(431\) −17.0291 −0.820261 −0.410131 0.912027i \(-0.634517\pi\)
−0.410131 + 0.912027i \(0.634517\pi\)
\(432\) −1.93599 −0.0931454
\(433\) −3.50404 −0.168394 −0.0841968 0.996449i \(-0.526832\pi\)
−0.0841968 + 0.996449i \(0.526832\pi\)
\(434\) −0.0553182 −0.00265536
\(435\) −8.16159 −0.391318
\(436\) 40.3688 1.93331
\(437\) 6.73094 0.321985
\(438\) 52.4714 2.50718
\(439\) 34.1640 1.63056 0.815279 0.579069i \(-0.196584\pi\)
0.815279 + 0.579069i \(0.196584\pi\)
\(440\) −0.711304 −0.0339101
\(441\) −32.9505 −1.56907
\(442\) 0.630431 0.0299865
\(443\) 3.97717 0.188961 0.0944804 0.995527i \(-0.469881\pi\)
0.0944804 + 0.995527i \(0.469881\pi\)
\(444\) 20.3318 0.964905
\(445\) −36.9562 −1.75189
\(446\) −9.27105 −0.438997
\(447\) 40.5329 1.91714
\(448\) 0.0905868 0.00427982
\(449\) 12.1845 0.575020 0.287510 0.957778i \(-0.407172\pi\)
0.287510 + 0.957778i \(0.407172\pi\)
\(450\) −11.8252 −0.557447
\(451\) −0.447091 −0.0210527
\(452\) 35.1273 1.65225
\(453\) 11.4031 0.535764
\(454\) 34.6530 1.62635
\(455\) −0.0464393 −0.00217711
\(456\) 8.49279 0.397711
\(457\) −9.15968 −0.428472 −0.214236 0.976782i \(-0.568726\pi\)
−0.214236 + 0.976782i \(0.568726\pi\)
\(458\) 13.7391 0.641988
\(459\) 0.488372 0.0227953
\(460\) 55.2338 2.57529
\(461\) −5.04330 −0.234890 −0.117445 0.993079i \(-0.537470\pi\)
−0.117445 + 0.993079i \(0.537470\pi\)
\(462\) −0.00428560 −0.000199384 0
\(463\) −14.5978 −0.678415 −0.339208 0.940712i \(-0.610159\pi\)
−0.339208 + 0.940712i \(0.610159\pi\)
\(464\) 0.486660 0.0225926
\(465\) 23.1318 1.07271
\(466\) 40.9949 1.89905
\(467\) −19.8244 −0.917366 −0.458683 0.888600i \(-0.651679\pi\)
−0.458683 + 0.888600i \(0.651679\pi\)
\(468\) 41.5035 1.91850
\(469\) 0.0881784 0.00407170
\(470\) 32.7274 1.50960
\(471\) −38.6214 −1.77958
\(472\) 46.1706 2.12518
\(473\) 0.0267663 0.00123072
\(474\) −84.9971 −3.90405
\(475\) 1.08858 0.0499473
\(476\) 0.00243253 0.000111495 0
\(477\) −38.0887 −1.74396
\(478\) −17.9788 −0.822329
\(479\) −31.5237 −1.44036 −0.720178 0.693789i \(-0.755940\pi\)
−0.720178 + 0.693789i \(0.755940\pi\)
\(480\) −35.4547 −1.61828
\(481\) −5.83851 −0.266213
\(482\) −35.7427 −1.62804
\(483\) 0.132650 0.00603577
\(484\) −36.5522 −1.66146
\(485\) 33.4237 1.51769
\(486\) −38.9868 −1.76848
\(487\) −10.6169 −0.481097 −0.240548 0.970637i \(-0.577327\pi\)
−0.240548 + 0.970637i \(0.577327\pi\)
\(488\) −19.5906 −0.886826
\(489\) 18.6753 0.844526
\(490\) 39.8600 1.80069
\(491\) 0.124979 0.00564020 0.00282010 0.999996i \(-0.499102\pi\)
0.00282010 + 0.999996i \(0.499102\pi\)
\(492\) 43.8047 1.97487
\(493\) −0.122765 −0.00552904
\(494\) −6.11831 −0.275276
\(495\) 1.09451 0.0491947
\(496\) −1.37931 −0.0619328
\(497\) −0.0358576 −0.00160843
\(498\) 16.0968 0.721313
\(499\) 37.5379 1.68043 0.840214 0.542255i \(-0.182429\pi\)
0.840214 + 0.542255i \(0.182429\pi\)
\(500\) −32.0970 −1.43542
\(501\) 33.0885 1.47828
\(502\) 69.5619 3.10470
\(503\) −6.71478 −0.299397 −0.149699 0.988732i \(-0.547830\pi\)
−0.149699 + 0.988732i \(0.547830\pi\)
\(504\) 0.102223 0.00455337
\(505\) 4.62801 0.205944
\(506\) −1.46372 −0.0650702
\(507\) 16.5767 0.736195
\(508\) 68.5399 3.04097
\(509\) 1.79275 0.0794623 0.0397311 0.999210i \(-0.487350\pi\)
0.0397311 + 0.999210i \(0.487350\pi\)
\(510\) −1.62891 −0.0721295
\(511\) −0.0581392 −0.00257193
\(512\) 4.61323 0.203878
\(513\) −4.73963 −0.209260
\(514\) −31.5934 −1.39353
\(515\) −41.8683 −1.84494
\(516\) −2.62249 −0.115449
\(517\) −0.541583 −0.0238188
\(518\) −0.0360762 −0.00158510
\(519\) −10.6977 −0.469579
\(520\) −20.0127 −0.877614
\(521\) −44.5121 −1.95011 −0.975056 0.221959i \(-0.928755\pi\)
−0.975056 + 0.221959i \(0.928755\pi\)
\(522\) −12.9425 −0.566478
\(523\) −25.7186 −1.12460 −0.562299 0.826934i \(-0.690083\pi\)
−0.562299 + 0.826934i \(0.690083\pi\)
\(524\) −29.2822 −1.27920
\(525\) 0.0214531 0.000936288 0
\(526\) 13.4440 0.586184
\(527\) 0.347944 0.0151567
\(528\) −0.106857 −0.00465037
\(529\) 22.3056 0.969808
\(530\) 46.0758 2.00140
\(531\) −71.0447 −3.08308
\(532\) −0.0236076 −0.00102352
\(533\) −12.5790 −0.544857
\(534\) −95.9541 −4.15234
\(535\) −44.5413 −1.92569
\(536\) 37.9999 1.64135
\(537\) −28.5315 −1.23123
\(538\) −14.0204 −0.604463
\(539\) −0.659616 −0.0284117
\(540\) −38.8932 −1.67370
\(541\) −0.404887 −0.0174074 −0.00870372 0.999962i \(-0.502771\pi\)
−0.00870372 + 0.999962i \(0.502771\pi\)
\(542\) −38.1482 −1.63860
\(543\) −25.9998 −1.11576
\(544\) −0.533301 −0.0228651
\(545\) 29.9524 1.28302
\(546\) −0.120576 −0.00516019
\(547\) 11.5896 0.495537 0.247769 0.968819i \(-0.420303\pi\)
0.247769 + 0.968819i \(0.420303\pi\)
\(548\) 61.3055 2.61884
\(549\) 30.1449 1.28655
\(550\) −0.236723 −0.0100939
\(551\) 1.19143 0.0507565
\(552\) 57.1645 2.43308
\(553\) 0.0941783 0.00400487
\(554\) −9.22745 −0.392037
\(555\) 15.0856 0.640348
\(556\) 26.0451 1.10456
\(557\) −36.2871 −1.53754 −0.768768 0.639528i \(-0.779130\pi\)
−0.768768 + 0.639528i \(0.779130\pi\)
\(558\) 36.6821 1.55288
\(559\) 0.753076 0.0318517
\(560\) −0.00715480 −0.000302345 0
\(561\) 0.0269558 0.00113807
\(562\) 2.04656 0.0863288
\(563\) −2.38673 −0.100589 −0.0502943 0.998734i \(-0.516016\pi\)
−0.0502943 + 0.998734i \(0.516016\pi\)
\(564\) 53.0628 2.23435
\(565\) 26.0634 1.09650
\(566\) −33.2204 −1.39636
\(567\) 0.00684032 0.000287266 0
\(568\) −15.4526 −0.648375
\(569\) −18.6287 −0.780957 −0.390478 0.920612i \(-0.627690\pi\)
−0.390478 + 0.920612i \(0.627690\pi\)
\(570\) 15.8086 0.662147
\(571\) 5.68741 0.238011 0.119005 0.992894i \(-0.462029\pi\)
0.119005 + 0.992894i \(0.462029\pi\)
\(572\) 0.830835 0.0347389
\(573\) 38.0387 1.58909
\(574\) −0.0777258 −0.00324421
\(575\) 7.32714 0.305563
\(576\) −60.0690 −2.50288
\(577\) 4.53220 0.188678 0.0943391 0.995540i \(-0.469926\pi\)
0.0943391 + 0.995540i \(0.469926\pi\)
\(578\) 39.2069 1.63079
\(579\) 29.3126 1.21819
\(580\) 9.77680 0.405959
\(581\) −0.0178355 −0.000739941 0
\(582\) 86.7823 3.59724
\(583\) −0.762477 −0.0315786
\(584\) −25.0547 −1.03677
\(585\) 30.7943 1.27319
\(586\) 0.428675 0.0177084
\(587\) −16.6321 −0.686482 −0.343241 0.939247i \(-0.611525\pi\)
−0.343241 + 0.939247i \(0.611525\pi\)
\(588\) 64.6273 2.66518
\(589\) −3.37678 −0.139138
\(590\) 85.9424 3.53819
\(591\) −63.0811 −2.59481
\(592\) −0.899526 −0.0369703
\(593\) −0.445303 −0.0182864 −0.00914321 0.999958i \(-0.502910\pi\)
−0.00914321 + 0.999958i \(0.502910\pi\)
\(594\) 1.03068 0.0422895
\(595\) 0.00180487 7.39923e−5 0
\(596\) −48.5545 −1.98887
\(597\) −4.45187 −0.182203
\(598\) −41.1820 −1.68406
\(599\) −26.0030 −1.06245 −0.531226 0.847230i \(-0.678269\pi\)
−0.531226 + 0.847230i \(0.678269\pi\)
\(600\) 9.24505 0.377428
\(601\) −7.63101 −0.311275 −0.155638 0.987814i \(-0.549743\pi\)
−0.155638 + 0.987814i \(0.549743\pi\)
\(602\) 0.00465327 0.000189653 0
\(603\) −58.4720 −2.38116
\(604\) −13.6598 −0.555810
\(605\) −27.1206 −1.10261
\(606\) 12.0163 0.488128
\(607\) −12.9441 −0.525387 −0.262693 0.964879i \(-0.584611\pi\)
−0.262693 + 0.964879i \(0.584611\pi\)
\(608\) 5.17567 0.209901
\(609\) 0.0234800 0.000951456 0
\(610\) −36.4661 −1.47647
\(611\) −15.2376 −0.616446
\(612\) −1.61304 −0.0652031
\(613\) 28.5776 1.15424 0.577119 0.816660i \(-0.304177\pi\)
0.577119 + 0.816660i \(0.304177\pi\)
\(614\) 13.6871 0.552367
\(615\) 32.5018 1.31060
\(616\) 0.00204634 8.24495e−5 0
\(617\) 11.6101 0.467406 0.233703 0.972308i \(-0.424916\pi\)
0.233703 + 0.972308i \(0.424916\pi\)
\(618\) −108.708 −4.37288
\(619\) 6.03758 0.242671 0.121335 0.992612i \(-0.461282\pi\)
0.121335 + 0.992612i \(0.461282\pi\)
\(620\) −27.7097 −1.11285
\(621\) −31.9022 −1.28019
\(622\) −56.7792 −2.27664
\(623\) 0.106319 0.00425957
\(624\) −3.00646 −0.120355
\(625\) −29.2579 −1.17032
\(626\) 39.5136 1.57928
\(627\) −0.261605 −0.0104475
\(628\) 46.2648 1.84617
\(629\) 0.226914 0.00904765
\(630\) 0.190279 0.00758088
\(631\) 24.0925 0.959106 0.479553 0.877513i \(-0.340799\pi\)
0.479553 + 0.877513i \(0.340799\pi\)
\(632\) 40.5855 1.61440
\(633\) −2.77619 −0.110344
\(634\) 74.3388 2.95237
\(635\) 50.8546 2.01810
\(636\) 74.7052 2.96226
\(637\) −18.5584 −0.735312
\(638\) −0.259089 −0.0102574
\(639\) 23.7775 0.940624
\(640\) 47.1232 1.86271
\(641\) 23.1153 0.913001 0.456501 0.889723i \(-0.349103\pi\)
0.456501 + 0.889723i \(0.349103\pi\)
\(642\) −115.648 −4.56427
\(643\) 20.4235 0.805423 0.402712 0.915327i \(-0.368068\pi\)
0.402712 + 0.915327i \(0.368068\pi\)
\(644\) −0.158902 −0.00626160
\(645\) −1.94581 −0.0766161
\(646\) 0.237788 0.00935566
\(647\) 39.3756 1.54802 0.774008 0.633175i \(-0.218249\pi\)
0.774008 + 0.633175i \(0.218249\pi\)
\(648\) 2.94779 0.115800
\(649\) −1.42220 −0.0558263
\(650\) −6.66024 −0.261236
\(651\) −0.0665477 −0.00260821
\(652\) −22.3712 −0.876125
\(653\) 40.6583 1.59108 0.795542 0.605899i \(-0.207186\pi\)
0.795542 + 0.605899i \(0.207186\pi\)
\(654\) 77.7694 3.04102
\(655\) −21.7265 −0.848926
\(656\) −1.93802 −0.0756670
\(657\) 38.5527 1.50408
\(658\) −0.0941531 −0.00367047
\(659\) 2.19351 0.0854472 0.0427236 0.999087i \(-0.486397\pi\)
0.0427236 + 0.999087i \(0.486397\pi\)
\(660\) −2.14672 −0.0835610
\(661\) −37.3415 −1.45242 −0.726208 0.687475i \(-0.758719\pi\)
−0.726208 + 0.687475i \(0.758719\pi\)
\(662\) 48.3470 1.87906
\(663\) 0.758407 0.0294541
\(664\) −7.68609 −0.298278
\(665\) −0.0175162 −0.000679247 0
\(666\) 23.9225 0.926978
\(667\) 8.01942 0.310513
\(668\) −39.6368 −1.53359
\(669\) −11.1530 −0.431202
\(670\) 70.7333 2.73267
\(671\) 0.603453 0.0232961
\(672\) 0.101999 0.00393471
\(673\) −1.01672 −0.0391918 −0.0195959 0.999808i \(-0.506238\pi\)
−0.0195959 + 0.999808i \(0.506238\pi\)
\(674\) −40.9326 −1.57666
\(675\) −5.15945 −0.198587
\(676\) −19.8572 −0.763740
\(677\) 28.9019 1.11079 0.555395 0.831586i \(-0.312567\pi\)
0.555395 + 0.831586i \(0.312567\pi\)
\(678\) 67.6718 2.59892
\(679\) −0.0961563 −0.00369014
\(680\) 0.777795 0.0298271
\(681\) 41.6875 1.59747
\(682\) 0.734318 0.0281185
\(683\) −10.9535 −0.419123 −0.209561 0.977795i \(-0.567204\pi\)
−0.209561 + 0.977795i \(0.567204\pi\)
\(684\) 15.6545 0.598563
\(685\) 45.4868 1.73796
\(686\) −0.229346 −0.00875649
\(687\) 16.5282 0.630588
\(688\) 0.116025 0.00442341
\(689\) −21.4524 −0.817273
\(690\) 106.406 4.05082
\(691\) −1.00609 −0.0382735 −0.0191368 0.999817i \(-0.506092\pi\)
−0.0191368 + 0.999817i \(0.506092\pi\)
\(692\) 12.8149 0.487148
\(693\) −0.00314879 −0.000119613 0
\(694\) 51.6365 1.96009
\(695\) 19.3247 0.733027
\(696\) 10.1185 0.383542
\(697\) 0.488884 0.0185178
\(698\) 47.2206 1.78733
\(699\) 49.3168 1.86533
\(700\) −0.0256987 −0.000971320 0
\(701\) −30.8253 −1.16426 −0.582128 0.813097i \(-0.697780\pi\)
−0.582128 + 0.813097i \(0.697780\pi\)
\(702\) 28.9985 1.09448
\(703\) −2.20219 −0.0830572
\(704\) −1.20249 −0.0453204
\(705\) 39.3710 1.48280
\(706\) −4.55817 −0.171549
\(707\) −0.0133143 −0.000500734 0
\(708\) 139.343 5.23684
\(709\) −29.4238 −1.10503 −0.552517 0.833501i \(-0.686333\pi\)
−0.552517 + 0.833501i \(0.686333\pi\)
\(710\) −28.7635 −1.07948
\(711\) −62.4506 −2.34208
\(712\) 45.8174 1.71708
\(713\) −22.7289 −0.851204
\(714\) 0.00468620 0.000175377 0
\(715\) 0.616454 0.0230541
\(716\) 34.1781 1.27729
\(717\) −21.6284 −0.807727
\(718\) 12.1998 0.455294
\(719\) 16.7108 0.623207 0.311604 0.950212i \(-0.399134\pi\)
0.311604 + 0.950212i \(0.399134\pi\)
\(720\) 4.74442 0.176814
\(721\) 0.120450 0.00448581
\(722\) −2.30773 −0.0858848
\(723\) −42.9984 −1.59913
\(724\) 31.1453 1.15751
\(725\) 1.29696 0.0481678
\(726\) −70.4168 −2.61341
\(727\) −32.8965 −1.22007 −0.610033 0.792376i \(-0.708844\pi\)
−0.610033 + 0.792376i \(0.708844\pi\)
\(728\) 0.0575743 0.00213384
\(729\) −44.0103 −1.63001
\(730\) −46.6370 −1.72611
\(731\) −0.0292684 −0.00108253
\(732\) −59.1246 −2.18531
\(733\) −1.18341 −0.0437101 −0.0218550 0.999761i \(-0.506957\pi\)
−0.0218550 + 0.999761i \(0.506957\pi\)
\(734\) 18.8703 0.696514
\(735\) 47.9515 1.76872
\(736\) 34.8371 1.28411
\(737\) −1.17052 −0.0431166
\(738\) 51.5408 1.89724
\(739\) 38.2843 1.40831 0.704155 0.710046i \(-0.251326\pi\)
0.704155 + 0.710046i \(0.251326\pi\)
\(740\) −18.0711 −0.664307
\(741\) −7.36031 −0.270388
\(742\) −0.132555 −0.00486624
\(743\) 4.13006 0.151517 0.0757586 0.997126i \(-0.475862\pi\)
0.0757586 + 0.997126i \(0.475862\pi\)
\(744\) −28.6783 −1.05140
\(745\) −36.0260 −1.31989
\(746\) −75.0764 −2.74874
\(747\) 11.8269 0.432724
\(748\) −0.0322905 −0.00118066
\(749\) 0.128140 0.00468215
\(750\) −61.8340 −2.25786
\(751\) 39.9230 1.45681 0.728406 0.685146i \(-0.240261\pi\)
0.728406 + 0.685146i \(0.240261\pi\)
\(752\) −2.34762 −0.0856088
\(753\) 83.6827 3.04957
\(754\) −7.28951 −0.265468
\(755\) −10.1352 −0.368856
\(756\) 0.111891 0.00406945
\(757\) 40.7776 1.48209 0.741044 0.671456i \(-0.234331\pi\)
0.741044 + 0.671456i \(0.234331\pi\)
\(758\) 49.9136 1.81294
\(759\) −1.76085 −0.0639147
\(760\) −7.54847 −0.273812
\(761\) −2.37731 −0.0861775 −0.0430887 0.999071i \(-0.513720\pi\)
−0.0430887 + 0.999071i \(0.513720\pi\)
\(762\) 132.040 4.78332
\(763\) −0.0861698 −0.00311956
\(764\) −45.5667 −1.64854
\(765\) −1.19682 −0.0432713
\(766\) 50.9344 1.84033
\(767\) −40.0140 −1.44482
\(768\) 51.4983 1.85828
\(769\) −43.4133 −1.56553 −0.782763 0.622320i \(-0.786190\pi\)
−0.782763 + 0.622320i \(0.786190\pi\)
\(770\) 0.00380908 0.000137270 0
\(771\) −38.0068 −1.36878
\(772\) −35.1136 −1.26377
\(773\) 47.8041 1.71939 0.859697 0.510805i \(-0.170653\pi\)
0.859697 + 0.510805i \(0.170653\pi\)
\(774\) −3.08563 −0.110911
\(775\) −3.67588 −0.132042
\(776\) −41.4379 −1.48753
\(777\) −0.0433996 −0.00155695
\(778\) −0.619534 −0.0222114
\(779\) −4.74460 −0.169993
\(780\) −60.3984 −2.16261
\(781\) 0.475988 0.0170322
\(782\) 1.60054 0.0572352
\(783\) −5.64692 −0.201805
\(784\) −2.85926 −0.102116
\(785\) 34.3271 1.22519
\(786\) −56.4114 −2.01213
\(787\) 3.04033 0.108376 0.0541880 0.998531i \(-0.482743\pi\)
0.0541880 + 0.998531i \(0.482743\pi\)
\(788\) 75.5650 2.69189
\(789\) 16.1731 0.575776
\(790\) 75.5462 2.68781
\(791\) −0.0749816 −0.00266604
\(792\) −1.35695 −0.0482171
\(793\) 16.9783 0.602916
\(794\) −52.4043 −1.85976
\(795\) 55.4290 1.96587
\(796\) 5.33291 0.189020
\(797\) 17.6721 0.625976 0.312988 0.949757i \(-0.398670\pi\)
0.312988 + 0.949757i \(0.398670\pi\)
\(798\) −0.0454794 −0.00160995
\(799\) 0.592209 0.0209508
\(800\) 5.63411 0.199196
\(801\) −70.5011 −2.49103
\(802\) −7.39218 −0.261027
\(803\) 0.771764 0.0272350
\(804\) 114.684 4.04459
\(805\) −0.117900 −0.00415544
\(806\) 20.6602 0.727724
\(807\) −16.8665 −0.593730
\(808\) −5.73769 −0.201851
\(809\) −6.89589 −0.242447 −0.121223 0.992625i \(-0.538682\pi\)
−0.121223 + 0.992625i \(0.538682\pi\)
\(810\) 5.48704 0.192795
\(811\) 23.3139 0.818662 0.409331 0.912386i \(-0.365762\pi\)
0.409331 + 0.912386i \(0.365762\pi\)
\(812\) −0.0281267 −0.000987055 0
\(813\) −45.8922 −1.60951
\(814\) 0.478891 0.0167851
\(815\) −16.5988 −0.581430
\(816\) 0.116846 0.00409043
\(817\) 0.284048 0.00993760
\(818\) 7.36649 0.257563
\(819\) −0.0885919 −0.00309565
\(820\) −38.9340 −1.35963
\(821\) −40.5426 −1.41495 −0.707474 0.706740i \(-0.750165\pi\)
−0.707474 + 0.706740i \(0.750165\pi\)
\(822\) 118.103 4.11933
\(823\) 50.2726 1.75239 0.876196 0.481955i \(-0.160073\pi\)
0.876196 + 0.481955i \(0.160073\pi\)
\(824\) 51.9073 1.80828
\(825\) −0.284777 −0.00991466
\(826\) −0.247247 −0.00860281
\(827\) −35.8507 −1.24665 −0.623326 0.781962i \(-0.714219\pi\)
−0.623326 + 0.781962i \(0.714219\pi\)
\(828\) 105.369 3.66184
\(829\) 34.7719 1.20768 0.603839 0.797106i \(-0.293637\pi\)
0.603839 + 0.797106i \(0.293637\pi\)
\(830\) −14.3069 −0.496601
\(831\) −11.1006 −0.385076
\(832\) −33.8322 −1.17292
\(833\) 0.721275 0.0249907
\(834\) 50.1751 1.73742
\(835\) −29.4093 −1.01775
\(836\) 0.313378 0.0108384
\(837\) 16.0047 0.553203
\(838\) 25.4963 0.880756
\(839\) 38.1379 1.31667 0.658333 0.752726i \(-0.271262\pi\)
0.658333 + 0.752726i \(0.271262\pi\)
\(840\) −0.148761 −0.00513274
\(841\) −27.5805 −0.951052
\(842\) −45.7021 −1.57500
\(843\) 2.46200 0.0847959
\(844\) 3.32561 0.114472
\(845\) −14.7335 −0.506847
\(846\) 62.4338 2.14652
\(847\) 0.0780230 0.00268090
\(848\) −3.30513 −0.113499
\(849\) −39.9640 −1.37156
\(850\) 0.258851 0.00887851
\(851\) −14.8228 −0.508120
\(852\) −46.6359 −1.59772
\(853\) −28.5963 −0.979119 −0.489560 0.871970i \(-0.662842\pi\)
−0.489560 + 0.871970i \(0.662842\pi\)
\(854\) 0.104909 0.00358991
\(855\) 11.6151 0.397229
\(856\) 55.2212 1.88742
\(857\) 34.4331 1.17621 0.588107 0.808783i \(-0.299873\pi\)
0.588107 + 0.808783i \(0.299873\pi\)
\(858\) 1.60058 0.0546429
\(859\) −34.6922 −1.18368 −0.591841 0.806055i \(-0.701599\pi\)
−0.591841 + 0.806055i \(0.701599\pi\)
\(860\) 2.33089 0.0794827
\(861\) −0.0935040 −0.00318661
\(862\) 39.2985 1.33851
\(863\) −52.4408 −1.78510 −0.892552 0.450944i \(-0.851088\pi\)
−0.892552 + 0.450944i \(0.851088\pi\)
\(864\) −24.5308 −0.834554
\(865\) 9.50825 0.323290
\(866\) 8.08638 0.274787
\(867\) 47.1658 1.60183
\(868\) 0.0797178 0.00270580
\(869\) −1.25016 −0.0424088
\(870\) 18.8347 0.638557
\(871\) −32.9328 −1.11588
\(872\) −37.1343 −1.25753
\(873\) 63.7622 2.15802
\(874\) −15.5332 −0.525418
\(875\) 0.0685131 0.00231617
\(876\) −75.6152 −2.55480
\(877\) −35.1235 −1.18604 −0.593019 0.805189i \(-0.702064\pi\)
−0.593019 + 0.805189i \(0.702064\pi\)
\(878\) −78.8412 −2.66076
\(879\) 0.515694 0.0173939
\(880\) 0.0949758 0.00320163
\(881\) 37.2891 1.25630 0.628151 0.778091i \(-0.283812\pi\)
0.628151 + 0.778091i \(0.283812\pi\)
\(882\) 76.0407 2.56042
\(883\) 14.7557 0.496569 0.248284 0.968687i \(-0.420133\pi\)
0.248284 + 0.968687i \(0.420133\pi\)
\(884\) −0.908498 −0.0305561
\(885\) 103.389 3.47537
\(886\) −9.17822 −0.308348
\(887\) −4.52761 −0.152022 −0.0760111 0.997107i \(-0.524218\pi\)
−0.0760111 + 0.997107i \(0.524218\pi\)
\(888\) −18.7028 −0.627623
\(889\) −0.146303 −0.00490684
\(890\) 85.2848 2.85875
\(891\) −0.0908012 −0.00304196
\(892\) 13.3603 0.447335
\(893\) −5.74737 −0.192328
\(894\) −93.5389 −3.12841
\(895\) 25.3591 0.847661
\(896\) −0.135568 −0.00452902
\(897\) −49.5418 −1.65415
\(898\) −28.1184 −0.938324
\(899\) −4.02318 −0.134181
\(900\) 17.0411 0.568036
\(901\) 0.833750 0.0277763
\(902\) 1.03177 0.0343540
\(903\) 0.00559787 0.000186285 0
\(904\) −32.3128 −1.07471
\(905\) 23.1089 0.768165
\(906\) −26.3152 −0.874265
\(907\) −41.5394 −1.37929 −0.689646 0.724147i \(-0.742234\pi\)
−0.689646 + 0.724147i \(0.742234\pi\)
\(908\) −49.9376 −1.65724
\(909\) 8.82882 0.292833
\(910\) 0.107169 0.00355263
\(911\) −4.23885 −0.140439 −0.0702197 0.997532i \(-0.522370\pi\)
−0.0702197 + 0.997532i \(0.522370\pi\)
\(912\) −1.13399 −0.0375501
\(913\) 0.236756 0.00783548
\(914\) 21.1380 0.699185
\(915\) −43.8687 −1.45025
\(916\) −19.7991 −0.654182
\(917\) 0.0625048 0.00206409
\(918\) −1.12703 −0.0371975
\(919\) −52.8433 −1.74314 −0.871570 0.490270i \(-0.836898\pi\)
−0.871570 + 0.490270i \(0.836898\pi\)
\(920\) −50.8083 −1.67510
\(921\) 16.4656 0.542559
\(922\) 11.6386 0.383296
\(923\) 13.3920 0.440804
\(924\) 0.00617587 0.000203171 0
\(925\) −2.39725 −0.0788212
\(926\) 33.6877 1.10705
\(927\) −79.8719 −2.62334
\(928\) 6.16643 0.202423
\(929\) −27.6191 −0.906152 −0.453076 0.891472i \(-0.649673\pi\)
−0.453076 + 0.891472i \(0.649673\pi\)
\(930\) −53.3820 −1.75046
\(931\) −6.99995 −0.229414
\(932\) −59.0768 −1.93512
\(933\) −68.3052 −2.23621
\(934\) 45.7494 1.49697
\(935\) −0.0239585 −0.000783528 0
\(936\) −38.1781 −1.24789
\(937\) 38.6693 1.26327 0.631635 0.775266i \(-0.282384\pi\)
0.631635 + 0.775266i \(0.282384\pi\)
\(938\) −0.203492 −0.00664425
\(939\) 47.5347 1.55124
\(940\) −47.1626 −1.53828
\(941\) 27.5414 0.897824 0.448912 0.893576i \(-0.351812\pi\)
0.448912 + 0.893576i \(0.351812\pi\)
\(942\) 89.1278 2.90394
\(943\) −31.9356 −1.03997
\(944\) −6.16487 −0.200649
\(945\) 0.0830201 0.00270065
\(946\) −0.0617695 −0.00200830
\(947\) −11.3735 −0.369589 −0.184794 0.982777i \(-0.559162\pi\)
−0.184794 + 0.982777i \(0.559162\pi\)
\(948\) 122.487 3.97820
\(949\) 21.7137 0.704858
\(950\) −2.51214 −0.0815045
\(951\) 89.4294 2.89995
\(952\) −0.00223763 −7.25220e−5 0
\(953\) −36.7727 −1.19118 −0.595592 0.803287i \(-0.703083\pi\)
−0.595592 + 0.803287i \(0.703083\pi\)
\(954\) 87.8985 2.84582
\(955\) −33.8091 −1.09404
\(956\) 25.9087 0.837948
\(957\) −0.311683 −0.0100753
\(958\) 72.7482 2.35039
\(959\) −0.130861 −0.00422571
\(960\) 87.4161 2.82134
\(961\) −19.5974 −0.632173
\(962\) 13.4737 0.434409
\(963\) −84.9712 −2.73816
\(964\) 51.5080 1.65896
\(965\) −26.0533 −0.838684
\(966\) −0.306120 −0.00984923
\(967\) −53.0647 −1.70645 −0.853223 0.521546i \(-0.825355\pi\)
−0.853223 + 0.521546i \(0.825355\pi\)
\(968\) 33.6235 1.08070
\(969\) 0.286059 0.00918954
\(970\) −77.1329 −2.47659
\(971\) 13.2999 0.426814 0.213407 0.976963i \(-0.431544\pi\)
0.213407 + 0.976963i \(0.431544\pi\)
\(972\) 56.1830 1.80207
\(973\) −0.0555949 −0.00178229
\(974\) 24.5009 0.785059
\(975\) −8.01226 −0.256598
\(976\) 2.61581 0.0837300
\(977\) −45.5049 −1.45583 −0.727915 0.685667i \(-0.759511\pi\)
−0.727915 + 0.685667i \(0.759511\pi\)
\(978\) −43.0975 −1.37811
\(979\) −1.41132 −0.0451060
\(980\) −57.4413 −1.83490
\(981\) 57.1401 1.82434
\(982\) −0.288417 −0.00920375
\(983\) 15.8820 0.506558 0.253279 0.967393i \(-0.418491\pi\)
0.253279 + 0.967393i \(0.418491\pi\)
\(984\) −40.2949 −1.28455
\(985\) 56.0670 1.78644
\(986\) 0.283307 0.00902235
\(987\) −0.113266 −0.00360529
\(988\) 8.81694 0.280504
\(989\) 1.91191 0.0607953
\(990\) −2.52584 −0.0802764
\(991\) 17.7974 0.565354 0.282677 0.959215i \(-0.408777\pi\)
0.282677 + 0.959215i \(0.408777\pi\)
\(992\) −17.4771 −0.554898
\(993\) 58.1613 1.84569
\(994\) 0.0827495 0.00262465
\(995\) 3.95686 0.125441
\(996\) −23.1967 −0.735014
\(997\) −42.0476 −1.33166 −0.665830 0.746103i \(-0.731923\pi\)
−0.665830 + 0.746103i \(0.731923\pi\)
\(998\) −86.6273 −2.74214
\(999\) 10.4376 0.330230
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 \(a_p\))