Properties

Label 4009.2.a.c.1.3
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 1.3
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.69837 q^{2}\) \(+1.88273 q^{3}\) \(+5.28118 q^{4}\) \(-2.05530 q^{5}\) \(-5.08030 q^{6}\) \(+0.784756 q^{7}\) \(-8.85381 q^{8}\) \(+0.544674 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.69837 q^{2}\) \(+1.88273 q^{3}\) \(+5.28118 q^{4}\) \(-2.05530 q^{5}\) \(-5.08030 q^{6}\) \(+0.784756 q^{7}\) \(-8.85381 q^{8}\) \(+0.544674 q^{9}\) \(+5.54594 q^{10}\) \(-2.34721 q^{11}\) \(+9.94303 q^{12}\) \(+4.30855 q^{13}\) \(-2.11756 q^{14}\) \(-3.86957 q^{15}\) \(+13.3285 q^{16}\) \(-2.48420 q^{17}\) \(-1.46973 q^{18}\) \(+1.00000 q^{19}\) \(-10.8544 q^{20}\) \(+1.47748 q^{21}\) \(+6.33362 q^{22}\) \(+4.84592 q^{23}\) \(-16.6693 q^{24}\) \(-0.775762 q^{25}\) \(-11.6260 q^{26}\) \(-4.62272 q^{27}\) \(+4.14444 q^{28}\) \(+2.17707 q^{29}\) \(+10.4415 q^{30}\) \(+0.527020 q^{31}\) \(-18.2575 q^{32}\) \(-4.41916 q^{33}\) \(+6.70329 q^{34}\) \(-1.61291 q^{35}\) \(+2.87652 q^{36}\) \(-5.01494 q^{37}\) \(-2.69837 q^{38}\) \(+8.11184 q^{39}\) \(+18.1972 q^{40}\) \(-1.52853 q^{41}\) \(-3.98679 q^{42}\) \(-4.10155 q^{43}\) \(-12.3960 q^{44}\) \(-1.11947 q^{45}\) \(-13.0761 q^{46}\) \(+0.0151453 q^{47}\) \(+25.0939 q^{48}\) \(-6.38416 q^{49}\) \(+2.09329 q^{50}\) \(-4.67708 q^{51}\) \(+22.7542 q^{52}\) \(+2.70200 q^{53}\) \(+12.4738 q^{54}\) \(+4.82420 q^{55}\) \(-6.94809 q^{56}\) \(+1.88273 q^{57}\) \(-5.87454 q^{58}\) \(-10.7088 q^{59}\) \(-20.4359 q^{60}\) \(+5.59481 q^{61}\) \(-1.42209 q^{62}\) \(+0.427436 q^{63}\) \(+22.6084 q^{64}\) \(-8.85534 q^{65}\) \(+11.9245 q^{66}\) \(+5.88688 q^{67}\) \(-13.1195 q^{68}\) \(+9.12357 q^{69}\) \(+4.35221 q^{70}\) \(+13.0097 q^{71}\) \(-4.82244 q^{72}\) \(+1.58068 q^{73}\) \(+13.5321 q^{74}\) \(-1.46055 q^{75}\) \(+5.28118 q^{76}\) \(-1.84199 q^{77}\) \(-21.8887 q^{78}\) \(+15.7171 q^{79}\) \(-27.3939 q^{80}\) \(-10.3374 q^{81}\) \(+4.12453 q^{82}\) \(-13.9489 q^{83}\) \(+7.80286 q^{84}\) \(+5.10577 q^{85}\) \(+11.0675 q^{86}\) \(+4.09884 q^{87}\) \(+20.7817 q^{88}\) \(-11.7529 q^{89}\) \(+3.02073 q^{90}\) \(+3.38116 q^{91}\) \(+25.5922 q^{92}\) \(+0.992236 q^{93}\) \(-0.0408675 q^{94}\) \(-2.05530 q^{95}\) \(-34.3739 q^{96}\) \(-1.28700 q^{97}\) \(+17.2268 q^{98}\) \(-1.27846 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69837 −1.90803 −0.954016 0.299755i \(-0.903095\pi\)
−0.954016 + 0.299755i \(0.903095\pi\)
\(3\) 1.88273 1.08699 0.543497 0.839411i \(-0.317100\pi\)
0.543497 + 0.839411i \(0.317100\pi\)
\(4\) 5.28118 2.64059
\(5\) −2.05530 −0.919156 −0.459578 0.888137i \(-0.651999\pi\)
−0.459578 + 0.888137i \(0.651999\pi\)
\(6\) −5.08030 −2.07402
\(7\) 0.784756 0.296610 0.148305 0.988942i \(-0.452618\pi\)
0.148305 + 0.988942i \(0.452618\pi\)
\(8\) −8.85381 −3.13030
\(9\) 0.544674 0.181558
\(10\) 5.54594 1.75378
\(11\) −2.34721 −0.707710 −0.353855 0.935300i \(-0.615129\pi\)
−0.353855 + 0.935300i \(0.615129\pi\)
\(12\) 9.94303 2.87031
\(13\) 4.30855 1.19498 0.597488 0.801878i \(-0.296165\pi\)
0.597488 + 0.801878i \(0.296165\pi\)
\(14\) −2.11756 −0.565942
\(15\) −3.86957 −0.999118
\(16\) 13.3285 3.33212
\(17\) −2.48420 −0.602508 −0.301254 0.953544i \(-0.597405\pi\)
−0.301254 + 0.953544i \(0.597405\pi\)
\(18\) −1.46973 −0.346419
\(19\) 1.00000 0.229416
\(20\) −10.8544 −2.42711
\(21\) 1.47748 0.322414
\(22\) 6.33362 1.35033
\(23\) 4.84592 1.01045 0.505223 0.862989i \(-0.331410\pi\)
0.505223 + 0.862989i \(0.331410\pi\)
\(24\) −16.6693 −3.40262
\(25\) −0.775762 −0.155152
\(26\) −11.6260 −2.28005
\(27\) −4.62272 −0.889642
\(28\) 4.14444 0.783225
\(29\) 2.17707 0.404272 0.202136 0.979357i \(-0.435212\pi\)
0.202136 + 0.979357i \(0.435212\pi\)
\(30\) 10.4415 1.90635
\(31\) 0.527020 0.0946555 0.0473278 0.998879i \(-0.484929\pi\)
0.0473278 + 0.998879i \(0.484929\pi\)
\(32\) −18.2575 −3.22749
\(33\) −4.41916 −0.769277
\(34\) 6.70329 1.14960
\(35\) −1.61291 −0.272631
\(36\) 2.87652 0.479420
\(37\) −5.01494 −0.824451 −0.412226 0.911082i \(-0.635248\pi\)
−0.412226 + 0.911082i \(0.635248\pi\)
\(38\) −2.69837 −0.437733
\(39\) 8.11184 1.29893
\(40\) 18.1972 2.87723
\(41\) −1.52853 −0.238716 −0.119358 0.992851i \(-0.538084\pi\)
−0.119358 + 0.992851i \(0.538084\pi\)
\(42\) −3.98679 −0.615176
\(43\) −4.10155 −0.625480 −0.312740 0.949839i \(-0.601247\pi\)
−0.312740 + 0.949839i \(0.601247\pi\)
\(44\) −12.3960 −1.86877
\(45\) −1.11947 −0.166880
\(46\) −13.0761 −1.92796
\(47\) 0.0151453 0.00220916 0.00110458 0.999999i \(-0.499648\pi\)
0.00110458 + 0.999999i \(0.499648\pi\)
\(48\) 25.0939 3.62200
\(49\) −6.38416 −0.912022
\(50\) 2.09329 0.296036
\(51\) −4.67708 −0.654923
\(52\) 22.7542 3.15544
\(53\) 2.70200 0.371148 0.185574 0.982630i \(-0.440586\pi\)
0.185574 + 0.982630i \(0.440586\pi\)
\(54\) 12.4738 1.69747
\(55\) 4.82420 0.650496
\(56\) −6.94809 −0.928477
\(57\) 1.88273 0.249374
\(58\) −5.87454 −0.771365
\(59\) −10.7088 −1.39417 −0.697084 0.716990i \(-0.745519\pi\)
−0.697084 + 0.716990i \(0.745519\pi\)
\(60\) −20.4359 −2.63826
\(61\) 5.59481 0.716342 0.358171 0.933656i \(-0.383401\pi\)
0.358171 + 0.933656i \(0.383401\pi\)
\(62\) −1.42209 −0.180606
\(63\) 0.427436 0.0538519
\(64\) 22.6084 2.82605
\(65\) −8.85534 −1.09837
\(66\) 11.9245 1.46781
\(67\) 5.88688 0.719197 0.359599 0.933107i \(-0.382914\pi\)
0.359599 + 0.933107i \(0.382914\pi\)
\(68\) −13.1195 −1.59097
\(69\) 9.12357 1.09835
\(70\) 4.35221 0.520189
\(71\) 13.0097 1.54397 0.771985 0.635641i \(-0.219264\pi\)
0.771985 + 0.635641i \(0.219264\pi\)
\(72\) −4.82244 −0.568330
\(73\) 1.58068 0.185004 0.0925021 0.995712i \(-0.470514\pi\)
0.0925021 + 0.995712i \(0.470514\pi\)
\(74\) 13.5321 1.57308
\(75\) −1.46055 −0.168650
\(76\) 5.28118 0.605793
\(77\) −1.84199 −0.209914
\(78\) −21.8887 −2.47841
\(79\) 15.7171 1.76831 0.884157 0.467190i \(-0.154733\pi\)
0.884157 + 0.467190i \(0.154733\pi\)
\(80\) −27.3939 −3.06274
\(81\) −10.3374 −1.14859
\(82\) 4.12453 0.455478
\(83\) −13.9489 −1.53109 −0.765544 0.643384i \(-0.777530\pi\)
−0.765544 + 0.643384i \(0.777530\pi\)
\(84\) 7.80286 0.851362
\(85\) 5.10577 0.553798
\(86\) 11.0675 1.19344
\(87\) 4.09884 0.439442
\(88\) 20.7817 2.21534
\(89\) −11.7529 −1.24580 −0.622900 0.782301i \(-0.714046\pi\)
−0.622900 + 0.782301i \(0.714046\pi\)
\(90\) 3.02073 0.318413
\(91\) 3.38116 0.354442
\(92\) 25.5922 2.66817
\(93\) 0.992236 0.102890
\(94\) −0.0408675 −0.00421516
\(95\) −2.05530 −0.210869
\(96\) −34.3739 −3.50827
\(97\) −1.28700 −0.130675 −0.0653373 0.997863i \(-0.520812\pi\)
−0.0653373 + 0.997863i \(0.520812\pi\)
\(98\) 17.2268 1.74017
\(99\) −1.27846 −0.128490
\(100\) −4.09694 −0.409694
\(101\) 9.87358 0.982458 0.491229 0.871030i \(-0.336548\pi\)
0.491229 + 0.871030i \(0.336548\pi\)
\(102\) 12.6205 1.24961
\(103\) 0.332662 0.0327781 0.0163891 0.999866i \(-0.494783\pi\)
0.0163891 + 0.999866i \(0.494783\pi\)
\(104\) −38.1471 −3.74063
\(105\) −3.03667 −0.296348
\(106\) −7.29098 −0.708162
\(107\) −0.822910 −0.0795537 −0.0397769 0.999209i \(-0.512665\pi\)
−0.0397769 + 0.999209i \(0.512665\pi\)
\(108\) −24.4134 −2.34918
\(109\) −8.65733 −0.829222 −0.414611 0.909999i \(-0.636082\pi\)
−0.414611 + 0.909999i \(0.636082\pi\)
\(110\) −13.0175 −1.24117
\(111\) −9.44178 −0.896174
\(112\) 10.4596 0.988340
\(113\) −7.47827 −0.703496 −0.351748 0.936095i \(-0.614413\pi\)
−0.351748 + 0.936095i \(0.614413\pi\)
\(114\) −5.08030 −0.475813
\(115\) −9.95980 −0.928757
\(116\) 11.4975 1.06752
\(117\) 2.34676 0.216958
\(118\) 28.8963 2.66012
\(119\) −1.94949 −0.178710
\(120\) 34.2604 3.12753
\(121\) −5.49062 −0.499147
\(122\) −15.0968 −1.36680
\(123\) −2.87781 −0.259483
\(124\) 2.78328 0.249946
\(125\) 11.8709 1.06177
\(126\) −1.15338 −0.102751
\(127\) −9.92691 −0.880871 −0.440435 0.897784i \(-0.645176\pi\)
−0.440435 + 0.897784i \(0.645176\pi\)
\(128\) −24.4907 −2.16469
\(129\) −7.72211 −0.679894
\(130\) 23.8950 2.09573
\(131\) −19.8075 −1.73059 −0.865294 0.501265i \(-0.832868\pi\)
−0.865294 + 0.501265i \(0.832868\pi\)
\(132\) −23.3384 −2.03134
\(133\) 0.784756 0.0680470
\(134\) −15.8850 −1.37225
\(135\) 9.50105 0.817720
\(136\) 21.9947 1.88603
\(137\) −0.314536 −0.0268726 −0.0134363 0.999910i \(-0.504277\pi\)
−0.0134363 + 0.999910i \(0.504277\pi\)
\(138\) −24.6187 −2.09569
\(139\) 1.40641 0.119290 0.0596451 0.998220i \(-0.481003\pi\)
0.0596451 + 0.998220i \(0.481003\pi\)
\(140\) −8.51804 −0.719906
\(141\) 0.0285145 0.00240135
\(142\) −35.1050 −2.94594
\(143\) −10.1131 −0.845697
\(144\) 7.25967 0.604973
\(145\) −4.47453 −0.371589
\(146\) −4.26524 −0.352994
\(147\) −12.0196 −0.991364
\(148\) −26.4848 −2.17704
\(149\) −16.7981 −1.37615 −0.688075 0.725639i \(-0.741544\pi\)
−0.688075 + 0.725639i \(0.741544\pi\)
\(150\) 3.94110 0.321790
\(151\) −9.37824 −0.763190 −0.381595 0.924330i \(-0.624625\pi\)
−0.381595 + 0.924330i \(0.624625\pi\)
\(152\) −8.85381 −0.718139
\(153\) −1.35308 −0.109390
\(154\) 4.97035 0.400522
\(155\) −1.08318 −0.0870032
\(156\) 42.8401 3.42995
\(157\) −0.457209 −0.0364892 −0.0182446 0.999834i \(-0.505808\pi\)
−0.0182446 + 0.999834i \(0.505808\pi\)
\(158\) −42.4105 −3.37400
\(159\) 5.08713 0.403436
\(160\) 37.5245 2.96657
\(161\) 3.80287 0.299708
\(162\) 27.8940 2.19156
\(163\) 0.370943 0.0290545 0.0145273 0.999894i \(-0.495376\pi\)
0.0145273 + 0.999894i \(0.495376\pi\)
\(164\) −8.07243 −0.630351
\(165\) 9.08268 0.707085
\(166\) 37.6392 2.92136
\(167\) 5.26793 0.407645 0.203822 0.979008i \(-0.434663\pi\)
0.203822 + 0.979008i \(0.434663\pi\)
\(168\) −13.0814 −1.00925
\(169\) 5.56361 0.427970
\(170\) −13.7772 −1.05667
\(171\) 0.544674 0.0416523
\(172\) −21.6610 −1.65164
\(173\) −16.9153 −1.28605 −0.643023 0.765847i \(-0.722320\pi\)
−0.643023 + 0.765847i \(0.722320\pi\)
\(174\) −11.0602 −0.838470
\(175\) −0.608784 −0.0460198
\(176\) −31.2847 −2.35817
\(177\) −20.1618 −1.51545
\(178\) 31.7135 2.37703
\(179\) 10.2855 0.768773 0.384386 0.923172i \(-0.374413\pi\)
0.384386 + 0.923172i \(0.374413\pi\)
\(180\) −5.91210 −0.440662
\(181\) 9.96371 0.740597 0.370298 0.928913i \(-0.379255\pi\)
0.370298 + 0.928913i \(0.379255\pi\)
\(182\) −9.12361 −0.676287
\(183\) 10.5335 0.778660
\(184\) −42.9049 −3.16299
\(185\) 10.3072 0.757799
\(186\) −2.67741 −0.196318
\(187\) 5.83094 0.426401
\(188\) 0.0799848 0.00583349
\(189\) −3.62771 −0.263877
\(190\) 5.54594 0.402345
\(191\) −15.1598 −1.09692 −0.548462 0.836175i \(-0.684787\pi\)
−0.548462 + 0.836175i \(0.684787\pi\)
\(192\) 42.5655 3.07190
\(193\) −1.98183 −0.142655 −0.0713277 0.997453i \(-0.522724\pi\)
−0.0713277 + 0.997453i \(0.522724\pi\)
\(194\) 3.47278 0.249331
\(195\) −16.6722 −1.19392
\(196\) −33.7159 −2.40828
\(197\) −6.30309 −0.449077 −0.224538 0.974465i \(-0.572087\pi\)
−0.224538 + 0.974465i \(0.572087\pi\)
\(198\) 3.44976 0.245164
\(199\) −6.01077 −0.426092 −0.213046 0.977042i \(-0.568338\pi\)
−0.213046 + 0.977042i \(0.568338\pi\)
\(200\) 6.86846 0.485673
\(201\) 11.0834 0.781764
\(202\) −26.6425 −1.87456
\(203\) 1.70847 0.119911
\(204\) −24.7005 −1.72938
\(205\) 3.14158 0.219417
\(206\) −0.897642 −0.0625417
\(207\) 2.63945 0.183454
\(208\) 57.4264 3.98180
\(209\) −2.34721 −0.162360
\(210\) 8.19404 0.565442
\(211\) 1.00000 0.0688428
\(212\) 14.2697 0.980049
\(213\) 24.4938 1.67829
\(214\) 2.22051 0.151791
\(215\) 8.42989 0.574914
\(216\) 40.9287 2.78484
\(217\) 0.413582 0.0280758
\(218\) 23.3606 1.58218
\(219\) 2.97599 0.201099
\(220\) 25.4775 1.71769
\(221\) −10.7033 −0.719983
\(222\) 25.4774 1.70993
\(223\) −24.4009 −1.63400 −0.817002 0.576635i \(-0.804366\pi\)
−0.817002 + 0.576635i \(0.804366\pi\)
\(224\) −14.3277 −0.957307
\(225\) −0.422538 −0.0281692
\(226\) 20.1791 1.34229
\(227\) 14.3866 0.954873 0.477437 0.878666i \(-0.341566\pi\)
0.477437 + 0.878666i \(0.341566\pi\)
\(228\) 9.94303 0.658493
\(229\) 6.16069 0.407110 0.203555 0.979064i \(-0.434750\pi\)
0.203555 + 0.979064i \(0.434750\pi\)
\(230\) 26.8752 1.77210
\(231\) −3.46796 −0.228175
\(232\) −19.2754 −1.26549
\(233\) 7.71844 0.505652 0.252826 0.967512i \(-0.418640\pi\)
0.252826 + 0.967512i \(0.418640\pi\)
\(234\) −6.33240 −0.413962
\(235\) −0.0311280 −0.00203057
\(236\) −56.5551 −3.68142
\(237\) 29.5911 1.92215
\(238\) 5.26045 0.340984
\(239\) −5.35067 −0.346106 −0.173053 0.984913i \(-0.555363\pi\)
−0.173053 + 0.984913i \(0.555363\pi\)
\(240\) −51.5754 −3.32918
\(241\) −12.2947 −0.791974 −0.395987 0.918256i \(-0.629597\pi\)
−0.395987 + 0.918256i \(0.629597\pi\)
\(242\) 14.8157 0.952388
\(243\) −5.59430 −0.358874
\(244\) 29.5472 1.89156
\(245\) 13.1213 0.838291
\(246\) 7.76537 0.495102
\(247\) 4.30855 0.274146
\(248\) −4.66613 −0.296300
\(249\) −26.2620 −1.66428
\(250\) −32.0320 −2.02588
\(251\) −4.80456 −0.303261 −0.151631 0.988437i \(-0.548452\pi\)
−0.151631 + 0.988437i \(0.548452\pi\)
\(252\) 2.25737 0.142201
\(253\) −11.3744 −0.715102
\(254\) 26.7864 1.68073
\(255\) 9.61279 0.601976
\(256\) 20.8682 1.30426
\(257\) 5.29185 0.330096 0.165048 0.986285i \(-0.447222\pi\)
0.165048 + 0.986285i \(0.447222\pi\)
\(258\) 20.8371 1.29726
\(259\) −3.93551 −0.244541
\(260\) −46.7666 −2.90034
\(261\) 1.18580 0.0733989
\(262\) 53.4478 3.30202
\(263\) 2.89234 0.178350 0.0891748 0.996016i \(-0.471577\pi\)
0.0891748 + 0.996016i \(0.471577\pi\)
\(264\) 39.1264 2.40806
\(265\) −5.55340 −0.341143
\(266\) −2.11756 −0.129836
\(267\) −22.1275 −1.35418
\(268\) 31.0897 1.89910
\(269\) 29.8616 1.82069 0.910347 0.413846i \(-0.135815\pi\)
0.910347 + 0.413846i \(0.135815\pi\)
\(270\) −25.6373 −1.56024
\(271\) 0.174135 0.0105779 0.00528896 0.999986i \(-0.498316\pi\)
0.00528896 + 0.999986i \(0.498316\pi\)
\(272\) −33.1106 −2.00763
\(273\) 6.36582 0.385277
\(274\) 0.848732 0.0512738
\(275\) 1.82088 0.109803
\(276\) 48.1832 2.90029
\(277\) −7.65965 −0.460224 −0.230112 0.973164i \(-0.573909\pi\)
−0.230112 + 0.973164i \(0.573909\pi\)
\(278\) −3.79501 −0.227610
\(279\) 0.287054 0.0171855
\(280\) 14.2804 0.853415
\(281\) −24.9921 −1.49090 −0.745451 0.666561i \(-0.767766\pi\)
−0.745451 + 0.666561i \(0.767766\pi\)
\(282\) −0.0769424 −0.00458185
\(283\) 4.40963 0.262125 0.131063 0.991374i \(-0.458161\pi\)
0.131063 + 0.991374i \(0.458161\pi\)
\(284\) 68.7066 4.07699
\(285\) −3.86957 −0.229213
\(286\) 27.2887 1.61362
\(287\) −1.19952 −0.0708055
\(288\) −9.94437 −0.585977
\(289\) −10.8287 −0.636985
\(290\) 12.0739 0.709005
\(291\) −2.42307 −0.142043
\(292\) 8.34783 0.488520
\(293\) −8.08961 −0.472600 −0.236300 0.971680i \(-0.575935\pi\)
−0.236300 + 0.971680i \(0.575935\pi\)
\(294\) 32.4334 1.89155
\(295\) 22.0097 1.28146
\(296\) 44.4014 2.58078
\(297\) 10.8505 0.629609
\(298\) 45.3273 2.62574
\(299\) 20.8789 1.20746
\(300\) −7.71343 −0.445335
\(301\) −3.21872 −0.185524
\(302\) 25.3059 1.45619
\(303\) 18.5893 1.06793
\(304\) 13.3285 0.764440
\(305\) −11.4990 −0.658430
\(306\) 3.65111 0.208720
\(307\) −26.7688 −1.52777 −0.763887 0.645350i \(-0.776711\pi\)
−0.763887 + 0.645350i \(0.776711\pi\)
\(308\) −9.72786 −0.554296
\(309\) 0.626312 0.0356296
\(310\) 2.92282 0.166005
\(311\) 5.98927 0.339620 0.169810 0.985477i \(-0.445685\pi\)
0.169810 + 0.985477i \(0.445685\pi\)
\(312\) −71.8207 −4.06605
\(313\) 1.56947 0.0887115 0.0443557 0.999016i \(-0.485876\pi\)
0.0443557 + 0.999016i \(0.485876\pi\)
\(314\) 1.23372 0.0696227
\(315\) −0.878508 −0.0494983
\(316\) 83.0049 4.66939
\(317\) 1.75982 0.0988416 0.0494208 0.998778i \(-0.484262\pi\)
0.0494208 + 0.998778i \(0.484262\pi\)
\(318\) −13.7269 −0.769769
\(319\) −5.11004 −0.286108
\(320\) −46.4669 −2.59758
\(321\) −1.54932 −0.0864745
\(322\) −10.2615 −0.571853
\(323\) −2.48420 −0.138225
\(324\) −54.5934 −3.03297
\(325\) −3.34241 −0.185404
\(326\) −1.00094 −0.0554369
\(327\) −16.2994 −0.901360
\(328\) 13.5333 0.747252
\(329\) 0.0118853 0.000655260 0
\(330\) −24.5084 −1.34914
\(331\) −32.2037 −1.77008 −0.885038 0.465519i \(-0.845868\pi\)
−0.885038 + 0.465519i \(0.845868\pi\)
\(332\) −73.6664 −4.04297
\(333\) −2.73151 −0.149686
\(334\) −14.2148 −0.777800
\(335\) −12.0993 −0.661054
\(336\) 19.6926 1.07432
\(337\) 31.9035 1.73790 0.868948 0.494903i \(-0.164796\pi\)
0.868948 + 0.494903i \(0.164796\pi\)
\(338\) −15.0126 −0.816580
\(339\) −14.0796 −0.764697
\(340\) 26.9645 1.46235
\(341\) −1.23702 −0.0669886
\(342\) −1.46973 −0.0794739
\(343\) −10.5033 −0.567125
\(344\) 36.3143 1.95794
\(345\) −18.7516 −1.00955
\(346\) 45.6436 2.45382
\(347\) 20.2132 1.08510 0.542550 0.840024i \(-0.317459\pi\)
0.542550 + 0.840024i \(0.317459\pi\)
\(348\) 21.6467 1.16039
\(349\) −5.99779 −0.321054 −0.160527 0.987031i \(-0.551319\pi\)
−0.160527 + 0.987031i \(0.551319\pi\)
\(350\) 1.64272 0.0878072
\(351\) −19.9172 −1.06310
\(352\) 42.8541 2.28413
\(353\) −10.1564 −0.540570 −0.270285 0.962780i \(-0.587118\pi\)
−0.270285 + 0.962780i \(0.587118\pi\)
\(354\) 54.4039 2.89153
\(355\) −26.7388 −1.41915
\(356\) −62.0689 −3.28965
\(357\) −3.67037 −0.194257
\(358\) −27.7540 −1.46684
\(359\) 12.5552 0.662640 0.331320 0.943518i \(-0.392506\pi\)
0.331320 + 0.943518i \(0.392506\pi\)
\(360\) 9.91154 0.522384
\(361\) 1.00000 0.0526316
\(362\) −26.8857 −1.41308
\(363\) −10.3373 −0.542570
\(364\) 17.8565 0.935936
\(365\) −3.24876 −0.170048
\(366\) −28.4233 −1.48571
\(367\) −7.53113 −0.393122 −0.196561 0.980492i \(-0.562977\pi\)
−0.196561 + 0.980492i \(0.562977\pi\)
\(368\) 64.5888 3.36692
\(369\) −0.832549 −0.0433408
\(370\) −27.8126 −1.44591
\(371\) 2.12041 0.110086
\(372\) 5.24017 0.271690
\(373\) −27.5410 −1.42602 −0.713008 0.701156i \(-0.752668\pi\)
−0.713008 + 0.701156i \(0.752668\pi\)
\(374\) −15.7340 −0.813586
\(375\) 22.3497 1.15413
\(376\) −0.134093 −0.00691534
\(377\) 9.38003 0.483096
\(378\) 9.78888 0.503486
\(379\) 7.58220 0.389472 0.194736 0.980856i \(-0.437615\pi\)
0.194736 + 0.980856i \(0.437615\pi\)
\(380\) −10.8544 −0.556818
\(381\) −18.6897 −0.957502
\(382\) 40.9067 2.09297
\(383\) −22.0172 −1.12503 −0.562514 0.826787i \(-0.690166\pi\)
−0.562514 + 0.826787i \(0.690166\pi\)
\(384\) −46.1094 −2.35301
\(385\) 3.78583 0.192944
\(386\) 5.34771 0.272191
\(387\) −2.23401 −0.113561
\(388\) −6.79685 −0.345058
\(389\) 14.9288 0.756921 0.378460 0.925617i \(-0.376454\pi\)
0.378460 + 0.925617i \(0.376454\pi\)
\(390\) 44.9878 2.27804
\(391\) −12.0383 −0.608801
\(392\) 56.5241 2.85490
\(393\) −37.2921 −1.88114
\(394\) 17.0080 0.856853
\(395\) −32.3033 −1.62536
\(396\) −6.75179 −0.339290
\(397\) 33.4358 1.67810 0.839048 0.544058i \(-0.183113\pi\)
0.839048 + 0.544058i \(0.183113\pi\)
\(398\) 16.2192 0.812997
\(399\) 1.47748 0.0739668
\(400\) −10.3397 −0.516986
\(401\) −16.8221 −0.840056 −0.420028 0.907511i \(-0.637980\pi\)
−0.420028 + 0.907511i \(0.637980\pi\)
\(402\) −29.9071 −1.49163
\(403\) 2.27069 0.113111
\(404\) 52.1441 2.59427
\(405\) 21.2463 1.05574
\(406\) −4.61008 −0.228795
\(407\) 11.7711 0.583472
\(408\) 41.4100 2.05010
\(409\) −1.73474 −0.0857775 −0.0428888 0.999080i \(-0.513656\pi\)
−0.0428888 + 0.999080i \(0.513656\pi\)
\(410\) −8.47712 −0.418655
\(411\) −0.592186 −0.0292104
\(412\) 1.75684 0.0865535
\(413\) −8.40380 −0.413524
\(414\) −7.12220 −0.350037
\(415\) 28.6690 1.40731
\(416\) −78.6632 −3.85678
\(417\) 2.64789 0.129668
\(418\) 6.33362 0.309788
\(419\) −6.96118 −0.340076 −0.170038 0.985438i \(-0.554389\pi\)
−0.170038 + 0.985438i \(0.554389\pi\)
\(420\) −16.0372 −0.782534
\(421\) −22.9133 −1.11673 −0.558363 0.829597i \(-0.688570\pi\)
−0.558363 + 0.829597i \(0.688570\pi\)
\(422\) −2.69837 −0.131354
\(423\) 0.00824923 0.000401091 0
\(424\) −23.9230 −1.16180
\(425\) 1.92715 0.0934805
\(426\) −66.0932 −3.20223
\(427\) 4.39056 0.212474
\(428\) −4.34593 −0.210069
\(429\) −19.0402 −0.919268
\(430\) −22.7469 −1.09695
\(431\) −1.26689 −0.0610240 −0.0305120 0.999534i \(-0.509714\pi\)
−0.0305120 + 0.999534i \(0.509714\pi\)
\(432\) −61.6138 −2.96439
\(433\) −21.7603 −1.04573 −0.522866 0.852415i \(-0.675137\pi\)
−0.522866 + 0.852415i \(0.675137\pi\)
\(434\) −1.11600 −0.0535695
\(435\) −8.42433 −0.403916
\(436\) −45.7209 −2.18963
\(437\) 4.84592 0.231812
\(438\) −8.03030 −0.383703
\(439\) −4.38773 −0.209415 −0.104707 0.994503i \(-0.533391\pi\)
−0.104707 + 0.994503i \(0.533391\pi\)
\(440\) −42.7126 −2.03624
\(441\) −3.47728 −0.165585
\(442\) 28.8814 1.37375
\(443\) 31.2985 1.48704 0.743518 0.668716i \(-0.233156\pi\)
0.743518 + 0.668716i \(0.233156\pi\)
\(444\) −49.8637 −2.36643
\(445\) 24.1556 1.14508
\(446\) 65.8425 3.11773
\(447\) −31.6262 −1.49587
\(448\) 17.7421 0.838234
\(449\) −24.8735 −1.17385 −0.586925 0.809641i \(-0.699662\pi\)
−0.586925 + 0.809641i \(0.699662\pi\)
\(450\) 1.14016 0.0537477
\(451\) 3.58777 0.168942
\(452\) −39.4940 −1.85764
\(453\) −17.6567 −0.829584
\(454\) −38.8204 −1.82193
\(455\) −6.94929 −0.325788
\(456\) −16.6693 −0.780614
\(457\) −27.0787 −1.26669 −0.633345 0.773870i \(-0.718319\pi\)
−0.633345 + 0.773870i \(0.718319\pi\)
\(458\) −16.6238 −0.776778
\(459\) 11.4838 0.536016
\(460\) −52.5995 −2.45246
\(461\) −30.9269 −1.44041 −0.720205 0.693761i \(-0.755952\pi\)
−0.720205 + 0.693761i \(0.755952\pi\)
\(462\) 9.35783 0.435366
\(463\) −0.188386 −0.00875505 −0.00437753 0.999990i \(-0.501393\pi\)
−0.00437753 + 0.999990i \(0.501393\pi\)
\(464\) 29.0171 1.34708
\(465\) −2.03934 −0.0945720
\(466\) −20.8272 −0.964800
\(467\) 19.6298 0.908358 0.454179 0.890910i \(-0.349933\pi\)
0.454179 + 0.890910i \(0.349933\pi\)
\(468\) 12.3936 0.572896
\(469\) 4.61977 0.213321
\(470\) 0.0839947 0.00387439
\(471\) −0.860801 −0.0396636
\(472\) 94.8137 4.36416
\(473\) 9.62719 0.442658
\(474\) −79.8476 −3.66752
\(475\) −0.775762 −0.0355944
\(476\) −10.2956 −0.471899
\(477\) 1.47171 0.0673849
\(478\) 14.4381 0.660382
\(479\) 0.338785 0.0154795 0.00773973 0.999970i \(-0.497536\pi\)
0.00773973 + 0.999970i \(0.497536\pi\)
\(480\) 70.6485 3.22465
\(481\) −21.6071 −0.985200
\(482\) 33.1757 1.51111
\(483\) 7.15978 0.325781
\(484\) −28.9969 −1.31804
\(485\) 2.64516 0.120110
\(486\) 15.0955 0.684744
\(487\) −15.5325 −0.703846 −0.351923 0.936029i \(-0.614472\pi\)
−0.351923 + 0.936029i \(0.614472\pi\)
\(488\) −49.5354 −2.24236
\(489\) 0.698386 0.0315821
\(490\) −35.4061 −1.59949
\(491\) −3.32182 −0.149912 −0.0749558 0.997187i \(-0.523882\pi\)
−0.0749558 + 0.997187i \(0.523882\pi\)
\(492\) −15.1982 −0.685188
\(493\) −5.40829 −0.243577
\(494\) −11.6260 −0.523080
\(495\) 2.62762 0.118103
\(496\) 7.02437 0.315403
\(497\) 10.2095 0.457957
\(498\) 70.8644 3.17551
\(499\) −21.0866 −0.943965 −0.471982 0.881608i \(-0.656461\pi\)
−0.471982 + 0.881608i \(0.656461\pi\)
\(500\) 62.6923 2.80368
\(501\) 9.91810 0.443108
\(502\) 12.9645 0.578633
\(503\) 8.59351 0.383165 0.191583 0.981476i \(-0.438638\pi\)
0.191583 + 0.981476i \(0.438638\pi\)
\(504\) −3.78444 −0.168572
\(505\) −20.2931 −0.903032
\(506\) 30.6923 1.36444
\(507\) 10.4748 0.465201
\(508\) −52.4258 −2.32602
\(509\) −22.5424 −0.999175 −0.499588 0.866263i \(-0.666515\pi\)
−0.499588 + 0.866263i \(0.666515\pi\)
\(510\) −25.9388 −1.14859
\(511\) 1.24045 0.0548741
\(512\) −7.32850 −0.323877
\(513\) −4.62272 −0.204098
\(514\) −14.2793 −0.629835
\(515\) −0.683718 −0.0301282
\(516\) −40.7818 −1.79532
\(517\) −0.0355491 −0.00156345
\(518\) 10.6194 0.466591
\(519\) −31.8469 −1.39792
\(520\) 78.4036 3.43822
\(521\) 21.6596 0.948923 0.474462 0.880276i \(-0.342643\pi\)
0.474462 + 0.880276i \(0.342643\pi\)
\(522\) −3.19971 −0.140047
\(523\) 10.0467 0.439312 0.219656 0.975577i \(-0.429507\pi\)
0.219656 + 0.975577i \(0.429507\pi\)
\(524\) −104.607 −4.56977
\(525\) −1.14618 −0.0500233
\(526\) −7.80460 −0.340297
\(527\) −1.30922 −0.0570307
\(528\) −58.9007 −2.56332
\(529\) 0.482982 0.0209992
\(530\) 14.9851 0.650912
\(531\) −5.83281 −0.253122
\(532\) 4.14444 0.179684
\(533\) −6.58574 −0.285260
\(534\) 59.7080 2.58382
\(535\) 1.69132 0.0731223
\(536\) −52.1214 −2.25130
\(537\) 19.3648 0.835652
\(538\) −80.5775 −3.47394
\(539\) 14.9849 0.645447
\(540\) 50.1767 2.15926
\(541\) −20.2534 −0.870761 −0.435381 0.900246i \(-0.643386\pi\)
−0.435381 + 0.900246i \(0.643386\pi\)
\(542\) −0.469879 −0.0201830
\(543\) 18.7590 0.805025
\(544\) 45.3552 1.94459
\(545\) 17.7934 0.762184
\(546\) −17.1773 −0.735121
\(547\) −33.0050 −1.41119 −0.705596 0.708614i \(-0.749321\pi\)
−0.705596 + 0.708614i \(0.749321\pi\)
\(548\) −1.66112 −0.0709594
\(549\) 3.04735 0.130058
\(550\) −4.91339 −0.209508
\(551\) 2.17707 0.0927465
\(552\) −80.7784 −3.43816
\(553\) 12.3341 0.524500
\(554\) 20.6685 0.878121
\(555\) 19.4057 0.823724
\(556\) 7.42751 0.314996
\(557\) 35.5025 1.50429 0.752145 0.658997i \(-0.229019\pi\)
0.752145 + 0.658997i \(0.229019\pi\)
\(558\) −0.774576 −0.0327904
\(559\) −17.6717 −0.747434
\(560\) −21.4976 −0.908438
\(561\) 10.9781 0.463495
\(562\) 67.4377 2.84469
\(563\) −14.9566 −0.630345 −0.315172 0.949034i \(-0.602062\pi\)
−0.315172 + 0.949034i \(0.602062\pi\)
\(564\) 0.150590 0.00634098
\(565\) 15.3700 0.646623
\(566\) −11.8988 −0.500144
\(567\) −8.11230 −0.340685
\(568\) −115.186 −4.83308
\(569\) −20.6636 −0.866265 −0.433133 0.901330i \(-0.642592\pi\)
−0.433133 + 0.901330i \(0.642592\pi\)
\(570\) 10.4415 0.437347
\(571\) −12.3457 −0.516651 −0.258325 0.966058i \(-0.583171\pi\)
−0.258325 + 0.966058i \(0.583171\pi\)
\(572\) −53.4089 −2.23314
\(573\) −28.5418 −1.19235
\(574\) 3.23675 0.135099
\(575\) −3.75929 −0.156773
\(576\) 12.3142 0.513091
\(577\) 40.6935 1.69409 0.847047 0.531518i \(-0.178378\pi\)
0.847047 + 0.531518i \(0.178378\pi\)
\(578\) 29.2199 1.21539
\(579\) −3.73126 −0.155066
\(580\) −23.6308 −0.981215
\(581\) −10.9465 −0.454136
\(582\) 6.53832 0.271022
\(583\) −6.34215 −0.262665
\(584\) −13.9950 −0.579118
\(585\) −4.82327 −0.199418
\(586\) 21.8287 0.901736
\(587\) 2.28351 0.0942505 0.0471253 0.998889i \(-0.484994\pi\)
0.0471253 + 0.998889i \(0.484994\pi\)
\(588\) −63.4779 −2.61778
\(589\) 0.527020 0.0217155
\(590\) −59.3903 −2.44506
\(591\) −11.8670 −0.488144
\(592\) −66.8415 −2.74717
\(593\) −47.7074 −1.95911 −0.979554 0.201183i \(-0.935521\pi\)
−0.979554 + 0.201183i \(0.935521\pi\)
\(594\) −29.2786 −1.20131
\(595\) 4.00679 0.164262
\(596\) −88.7135 −3.63385
\(597\) −11.3167 −0.463160
\(598\) −56.3389 −2.30387
\(599\) −16.4601 −0.672542 −0.336271 0.941765i \(-0.609166\pi\)
−0.336271 + 0.941765i \(0.609166\pi\)
\(600\) 12.9315 0.527924
\(601\) 1.97498 0.0805611 0.0402806 0.999188i \(-0.487175\pi\)
0.0402806 + 0.999188i \(0.487175\pi\)
\(602\) 8.68527 0.353985
\(603\) 3.20643 0.130576
\(604\) −49.5281 −2.01527
\(605\) 11.2848 0.458794
\(606\) −50.1607 −2.03764
\(607\) 12.9583 0.525959 0.262980 0.964801i \(-0.415295\pi\)
0.262980 + 0.964801i \(0.415295\pi\)
\(608\) −18.2575 −0.740438
\(609\) 3.21659 0.130343
\(610\) 31.0285 1.25631
\(611\) 0.0652541 0.00263990
\(612\) −7.14586 −0.288854
\(613\) −44.0322 −1.77844 −0.889222 0.457475i \(-0.848754\pi\)
−0.889222 + 0.457475i \(0.848754\pi\)
\(614\) 72.2319 2.91504
\(615\) 5.91474 0.238505
\(616\) 16.3086 0.657092
\(617\) 45.2637 1.82225 0.911124 0.412132i \(-0.135216\pi\)
0.911124 + 0.412132i \(0.135216\pi\)
\(618\) −1.69002 −0.0679825
\(619\) 4.60886 0.185246 0.0926228 0.995701i \(-0.470475\pi\)
0.0926228 + 0.995701i \(0.470475\pi\)
\(620\) −5.72047 −0.229740
\(621\) −22.4013 −0.898935
\(622\) −16.1612 −0.648006
\(623\) −9.22313 −0.369517
\(624\) 108.118 4.32820
\(625\) −20.5194 −0.820775
\(626\) −4.23499 −0.169264
\(627\) −4.41916 −0.176484
\(628\) −2.41460 −0.0963531
\(629\) 12.4581 0.496738
\(630\) 2.37054 0.0944444
\(631\) −21.0880 −0.839502 −0.419751 0.907639i \(-0.637883\pi\)
−0.419751 + 0.907639i \(0.637883\pi\)
\(632\) −139.156 −5.53535
\(633\) 1.88273 0.0748318
\(634\) −4.74865 −0.188593
\(635\) 20.4027 0.809658
\(636\) 26.8660 1.06531
\(637\) −27.5065 −1.08985
\(638\) 13.7888 0.545903
\(639\) 7.08605 0.280320
\(640\) 50.3356 1.98969
\(641\) 0.752111 0.0297066 0.0148533 0.999890i \(-0.495272\pi\)
0.0148533 + 0.999890i \(0.495272\pi\)
\(642\) 4.18063 0.164996
\(643\) −3.12613 −0.123283 −0.0616413 0.998098i \(-0.519633\pi\)
−0.0616413 + 0.998098i \(0.519633\pi\)
\(644\) 20.0836 0.791406
\(645\) 15.8712 0.624928
\(646\) 6.70329 0.263737
\(647\) 30.5402 1.20066 0.600329 0.799753i \(-0.295036\pi\)
0.600329 + 0.799753i \(0.295036\pi\)
\(648\) 91.5250 3.59544
\(649\) 25.1358 0.986666
\(650\) 9.01905 0.353756
\(651\) 0.778663 0.0305182
\(652\) 1.95902 0.0767210
\(653\) 3.93799 0.154105 0.0770527 0.997027i \(-0.475449\pi\)
0.0770527 + 0.997027i \(0.475449\pi\)
\(654\) 43.9818 1.71982
\(655\) 40.7102 1.59068
\(656\) −20.3729 −0.795430
\(657\) 0.860954 0.0335890
\(658\) −0.0320710 −0.00125026
\(659\) −8.54748 −0.332963 −0.166481 0.986045i \(-0.553241\pi\)
−0.166481 + 0.986045i \(0.553241\pi\)
\(660\) 47.9672 1.86712
\(661\) −4.42306 −0.172037 −0.0860185 0.996294i \(-0.527414\pi\)
−0.0860185 + 0.996294i \(0.527414\pi\)
\(662\) 86.8974 3.37736
\(663\) −20.1515 −0.782618
\(664\) 123.501 4.79276
\(665\) −1.61291 −0.0625458
\(666\) 7.37061 0.285605
\(667\) 10.5499 0.408495
\(668\) 27.8209 1.07642
\(669\) −45.9403 −1.77615
\(670\) 32.6483 1.26131
\(671\) −13.1322 −0.506962
\(672\) −26.9751 −1.04059
\(673\) −49.9502 −1.92544 −0.962720 0.270499i \(-0.912811\pi\)
−0.962720 + 0.270499i \(0.912811\pi\)
\(674\) −86.0874 −3.31596
\(675\) 3.58613 0.138030
\(676\) 29.3824 1.13009
\(677\) −19.4525 −0.747619 −0.373810 0.927505i \(-0.621949\pi\)
−0.373810 + 0.927505i \(0.621949\pi\)
\(678\) 37.9918 1.45907
\(679\) −1.00998 −0.0387594
\(680\) −45.2055 −1.73355
\(681\) 27.0861 1.03794
\(682\) 3.33794 0.127816
\(683\) 41.2759 1.57938 0.789689 0.613507i \(-0.210242\pi\)
0.789689 + 0.613507i \(0.210242\pi\)
\(684\) 2.87652 0.109986
\(685\) 0.646463 0.0247001
\(686\) 28.3418 1.08209
\(687\) 11.5989 0.442526
\(688\) −54.6674 −2.08417
\(689\) 11.6417 0.443513
\(690\) 50.5987 1.92626
\(691\) 28.2809 1.07586 0.537929 0.842990i \(-0.319207\pi\)
0.537929 + 0.842990i \(0.319207\pi\)
\(692\) −89.3326 −3.39592
\(693\) −1.00328 −0.0381115
\(694\) −54.5425 −2.07041
\(695\) −2.89059 −0.109646
\(696\) −36.2904 −1.37558
\(697\) 3.79717 0.143828
\(698\) 16.1842 0.612582
\(699\) 14.5317 0.549641
\(700\) −3.21510 −0.121519
\(701\) −29.7240 −1.12266 −0.561331 0.827592i \(-0.689710\pi\)
−0.561331 + 0.827592i \(0.689710\pi\)
\(702\) 53.7439 2.02843
\(703\) −5.01494 −0.189142
\(704\) −53.0665 −2.00002
\(705\) −0.0586056 −0.00220721
\(706\) 27.4056 1.03142
\(707\) 7.74835 0.291407
\(708\) −106.478 −4.00169
\(709\) 43.1070 1.61892 0.809458 0.587178i \(-0.199761\pi\)
0.809458 + 0.587178i \(0.199761\pi\)
\(710\) 72.1511 2.70778
\(711\) 8.56071 0.321052
\(712\) 104.058 3.89972
\(713\) 2.55390 0.0956442
\(714\) 9.90400 0.370648
\(715\) 20.7853 0.777327
\(716\) 54.3194 2.03001
\(717\) −10.0739 −0.376215
\(718\) −33.8786 −1.26434
\(719\) −3.88139 −0.144751 −0.0723757 0.997377i \(-0.523058\pi\)
−0.0723757 + 0.997377i \(0.523058\pi\)
\(720\) −14.9208 −0.556064
\(721\) 0.261058 0.00972232
\(722\) −2.69837 −0.100423
\(723\) −23.1477 −0.860872
\(724\) 52.6201 1.95561
\(725\) −1.68889 −0.0627239
\(726\) 27.8939 1.03524
\(727\) 25.2017 0.934678 0.467339 0.884078i \(-0.345213\pi\)
0.467339 + 0.884078i \(0.345213\pi\)
\(728\) −29.9362 −1.10951
\(729\) 20.4795 0.758500
\(730\) 8.76634 0.324457
\(731\) 10.1891 0.376857
\(732\) 55.6294 2.05612
\(733\) 19.7762 0.730450 0.365225 0.930919i \(-0.380992\pi\)
0.365225 + 0.930919i \(0.380992\pi\)
\(734\) 20.3217 0.750089
\(735\) 24.7039 0.911218
\(736\) −88.4743 −3.26121
\(737\) −13.8177 −0.508983
\(738\) 2.24652 0.0826956
\(739\) 7.24558 0.266533 0.133267 0.991080i \(-0.457453\pi\)
0.133267 + 0.991080i \(0.457453\pi\)
\(740\) 54.4341 2.00104
\(741\) 8.11184 0.297996
\(742\) −5.72164 −0.210048
\(743\) −12.7573 −0.468019 −0.234009 0.972234i \(-0.575185\pi\)
−0.234009 + 0.972234i \(0.575185\pi\)
\(744\) −8.78507 −0.322076
\(745\) 34.5250 1.26490
\(746\) 74.3156 2.72089
\(747\) −7.59759 −0.277981
\(748\) 30.7942 1.12595
\(749\) −0.645784 −0.0235964
\(750\) −60.3077 −2.20212
\(751\) 13.8163 0.504164 0.252082 0.967706i \(-0.418885\pi\)
0.252082 + 0.967706i \(0.418885\pi\)
\(752\) 0.201863 0.00736120
\(753\) −9.04570 −0.329644
\(754\) −25.3108 −0.921763
\(755\) 19.2750 0.701491
\(756\) −19.1586 −0.696790
\(757\) −0.164360 −0.00597378 −0.00298689 0.999996i \(-0.500951\pi\)
−0.00298689 + 0.999996i \(0.500951\pi\)
\(758\) −20.4596 −0.743125
\(759\) −21.4149 −0.777312
\(760\) 18.1972 0.660082
\(761\) 17.6990 0.641588 0.320794 0.947149i \(-0.396050\pi\)
0.320794 + 0.947149i \(0.396050\pi\)
\(762\) 50.4316 1.82695
\(763\) −6.79390 −0.245956
\(764\) −80.0616 −2.89653
\(765\) 2.78098 0.100547
\(766\) 59.4106 2.14659
\(767\) −46.1394 −1.66600
\(768\) 39.2891 1.41772
\(769\) 6.47900 0.233639 0.116819 0.993153i \(-0.462730\pi\)
0.116819 + 0.993153i \(0.462730\pi\)
\(770\) −10.2155 −0.368143
\(771\) 9.96312 0.358813
\(772\) −10.4664 −0.376694
\(773\) −25.6099 −0.921123 −0.460562 0.887628i \(-0.652352\pi\)
−0.460562 + 0.887628i \(0.652352\pi\)
\(774\) 6.02817 0.216678
\(775\) −0.408842 −0.0146860
\(776\) 11.3948 0.409050
\(777\) −7.40950 −0.265814
\(778\) −40.2834 −1.44423
\(779\) −1.52853 −0.0547652
\(780\) −88.0490 −3.15266
\(781\) −30.5365 −1.09268
\(782\) 32.4836 1.16161
\(783\) −10.0640 −0.359658
\(784\) −85.0911 −3.03897
\(785\) 0.939699 0.0335393
\(786\) 100.628 3.58928
\(787\) 50.9896 1.81758 0.908791 0.417251i \(-0.137006\pi\)
0.908791 + 0.417251i \(0.137006\pi\)
\(788\) −33.2877 −1.18583
\(789\) 5.44550 0.193865
\(790\) 87.1662 3.10123
\(791\) −5.86862 −0.208664
\(792\) 11.3193 0.402213
\(793\) 24.1055 0.856012
\(794\) −90.2220 −3.20186
\(795\) −10.4556 −0.370820
\(796\) −31.7439 −1.12513
\(797\) 19.1130 0.677016 0.338508 0.940964i \(-0.390078\pi\)
0.338508 + 0.940964i \(0.390078\pi\)
\(798\) −3.98679 −0.141131
\(799\) −0.0376239 −0.00133104
\(800\) 14.1635 0.500754
\(801\) −6.40148 −0.226185
\(802\) 45.3922 1.60285
\(803\) −3.71018 −0.130929
\(804\) 58.5335 2.06432
\(805\) −7.81602 −0.275479
\(806\) −6.12715 −0.215820
\(807\) 56.2213 1.97909
\(808\) −87.4188 −3.07538
\(809\) 55.5916 1.95450 0.977248 0.212098i \(-0.0680297\pi\)
0.977248 + 0.212098i \(0.0680297\pi\)
\(810\) −57.3303 −2.01438
\(811\) −3.61666 −0.126998 −0.0634991 0.997982i \(-0.520226\pi\)
−0.0634991 + 0.997982i \(0.520226\pi\)
\(812\) 9.02275 0.316636
\(813\) 0.327849 0.0114982
\(814\) −31.7628 −1.11328
\(815\) −0.762397 −0.0267056
\(816\) −62.3384 −2.18228
\(817\) −4.10155 −0.143495
\(818\) 4.68097 0.163666
\(819\) 1.84163 0.0643518
\(820\) 16.5912 0.579390
\(821\) 14.3160 0.499630 0.249815 0.968294i \(-0.419630\pi\)
0.249815 + 0.968294i \(0.419630\pi\)
\(822\) 1.59793 0.0557343
\(823\) −30.5654 −1.06544 −0.532721 0.846291i \(-0.678830\pi\)
−0.532721 + 0.846291i \(0.678830\pi\)
\(824\) −2.94532 −0.102605
\(825\) 3.42822 0.119355
\(826\) 22.6765 0.789017
\(827\) −38.8642 −1.35144 −0.675720 0.737158i \(-0.736167\pi\)
−0.675720 + 0.737158i \(0.736167\pi\)
\(828\) 13.9394 0.484427
\(829\) −49.9048 −1.73326 −0.866632 0.498948i \(-0.833720\pi\)
−0.866632 + 0.498948i \(0.833720\pi\)
\(830\) −77.3596 −2.68519
\(831\) −14.4210 −0.500261
\(832\) 97.4093 3.37706
\(833\) 15.8595 0.549501
\(834\) −7.14498 −0.247411
\(835\) −10.8272 −0.374689
\(836\) −12.3960 −0.428725
\(837\) −2.43626 −0.0842095
\(838\) 18.7838 0.648876
\(839\) 9.56997 0.330392 0.165196 0.986261i \(-0.447174\pi\)
0.165196 + 0.986261i \(0.447174\pi\)
\(840\) 26.8861 0.927658
\(841\) −24.2604 −0.836564
\(842\) 61.8284 2.13075
\(843\) −47.0533 −1.62060
\(844\) 5.28118 0.181786
\(845\) −11.4349 −0.393371
\(846\) −0.0222594 −0.000765295 0
\(847\) −4.30880 −0.148052
\(848\) 36.0135 1.23671
\(849\) 8.30215 0.284929
\(850\) −5.20016 −0.178364
\(851\) −24.3020 −0.833063
\(852\) 129.356 4.43166
\(853\) 27.3445 0.936258 0.468129 0.883660i \(-0.344928\pi\)
0.468129 + 0.883660i \(0.344928\pi\)
\(854\) −11.8473 −0.405408
\(855\) −1.11947 −0.0382849
\(856\) 7.28589 0.249027
\(857\) 31.3943 1.07241 0.536205 0.844088i \(-0.319857\pi\)
0.536205 + 0.844088i \(0.319857\pi\)
\(858\) 51.3773 1.75399
\(859\) 18.3779 0.627047 0.313523 0.949581i \(-0.398491\pi\)
0.313523 + 0.949581i \(0.398491\pi\)
\(860\) 44.5197 1.51811
\(861\) −2.25838 −0.0769653
\(862\) 3.41854 0.116436
\(863\) 23.8521 0.811934 0.405967 0.913888i \(-0.366935\pi\)
0.405967 + 0.913888i \(0.366935\pi\)
\(864\) 84.3991 2.87132
\(865\) 34.7659 1.18208
\(866\) 58.7171 1.99529
\(867\) −20.3876 −0.692399
\(868\) 2.18420 0.0741366
\(869\) −36.8913 −1.25145
\(870\) 22.7319 0.770684
\(871\) 25.3639 0.859424
\(872\) 76.6504 2.59571
\(873\) −0.700993 −0.0237250
\(874\) −13.0761 −0.442305
\(875\) 9.31576 0.314930
\(876\) 15.7167 0.531019
\(877\) 46.3708 1.56583 0.782915 0.622129i \(-0.213732\pi\)
0.782915 + 0.622129i \(0.213732\pi\)
\(878\) 11.8397 0.399570
\(879\) −15.2306 −0.513714
\(880\) 64.2993 2.16753
\(881\) −18.8495 −0.635054 −0.317527 0.948249i \(-0.602852\pi\)
−0.317527 + 0.948249i \(0.602852\pi\)
\(882\) 9.38298 0.315942
\(883\) 50.3381 1.69401 0.847006 0.531583i \(-0.178403\pi\)
0.847006 + 0.531583i \(0.178403\pi\)
\(884\) −56.5261 −1.90118
\(885\) 41.4384 1.39294
\(886\) −84.4548 −2.83731
\(887\) 0.424913 0.0142672 0.00713360 0.999975i \(-0.497729\pi\)
0.00713360 + 0.999975i \(0.497729\pi\)
\(888\) 83.5958 2.80529
\(889\) −7.79021 −0.261275
\(890\) −65.1806 −2.18486
\(891\) 24.2639 0.812872
\(892\) −128.865 −4.31473
\(893\) 0.0151453 0.000506817 0
\(894\) 85.3391 2.85417
\(895\) −21.1397 −0.706622
\(896\) −19.2192 −0.642070
\(897\) 39.3094 1.31250
\(898\) 67.1177 2.23975
\(899\) 1.14736 0.0382666
\(900\) −2.23150 −0.0743832
\(901\) −6.71231 −0.223619
\(902\) −9.68112 −0.322346
\(903\) −6.05998 −0.201663
\(904\) 66.2112 2.20215
\(905\) −20.4784 −0.680724
\(906\) 47.6442 1.58287
\(907\) 46.9168 1.55785 0.778923 0.627120i \(-0.215766\pi\)
0.778923 + 0.627120i \(0.215766\pi\)
\(908\) 75.9783 2.52143
\(909\) 5.37788 0.178373
\(910\) 18.7517 0.621613
\(911\) 9.58750 0.317648 0.158824 0.987307i \(-0.449230\pi\)
0.158824 + 0.987307i \(0.449230\pi\)
\(912\) 25.0939 0.830943
\(913\) 32.7409 1.08357
\(914\) 73.0683 2.41689
\(915\) −21.6495 −0.715710
\(916\) 32.5357 1.07501
\(917\) −15.5440 −0.513310
\(918\) −30.9874 −1.02274
\(919\) −0.449869 −0.0148398 −0.00741990 0.999972i \(-0.502362\pi\)
−0.00741990 + 0.999972i \(0.502362\pi\)
\(920\) 88.1823 2.90728
\(921\) −50.3984 −1.66068
\(922\) 83.4521 2.74835
\(923\) 56.0530 1.84501
\(924\) −18.3149 −0.602517
\(925\) 3.89040 0.127916
\(926\) 0.508335 0.0167049
\(927\) 0.181192 0.00595113
\(928\) −39.7478 −1.30479
\(929\) 29.5656 0.970016 0.485008 0.874510i \(-0.338817\pi\)
0.485008 + 0.874510i \(0.338817\pi\)
\(930\) 5.50288 0.180446
\(931\) −6.38416 −0.209232
\(932\) 40.7624 1.33522
\(933\) 11.2762 0.369165
\(934\) −52.9684 −1.73318
\(935\) −11.9843 −0.391929
\(936\) −20.7777 −0.679142
\(937\) 24.6765 0.806147 0.403074 0.915168i \(-0.367942\pi\)
0.403074 + 0.915168i \(0.367942\pi\)
\(938\) −12.4658 −0.407024
\(939\) 2.95488 0.0964289
\(940\) −0.164392 −0.00536189
\(941\) −40.6728 −1.32589 −0.662947 0.748666i \(-0.730695\pi\)
−0.662947 + 0.748666i \(0.730695\pi\)
\(942\) 2.32276 0.0756795
\(943\) −7.40713 −0.241209
\(944\) −142.732 −4.64553
\(945\) 7.45601 0.242544
\(946\) −25.9777 −0.844607
\(947\) −10.1414 −0.329553 −0.164776 0.986331i \(-0.552690\pi\)
−0.164776 + 0.986331i \(0.552690\pi\)
\(948\) 156.276 5.07560
\(949\) 6.81043 0.221076
\(950\) 2.09329 0.0679153
\(951\) 3.31327 0.107440
\(952\) 17.2605 0.559415
\(953\) 35.0584 1.13565 0.567826 0.823148i \(-0.307784\pi\)
0.567826 + 0.823148i \(0.307784\pi\)
\(954\) −3.97121 −0.128573
\(955\) 31.1579 1.00824
\(956\) −28.2578 −0.913924
\(957\) −9.62084 −0.310997
\(958\) −0.914164 −0.0295353
\(959\) −0.246834 −0.00797068
\(960\) −87.4846 −2.82355
\(961\) −30.7223 −0.991040
\(962\) 58.3039 1.87979
\(963\) −0.448218 −0.0144436
\(964\) −64.9307 −2.09128
\(965\) 4.07325 0.131123
\(966\) −19.3197 −0.621601
\(967\) −19.9634 −0.641980 −0.320990 0.947083i \(-0.604016\pi\)
−0.320990 + 0.947083i \(0.604016\pi\)
\(968\) 48.6129 1.56248
\(969\) −4.67708 −0.150250
\(970\) −7.13760 −0.229174
\(971\) −25.1142 −0.805954 −0.402977 0.915210i \(-0.632024\pi\)
−0.402977 + 0.915210i \(0.632024\pi\)
\(972\) −29.5445 −0.947639
\(973\) 1.10369 0.0353827
\(974\) 41.9125 1.34296
\(975\) −6.29286 −0.201533
\(976\) 74.5703 2.38694
\(977\) 9.79900 0.313498 0.156749 0.987638i \(-0.449899\pi\)
0.156749 + 0.987638i \(0.449899\pi\)
\(978\) −1.88450 −0.0602597
\(979\) 27.5864 0.881665
\(980\) 69.2960 2.21358
\(981\) −4.71542 −0.150552
\(982\) 8.96349 0.286036
\(983\) −15.5172 −0.494921 −0.247460 0.968898i \(-0.579596\pi\)
−0.247460 + 0.968898i \(0.579596\pi\)
\(984\) 25.4796 0.812259
\(985\) 12.9547 0.412771
\(986\) 14.5935 0.464753
\(987\) 0.0223769 0.000712265 0
\(988\) 22.7542 0.723908
\(989\) −19.8758 −0.632013
\(990\) −7.09028 −0.225344
\(991\) 35.7120 1.13443 0.567215 0.823570i \(-0.308021\pi\)
0.567215 + 0.823570i \(0.308021\pi\)
\(992\) −9.62204 −0.305500
\(993\) −60.6309 −1.92406
\(994\) −27.5489 −0.873797
\(995\) 12.3539 0.391645
\(996\) −138.694 −4.39469
\(997\) 29.2230 0.925500 0.462750 0.886489i \(-0.346863\pi\)
0.462750 + 0.886489i \(0.346863\pi\)
\(998\) 56.8993 1.80112
\(999\) 23.1827 0.733467
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 \(a_p\))