Properties

Label 8002.2.a.d.1.6
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-3.03319 q^{3}\) \(+1.00000 q^{4}\) \(-3.55972 q^{5}\) \(-3.03319 q^{6}\) \(-4.22109 q^{7}\) \(+1.00000 q^{8}\) \(+6.20023 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-3.03319 q^{3}\) \(+1.00000 q^{4}\) \(-3.55972 q^{5}\) \(-3.03319 q^{6}\) \(-4.22109 q^{7}\) \(+1.00000 q^{8}\) \(+6.20023 q^{9}\) \(-3.55972 q^{10}\) \(+0.539753 q^{11}\) \(-3.03319 q^{12}\) \(-2.53431 q^{13}\) \(-4.22109 q^{14}\) \(+10.7973 q^{15}\) \(+1.00000 q^{16}\) \(-7.56621 q^{17}\) \(+6.20023 q^{18}\) \(+8.08491 q^{19}\) \(-3.55972 q^{20}\) \(+12.8033 q^{21}\) \(+0.539753 q^{22}\) \(-8.07968 q^{23}\) \(-3.03319 q^{24}\) \(+7.67163 q^{25}\) \(-2.53431 q^{26}\) \(-9.70689 q^{27}\) \(-4.22109 q^{28}\) \(+5.32885 q^{29}\) \(+10.7973 q^{30}\) \(-8.35573 q^{31}\) \(+1.00000 q^{32}\) \(-1.63717 q^{33}\) \(-7.56621 q^{34}\) \(+15.0259 q^{35}\) \(+6.20023 q^{36}\) \(+2.83287 q^{37}\) \(+8.08491 q^{38}\) \(+7.68703 q^{39}\) \(-3.55972 q^{40}\) \(+0.736282 q^{41}\) \(+12.8033 q^{42}\) \(+5.40877 q^{43}\) \(+0.539753 q^{44}\) \(-22.0711 q^{45}\) \(-8.07968 q^{46}\) \(+10.8385 q^{47}\) \(-3.03319 q^{48}\) \(+10.8176 q^{49}\) \(+7.67163 q^{50}\) \(+22.9497 q^{51}\) \(-2.53431 q^{52}\) \(+4.18131 q^{53}\) \(-9.70689 q^{54}\) \(-1.92137 q^{55}\) \(-4.22109 q^{56}\) \(-24.5231 q^{57}\) \(+5.32885 q^{58}\) \(-2.94928 q^{59}\) \(+10.7973 q^{60}\) \(+11.7171 q^{61}\) \(-8.35573 q^{62}\) \(-26.1717 q^{63}\) \(+1.00000 q^{64}\) \(+9.02143 q^{65}\) \(-1.63717 q^{66}\) \(-0.652017 q^{67}\) \(-7.56621 q^{68}\) \(+24.5072 q^{69}\) \(+15.0259 q^{70}\) \(+6.46973 q^{71}\) \(+6.20023 q^{72}\) \(-13.6526 q^{73}\) \(+2.83287 q^{74}\) \(-23.2695 q^{75}\) \(+8.08491 q^{76}\) \(-2.27835 q^{77}\) \(+7.68703 q^{78}\) \(+9.44342 q^{79}\) \(-3.55972 q^{80}\) \(+10.8421 q^{81}\) \(+0.736282 q^{82}\) \(-3.28706 q^{83}\) \(+12.8033 q^{84}\) \(+26.9336 q^{85}\) \(+5.40877 q^{86}\) \(-16.1634 q^{87}\) \(+0.539753 q^{88}\) \(-9.91472 q^{89}\) \(-22.0711 q^{90}\) \(+10.6975 q^{91}\) \(-8.07968 q^{92}\) \(+25.3445 q^{93}\) \(+10.8385 q^{94}\) \(-28.7801 q^{95}\) \(-3.03319 q^{96}\) \(+12.6908 q^{97}\) \(+10.8176 q^{98}\) \(+3.34659 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −3.03319 −1.75121 −0.875606 0.483026i \(-0.839538\pi\)
−0.875606 + 0.483026i \(0.839538\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.55972 −1.59196 −0.795978 0.605325i \(-0.793043\pi\)
−0.795978 + 0.605325i \(0.793043\pi\)
\(6\) −3.03319 −1.23829
\(7\) −4.22109 −1.59542 −0.797710 0.603041i \(-0.793956\pi\)
−0.797710 + 0.603041i \(0.793956\pi\)
\(8\) 1.00000 0.353553
\(9\) 6.20023 2.06674
\(10\) −3.55972 −1.12568
\(11\) 0.539753 0.162742 0.0813709 0.996684i \(-0.474070\pi\)
0.0813709 + 0.996684i \(0.474070\pi\)
\(12\) −3.03319 −0.875606
\(13\) −2.53431 −0.702890 −0.351445 0.936209i \(-0.614310\pi\)
−0.351445 + 0.936209i \(0.614310\pi\)
\(14\) −4.22109 −1.12813
\(15\) 10.7973 2.78785
\(16\) 1.00000 0.250000
\(17\) −7.56621 −1.83508 −0.917538 0.397648i \(-0.869827\pi\)
−0.917538 + 0.397648i \(0.869827\pi\)
\(18\) 6.20023 1.46141
\(19\) 8.08491 1.85481 0.927403 0.374064i \(-0.122036\pi\)
0.927403 + 0.374064i \(0.122036\pi\)
\(20\) −3.55972 −0.795978
\(21\) 12.8033 2.79392
\(22\) 0.539753 0.115076
\(23\) −8.07968 −1.68473 −0.842365 0.538908i \(-0.818837\pi\)
−0.842365 + 0.538908i \(0.818837\pi\)
\(24\) −3.03319 −0.619147
\(25\) 7.67163 1.53433
\(26\) −2.53431 −0.497018
\(27\) −9.70689 −1.86809
\(28\) −4.22109 −0.797710
\(29\) 5.32885 0.989542 0.494771 0.869023i \(-0.335252\pi\)
0.494771 + 0.869023i \(0.335252\pi\)
\(30\) 10.7973 1.97131
\(31\) −8.35573 −1.50073 −0.750367 0.661022i \(-0.770123\pi\)
−0.750367 + 0.661022i \(0.770123\pi\)
\(32\) 1.00000 0.176777
\(33\) −1.63717 −0.284995
\(34\) −7.56621 −1.29759
\(35\) 15.0259 2.53984
\(36\) 6.20023 1.03337
\(37\) 2.83287 0.465721 0.232861 0.972510i \(-0.425191\pi\)
0.232861 + 0.972510i \(0.425191\pi\)
\(38\) 8.08491 1.31155
\(39\) 7.68703 1.23091
\(40\) −3.55972 −0.562842
\(41\) 0.736282 0.114988 0.0574940 0.998346i \(-0.481689\pi\)
0.0574940 + 0.998346i \(0.481689\pi\)
\(42\) 12.8033 1.97560
\(43\) 5.40877 0.824829 0.412414 0.910996i \(-0.364686\pi\)
0.412414 + 0.910996i \(0.364686\pi\)
\(44\) 0.539753 0.0813709
\(45\) −22.0711 −3.29016
\(46\) −8.07968 −1.19128
\(47\) 10.8385 1.58096 0.790482 0.612486i \(-0.209830\pi\)
0.790482 + 0.612486i \(0.209830\pi\)
\(48\) −3.03319 −0.437803
\(49\) 10.8176 1.54537
\(50\) 7.67163 1.08493
\(51\) 22.9497 3.21361
\(52\) −2.53431 −0.351445
\(53\) 4.18131 0.574348 0.287174 0.957878i \(-0.407284\pi\)
0.287174 + 0.957878i \(0.407284\pi\)
\(54\) −9.70689 −1.32094
\(55\) −1.92137 −0.259078
\(56\) −4.22109 −0.564066
\(57\) −24.5231 −3.24816
\(58\) 5.32885 0.699712
\(59\) −2.94928 −0.383964 −0.191982 0.981398i \(-0.561491\pi\)
−0.191982 + 0.981398i \(0.561491\pi\)
\(60\) 10.7973 1.39393
\(61\) 11.7171 1.50023 0.750113 0.661310i \(-0.229999\pi\)
0.750113 + 0.661310i \(0.229999\pi\)
\(62\) −8.35573 −1.06118
\(63\) −26.1717 −3.29732
\(64\) 1.00000 0.125000
\(65\) 9.02143 1.11897
\(66\) −1.63717 −0.201522
\(67\) −0.652017 −0.0796566 −0.0398283 0.999207i \(-0.512681\pi\)
−0.0398283 + 0.999207i \(0.512681\pi\)
\(68\) −7.56621 −0.917538
\(69\) 24.5072 2.95032
\(70\) 15.0259 1.79594
\(71\) 6.46973 0.767816 0.383908 0.923371i \(-0.374578\pi\)
0.383908 + 0.923371i \(0.374578\pi\)
\(72\) 6.20023 0.730704
\(73\) −13.6526 −1.59791 −0.798957 0.601388i \(-0.794614\pi\)
−0.798957 + 0.601388i \(0.794614\pi\)
\(74\) 2.83287 0.329315
\(75\) −23.2695 −2.68693
\(76\) 8.08491 0.927403
\(77\) −2.27835 −0.259642
\(78\) 7.68703 0.870384
\(79\) 9.44342 1.06247 0.531234 0.847225i \(-0.321728\pi\)
0.531234 + 0.847225i \(0.321728\pi\)
\(80\) −3.55972 −0.397989
\(81\) 10.8421 1.20468
\(82\) 0.736282 0.0813088
\(83\) −3.28706 −0.360802 −0.180401 0.983593i \(-0.557740\pi\)
−0.180401 + 0.983593i \(0.557740\pi\)
\(84\) 12.8033 1.39696
\(85\) 26.9336 2.92136
\(86\) 5.40877 0.583242
\(87\) −16.1634 −1.73290
\(88\) 0.539753 0.0575379
\(89\) −9.91472 −1.05096 −0.525479 0.850806i \(-0.676114\pi\)
−0.525479 + 0.850806i \(0.676114\pi\)
\(90\) −22.0711 −2.32650
\(91\) 10.6975 1.12141
\(92\) −8.07968 −0.842365
\(93\) 25.3445 2.62810
\(94\) 10.8385 1.11791
\(95\) −28.7801 −2.95277
\(96\) −3.03319 −0.309573
\(97\) 12.6908 1.28856 0.644279 0.764791i \(-0.277158\pi\)
0.644279 + 0.764791i \(0.277158\pi\)
\(98\) 10.8176 1.09274
\(99\) 3.34659 0.336345
\(100\) 7.67163 0.767163
\(101\) −11.7334 −1.16752 −0.583759 0.811927i \(-0.698419\pi\)
−0.583759 + 0.811927i \(0.698419\pi\)
\(102\) 22.9497 2.27236
\(103\) 15.2050 1.49819 0.749095 0.662462i \(-0.230488\pi\)
0.749095 + 0.662462i \(0.230488\pi\)
\(104\) −2.53431 −0.248509
\(105\) −45.5764 −4.44780
\(106\) 4.18131 0.406125
\(107\) −3.30305 −0.319318 −0.159659 0.987172i \(-0.551040\pi\)
−0.159659 + 0.987172i \(0.551040\pi\)
\(108\) −9.70689 −0.934046
\(109\) 1.08226 0.103662 0.0518308 0.998656i \(-0.483494\pi\)
0.0518308 + 0.998656i \(0.483494\pi\)
\(110\) −1.92137 −0.183196
\(111\) −8.59263 −0.815577
\(112\) −4.22109 −0.398855
\(113\) 11.4581 1.07789 0.538946 0.842340i \(-0.318823\pi\)
0.538946 + 0.842340i \(0.318823\pi\)
\(114\) −24.5231 −2.29679
\(115\) 28.7614 2.68202
\(116\) 5.32885 0.494771
\(117\) −15.7133 −1.45269
\(118\) −2.94928 −0.271503
\(119\) 31.9376 2.92772
\(120\) 10.7973 0.985655
\(121\) −10.7087 −0.973515
\(122\) 11.7171 1.06082
\(123\) −2.23328 −0.201368
\(124\) −8.35573 −0.750367
\(125\) −9.51028 −0.850625
\(126\) −26.1717 −2.33156
\(127\) 12.3867 1.09914 0.549571 0.835447i \(-0.314791\pi\)
0.549571 + 0.835447i \(0.314791\pi\)
\(128\) 1.00000 0.0883883
\(129\) −16.4058 −1.44445
\(130\) 9.02143 0.791232
\(131\) 11.8748 1.03751 0.518754 0.854924i \(-0.326396\pi\)
0.518754 + 0.854924i \(0.326396\pi\)
\(132\) −1.63717 −0.142498
\(133\) −34.1271 −2.95920
\(134\) −0.652017 −0.0563257
\(135\) 34.5538 2.97392
\(136\) −7.56621 −0.648797
\(137\) −20.4929 −1.75082 −0.875411 0.483379i \(-0.839409\pi\)
−0.875411 + 0.483379i \(0.839409\pi\)
\(138\) 24.5072 2.08619
\(139\) −11.0098 −0.933835 −0.466918 0.884301i \(-0.654636\pi\)
−0.466918 + 0.884301i \(0.654636\pi\)
\(140\) 15.0259 1.26992
\(141\) −32.8753 −2.76860
\(142\) 6.46973 0.542928
\(143\) −1.36790 −0.114390
\(144\) 6.20023 0.516686
\(145\) −18.9692 −1.57531
\(146\) −13.6526 −1.12990
\(147\) −32.8117 −2.70627
\(148\) 2.83287 0.232861
\(149\) 11.0189 0.902703 0.451352 0.892346i \(-0.350942\pi\)
0.451352 + 0.892346i \(0.350942\pi\)
\(150\) −23.2695 −1.89995
\(151\) 11.2698 0.917124 0.458562 0.888662i \(-0.348365\pi\)
0.458562 + 0.888662i \(0.348365\pi\)
\(152\) 8.08491 0.655773
\(153\) −46.9122 −3.79263
\(154\) −2.27835 −0.183594
\(155\) 29.7441 2.38910
\(156\) 7.68703 0.615455
\(157\) 8.35931 0.667145 0.333573 0.942724i \(-0.391746\pi\)
0.333573 + 0.942724i \(0.391746\pi\)
\(158\) 9.44342 0.751279
\(159\) −12.6827 −1.00580
\(160\) −3.55972 −0.281421
\(161\) 34.1050 2.68785
\(162\) 10.8421 0.851839
\(163\) 8.38009 0.656379 0.328190 0.944612i \(-0.393561\pi\)
0.328190 + 0.944612i \(0.393561\pi\)
\(164\) 0.736282 0.0574940
\(165\) 5.82788 0.453700
\(166\) −3.28706 −0.255126
\(167\) −16.8416 −1.30324 −0.651621 0.758545i \(-0.725911\pi\)
−0.651621 + 0.758545i \(0.725911\pi\)
\(168\) 12.8033 0.987800
\(169\) −6.57729 −0.505945
\(170\) 26.9336 2.06571
\(171\) 50.1283 3.83341
\(172\) 5.40877 0.412414
\(173\) 17.3463 1.31882 0.659408 0.751785i \(-0.270807\pi\)
0.659408 + 0.751785i \(0.270807\pi\)
\(174\) −16.1634 −1.22534
\(175\) −32.3826 −2.44790
\(176\) 0.539753 0.0406854
\(177\) 8.94572 0.672402
\(178\) −9.91472 −0.743140
\(179\) −3.22549 −0.241085 −0.120542 0.992708i \(-0.538463\pi\)
−0.120542 + 0.992708i \(0.538463\pi\)
\(180\) −22.0711 −1.64508
\(181\) −22.3274 −1.65958 −0.829791 0.558075i \(-0.811540\pi\)
−0.829791 + 0.558075i \(0.811540\pi\)
\(182\) 10.6975 0.792953
\(183\) −35.5403 −2.62721
\(184\) −8.07968 −0.595642
\(185\) −10.0842 −0.741408
\(186\) 25.3445 1.85835
\(187\) −4.08389 −0.298643
\(188\) 10.8385 0.790482
\(189\) 40.9736 2.98039
\(190\) −28.7801 −2.08792
\(191\) 2.14688 0.155343 0.0776713 0.996979i \(-0.475252\pi\)
0.0776713 + 0.996979i \(0.475252\pi\)
\(192\) −3.03319 −0.218901
\(193\) 3.12109 0.224661 0.112331 0.993671i \(-0.464168\pi\)
0.112331 + 0.993671i \(0.464168\pi\)
\(194\) 12.6908 0.911148
\(195\) −27.3637 −1.95955
\(196\) 10.8176 0.772684
\(197\) −13.9592 −0.994553 −0.497276 0.867592i \(-0.665666\pi\)
−0.497276 + 0.867592i \(0.665666\pi\)
\(198\) 3.34659 0.237832
\(199\) 19.4235 1.37689 0.688447 0.725287i \(-0.258293\pi\)
0.688447 + 0.725287i \(0.258293\pi\)
\(200\) 7.67163 0.542466
\(201\) 1.97769 0.139495
\(202\) −11.7334 −0.825560
\(203\) −22.4935 −1.57874
\(204\) 22.9497 1.60680
\(205\) −2.62096 −0.183056
\(206\) 15.2050 1.05938
\(207\) −50.0959 −3.48190
\(208\) −2.53431 −0.175723
\(209\) 4.36386 0.301854
\(210\) −45.5764 −3.14507
\(211\) −5.94554 −0.409308 −0.204654 0.978834i \(-0.565607\pi\)
−0.204654 + 0.978834i \(0.565607\pi\)
\(212\) 4.18131 0.287174
\(213\) −19.6239 −1.34461
\(214\) −3.30305 −0.225792
\(215\) −19.2537 −1.31309
\(216\) −9.70689 −0.660470
\(217\) 35.2703 2.39430
\(218\) 1.08226 0.0732998
\(219\) 41.4108 2.79829
\(220\) −1.92137 −0.129539
\(221\) 19.1751 1.28986
\(222\) −8.59263 −0.576700
\(223\) 12.4346 0.832683 0.416342 0.909208i \(-0.363312\pi\)
0.416342 + 0.909208i \(0.363312\pi\)
\(224\) −4.22109 −0.282033
\(225\) 47.5659 3.17106
\(226\) 11.4581 0.762185
\(227\) −20.3942 −1.35361 −0.676804 0.736164i \(-0.736635\pi\)
−0.676804 + 0.736164i \(0.736635\pi\)
\(228\) −24.5231 −1.62408
\(229\) −9.66862 −0.638921 −0.319460 0.947600i \(-0.603502\pi\)
−0.319460 + 0.947600i \(0.603502\pi\)
\(230\) 28.7614 1.89647
\(231\) 6.91065 0.454687
\(232\) 5.32885 0.349856
\(233\) 17.6336 1.15521 0.577607 0.816315i \(-0.303987\pi\)
0.577607 + 0.816315i \(0.303987\pi\)
\(234\) −15.7133 −1.02721
\(235\) −38.5822 −2.51683
\(236\) −2.94928 −0.191982
\(237\) −28.6437 −1.86061
\(238\) 31.9376 2.07021
\(239\) 3.61447 0.233801 0.116900 0.993144i \(-0.462704\pi\)
0.116900 + 0.993144i \(0.462704\pi\)
\(240\) 10.7973 0.696963
\(241\) −5.38886 −0.347127 −0.173564 0.984823i \(-0.555528\pi\)
−0.173564 + 0.984823i \(0.555528\pi\)
\(242\) −10.7087 −0.688379
\(243\) −3.76556 −0.241561
\(244\) 11.7171 0.750113
\(245\) −38.5076 −2.46016
\(246\) −2.23328 −0.142389
\(247\) −20.4896 −1.30372
\(248\) −8.35573 −0.530589
\(249\) 9.97028 0.631841
\(250\) −9.51028 −0.601483
\(251\) −25.1584 −1.58798 −0.793992 0.607929i \(-0.792001\pi\)
−0.793992 + 0.607929i \(0.792001\pi\)
\(252\) −26.1717 −1.64866
\(253\) −4.36103 −0.274176
\(254\) 12.3867 0.777211
\(255\) −81.6947 −5.11592
\(256\) 1.00000 0.0625000
\(257\) 15.5405 0.969389 0.484695 0.874683i \(-0.338931\pi\)
0.484695 + 0.874683i \(0.338931\pi\)
\(258\) −16.4058 −1.02138
\(259\) −11.9578 −0.743022
\(260\) 9.02143 0.559485
\(261\) 33.0401 2.04513
\(262\) 11.8748 0.733629
\(263\) −3.64861 −0.224983 −0.112492 0.993653i \(-0.535883\pi\)
−0.112492 + 0.993653i \(0.535883\pi\)
\(264\) −1.63717 −0.100761
\(265\) −14.8843 −0.914337
\(266\) −34.1271 −2.09247
\(267\) 30.0732 1.84045
\(268\) −0.652017 −0.0398283
\(269\) −26.9893 −1.64556 −0.822782 0.568357i \(-0.807579\pi\)
−0.822782 + 0.568357i \(0.807579\pi\)
\(270\) 34.5538 2.10288
\(271\) −14.8651 −0.902991 −0.451496 0.892273i \(-0.649109\pi\)
−0.451496 + 0.892273i \(0.649109\pi\)
\(272\) −7.56621 −0.458769
\(273\) −32.4476 −1.96382
\(274\) −20.4929 −1.23802
\(275\) 4.14079 0.249699
\(276\) 24.5072 1.47516
\(277\) −15.7356 −0.945458 −0.472729 0.881208i \(-0.656731\pi\)
−0.472729 + 0.881208i \(0.656731\pi\)
\(278\) −11.0098 −0.660321
\(279\) −51.8074 −3.10163
\(280\) 15.0259 0.897969
\(281\) −28.3852 −1.69332 −0.846660 0.532134i \(-0.821390\pi\)
−0.846660 + 0.532134i \(0.821390\pi\)
\(282\) −32.8753 −1.95770
\(283\) −31.9000 −1.89626 −0.948129 0.317886i \(-0.897027\pi\)
−0.948129 + 0.317886i \(0.897027\pi\)
\(284\) 6.46973 0.383908
\(285\) 87.2953 5.17093
\(286\) −1.36790 −0.0808856
\(287\) −3.10791 −0.183454
\(288\) 6.20023 0.365352
\(289\) 40.2476 2.36750
\(290\) −18.9692 −1.11391
\(291\) −38.4936 −2.25654
\(292\) −13.6526 −0.798957
\(293\) 30.1448 1.76108 0.880538 0.473976i \(-0.157182\pi\)
0.880538 + 0.473976i \(0.157182\pi\)
\(294\) −32.8117 −1.91362
\(295\) 10.4986 0.611254
\(296\) 2.83287 0.164657
\(297\) −5.23933 −0.304016
\(298\) 11.0189 0.638307
\(299\) 20.4764 1.18418
\(300\) −23.2695 −1.34347
\(301\) −22.8309 −1.31595
\(302\) 11.2698 0.648505
\(303\) 35.5896 2.04457
\(304\) 8.08491 0.463701
\(305\) −41.7098 −2.38829
\(306\) −46.9122 −2.68179
\(307\) 5.46963 0.312168 0.156084 0.987744i \(-0.450113\pi\)
0.156084 + 0.987744i \(0.450113\pi\)
\(308\) −2.27835 −0.129821
\(309\) −46.1195 −2.62365
\(310\) 29.7441 1.68935
\(311\) 22.6979 1.28708 0.643541 0.765411i \(-0.277464\pi\)
0.643541 + 0.765411i \(0.277464\pi\)
\(312\) 7.68703 0.435192
\(313\) −14.9946 −0.847542 −0.423771 0.905769i \(-0.639294\pi\)
−0.423771 + 0.905769i \(0.639294\pi\)
\(314\) 8.35931 0.471743
\(315\) 93.1640 5.24920
\(316\) 9.44342 0.531234
\(317\) −15.1517 −0.851004 −0.425502 0.904957i \(-0.639903\pi\)
−0.425502 + 0.904957i \(0.639903\pi\)
\(318\) −12.6827 −0.711211
\(319\) 2.87626 0.161040
\(320\) −3.55972 −0.198995
\(321\) 10.0188 0.559194
\(322\) 34.1050 1.90060
\(323\) −61.1722 −3.40371
\(324\) 10.8421 0.602341
\(325\) −19.4423 −1.07846
\(326\) 8.38009 0.464130
\(327\) −3.28269 −0.181533
\(328\) 0.736282 0.0406544
\(329\) −45.7504 −2.52230
\(330\) 5.82788 0.320814
\(331\) −21.1767 −1.16398 −0.581988 0.813198i \(-0.697725\pi\)
−0.581988 + 0.813198i \(0.697725\pi\)
\(332\) −3.28706 −0.180401
\(333\) 17.5645 0.962526
\(334\) −16.8416 −0.921531
\(335\) 2.32100 0.126810
\(336\) 12.8033 0.698480
\(337\) −19.0650 −1.03854 −0.519270 0.854610i \(-0.673796\pi\)
−0.519270 + 0.854610i \(0.673796\pi\)
\(338\) −6.57729 −0.357757
\(339\) −34.7547 −1.88762
\(340\) 26.9336 1.46068
\(341\) −4.51003 −0.244232
\(342\) 50.1283 2.71063
\(343\) −16.1143 −0.870090
\(344\) 5.40877 0.291621
\(345\) −87.2388 −4.69678
\(346\) 17.3463 0.932543
\(347\) 7.60292 0.408146 0.204073 0.978956i \(-0.434582\pi\)
0.204073 + 0.978956i \(0.434582\pi\)
\(348\) −16.1634 −0.866449
\(349\) 20.6054 1.10298 0.551490 0.834181i \(-0.314059\pi\)
0.551490 + 0.834181i \(0.314059\pi\)
\(350\) −32.3826 −1.73092
\(351\) 24.6002 1.31306
\(352\) 0.539753 0.0287689
\(353\) 2.77705 0.147807 0.0739037 0.997265i \(-0.476454\pi\)
0.0739037 + 0.997265i \(0.476454\pi\)
\(354\) 8.94572 0.475460
\(355\) −23.0305 −1.22233
\(356\) −9.91472 −0.525479
\(357\) −96.8728 −5.12705
\(358\) −3.22549 −0.170473
\(359\) −21.8966 −1.15566 −0.577828 0.816159i \(-0.696100\pi\)
−0.577828 + 0.816159i \(0.696100\pi\)
\(360\) −22.0711 −1.16325
\(361\) 46.3658 2.44030
\(362\) −22.3274 −1.17350
\(363\) 32.4814 1.70483
\(364\) 10.6975 0.560703
\(365\) 48.5994 2.54381
\(366\) −35.5403 −1.85772
\(367\) 21.9008 1.14321 0.571606 0.820529i \(-0.306321\pi\)
0.571606 + 0.820529i \(0.306321\pi\)
\(368\) −8.07968 −0.421182
\(369\) 4.56512 0.237650
\(370\) −10.0842 −0.524255
\(371\) −17.6497 −0.916326
\(372\) 25.3445 1.31405
\(373\) −12.2184 −0.632645 −0.316323 0.948652i \(-0.602448\pi\)
−0.316323 + 0.948652i \(0.602448\pi\)
\(374\) −4.08389 −0.211173
\(375\) 28.8465 1.48963
\(376\) 10.8385 0.558955
\(377\) −13.5049 −0.695540
\(378\) 40.9736 2.10746
\(379\) 0.908152 0.0466486 0.0233243 0.999728i \(-0.492575\pi\)
0.0233243 + 0.999728i \(0.492575\pi\)
\(380\) −28.7801 −1.47639
\(381\) −37.5712 −1.92483
\(382\) 2.14688 0.109844
\(383\) −24.3990 −1.24673 −0.623365 0.781931i \(-0.714235\pi\)
−0.623365 + 0.781931i \(0.714235\pi\)
\(384\) −3.03319 −0.154787
\(385\) 8.11028 0.413338
\(386\) 3.12109 0.158859
\(387\) 33.5356 1.70471
\(388\) 12.6908 0.644279
\(389\) 23.5296 1.19300 0.596498 0.802614i \(-0.296558\pi\)
0.596498 + 0.802614i \(0.296558\pi\)
\(390\) −27.3637 −1.38561
\(391\) 61.1326 3.09161
\(392\) 10.8176 0.546370
\(393\) −36.0186 −1.81690
\(394\) −13.9592 −0.703255
\(395\) −33.6160 −1.69140
\(396\) 3.34659 0.168173
\(397\) 8.10906 0.406982 0.203491 0.979077i \(-0.434771\pi\)
0.203491 + 0.979077i \(0.434771\pi\)
\(398\) 19.4235 0.973611
\(399\) 103.514 5.18218
\(400\) 7.67163 0.383582
\(401\) −21.3491 −1.06612 −0.533061 0.846077i \(-0.678958\pi\)
−0.533061 + 0.846077i \(0.678958\pi\)
\(402\) 1.97769 0.0986382
\(403\) 21.1760 1.05485
\(404\) −11.7334 −0.583759
\(405\) −38.5950 −1.91780
\(406\) −22.4935 −1.11634
\(407\) 1.52905 0.0757923
\(408\) 22.9497 1.13618
\(409\) 14.4921 0.716586 0.358293 0.933609i \(-0.383359\pi\)
0.358293 + 0.933609i \(0.383359\pi\)
\(410\) −2.62096 −0.129440
\(411\) 62.1587 3.06606
\(412\) 15.2050 0.749095
\(413\) 12.4492 0.612583
\(414\) −50.0959 −2.46208
\(415\) 11.7010 0.574382
\(416\) −2.53431 −0.124255
\(417\) 33.3946 1.63534
\(418\) 4.36386 0.213443
\(419\) 22.3852 1.09359 0.546795 0.837266i \(-0.315848\pi\)
0.546795 + 0.837266i \(0.315848\pi\)
\(420\) −45.5764 −2.22390
\(421\) 20.5334 1.00073 0.500367 0.865813i \(-0.333198\pi\)
0.500367 + 0.865813i \(0.333198\pi\)
\(422\) −5.94554 −0.289424
\(423\) 67.2014 3.26744
\(424\) 4.18131 0.203063
\(425\) −58.0452 −2.81561
\(426\) −19.6239 −0.950781
\(427\) −49.4590 −2.39349
\(428\) −3.30305 −0.159659
\(429\) 4.14910 0.200320
\(430\) −19.2537 −0.928496
\(431\) −20.7962 −1.00172 −0.500860 0.865528i \(-0.666983\pi\)
−0.500860 + 0.865528i \(0.666983\pi\)
\(432\) −9.70689 −0.467023
\(433\) −21.9824 −1.05641 −0.528203 0.849118i \(-0.677134\pi\)
−0.528203 + 0.849118i \(0.677134\pi\)
\(434\) 35.2703 1.69303
\(435\) 57.5372 2.75870
\(436\) 1.08226 0.0518308
\(437\) −65.3235 −3.12485
\(438\) 41.4108 1.97869
\(439\) 32.2123 1.53741 0.768706 0.639603i \(-0.220901\pi\)
0.768706 + 0.639603i \(0.220901\pi\)
\(440\) −1.92137 −0.0915979
\(441\) 67.0714 3.19388
\(442\) 19.1751 0.912067
\(443\) 32.4274 1.54067 0.770336 0.637639i \(-0.220089\pi\)
0.770336 + 0.637639i \(0.220089\pi\)
\(444\) −8.59263 −0.407788
\(445\) 35.2937 1.67308
\(446\) 12.4346 0.588796
\(447\) −33.4224 −1.58082
\(448\) −4.22109 −0.199428
\(449\) 32.9473 1.55488 0.777440 0.628957i \(-0.216518\pi\)
0.777440 + 0.628957i \(0.216518\pi\)
\(450\) 47.5659 2.24228
\(451\) 0.397411 0.0187133
\(452\) 11.4581 0.538946
\(453\) −34.1835 −1.60608
\(454\) −20.3942 −0.957145
\(455\) −38.0802 −1.78523
\(456\) −24.5231 −1.14840
\(457\) −32.8041 −1.53451 −0.767255 0.641343i \(-0.778378\pi\)
−0.767255 + 0.641343i \(0.778378\pi\)
\(458\) −9.66862 −0.451785
\(459\) 73.4444 3.42809
\(460\) 28.7614 1.34101
\(461\) −14.4291 −0.672029 −0.336014 0.941857i \(-0.609079\pi\)
−0.336014 + 0.941857i \(0.609079\pi\)
\(462\) 6.91065 0.321512
\(463\) 25.2189 1.17202 0.586011 0.810303i \(-0.300697\pi\)
0.586011 + 0.810303i \(0.300697\pi\)
\(464\) 5.32885 0.247386
\(465\) −90.2194 −4.18382
\(466\) 17.6336 0.816860
\(467\) 4.84703 0.224294 0.112147 0.993692i \(-0.464227\pi\)
0.112147 + 0.993692i \(0.464227\pi\)
\(468\) −15.7133 −0.726346
\(469\) 2.75222 0.127086
\(470\) −38.5822 −1.77966
\(471\) −25.3554 −1.16831
\(472\) −2.94928 −0.135752
\(473\) 2.91940 0.134234
\(474\) −28.6437 −1.31565
\(475\) 62.0245 2.84588
\(476\) 31.9376 1.46386
\(477\) 25.9251 1.18703
\(478\) 3.61447 0.165322
\(479\) −1.02461 −0.0468158 −0.0234079 0.999726i \(-0.507452\pi\)
−0.0234079 + 0.999726i \(0.507452\pi\)
\(480\) 10.7973 0.492828
\(481\) −7.17937 −0.327351
\(482\) −5.38886 −0.245456
\(483\) −103.447 −4.70700
\(484\) −10.7087 −0.486758
\(485\) −45.1758 −2.05133
\(486\) −3.76556 −0.170809
\(487\) −2.65034 −0.120098 −0.0600491 0.998195i \(-0.519126\pi\)
−0.0600491 + 0.998195i \(0.519126\pi\)
\(488\) 11.7171 0.530410
\(489\) −25.4184 −1.14946
\(490\) −38.5076 −1.73959
\(491\) −30.7111 −1.38597 −0.692987 0.720951i \(-0.743705\pi\)
−0.692987 + 0.720951i \(0.743705\pi\)
\(492\) −2.23328 −0.100684
\(493\) −40.3192 −1.81589
\(494\) −20.4896 −0.921873
\(495\) −11.9129 −0.535447
\(496\) −8.35573 −0.375183
\(497\) −27.3093 −1.22499
\(498\) 9.97028 0.446779
\(499\) 9.11311 0.407959 0.203979 0.978975i \(-0.434612\pi\)
0.203979 + 0.978975i \(0.434612\pi\)
\(500\) −9.51028 −0.425313
\(501\) 51.0837 2.28225
\(502\) −25.1584 −1.12287
\(503\) −6.56059 −0.292522 −0.146261 0.989246i \(-0.546724\pi\)
−0.146261 + 0.989246i \(0.546724\pi\)
\(504\) −26.1717 −1.16578
\(505\) 41.7677 1.85864
\(506\) −4.36103 −0.193872
\(507\) 19.9502 0.886018
\(508\) 12.3867 0.549571
\(509\) 7.46040 0.330676 0.165338 0.986237i \(-0.447128\pi\)
0.165338 + 0.986237i \(0.447128\pi\)
\(510\) −81.6947 −3.61750
\(511\) 57.6287 2.54934
\(512\) 1.00000 0.0441942
\(513\) −78.4793 −3.46495
\(514\) 15.5405 0.685462
\(515\) −54.1255 −2.38506
\(516\) −16.4058 −0.722225
\(517\) 5.85014 0.257289
\(518\) −11.9578 −0.525396
\(519\) −52.6146 −2.30953
\(520\) 9.02143 0.395616
\(521\) 3.74531 0.164085 0.0820425 0.996629i \(-0.473856\pi\)
0.0820425 + 0.996629i \(0.473856\pi\)
\(522\) 33.0401 1.44612
\(523\) −10.0070 −0.437574 −0.218787 0.975773i \(-0.570210\pi\)
−0.218787 + 0.975773i \(0.570210\pi\)
\(524\) 11.8748 0.518754
\(525\) 98.2226 4.28679
\(526\) −3.64861 −0.159087
\(527\) 63.2212 2.75396
\(528\) −1.63717 −0.0712488
\(529\) 42.2812 1.83831
\(530\) −14.8843 −0.646534
\(531\) −18.2862 −0.793554
\(532\) −34.1271 −1.47960
\(533\) −1.86596 −0.0808239
\(534\) 30.0732 1.30139
\(535\) 11.7580 0.508341
\(536\) −0.652017 −0.0281628
\(537\) 9.78353 0.422190
\(538\) −26.9893 −1.16359
\(539\) 5.83882 0.251496
\(540\) 34.5538 1.48696
\(541\) −7.73688 −0.332634 −0.166317 0.986072i \(-0.553188\pi\)
−0.166317 + 0.986072i \(0.553188\pi\)
\(542\) −14.8651 −0.638511
\(543\) 67.7231 2.90628
\(544\) −7.56621 −0.324399
\(545\) −3.85254 −0.165025
\(546\) −32.4476 −1.38863
\(547\) 9.64163 0.412246 0.206123 0.978526i \(-0.433915\pi\)
0.206123 + 0.978526i \(0.433915\pi\)
\(548\) −20.4929 −0.875411
\(549\) 72.6489 3.10058
\(550\) 4.14079 0.176564
\(551\) 43.0833 1.83541
\(552\) 24.5072 1.04310
\(553\) −39.8615 −1.69508
\(554\) −15.7356 −0.668540
\(555\) 30.5874 1.29836
\(556\) −11.0098 −0.466918
\(557\) −13.5265 −0.573135 −0.286568 0.958060i \(-0.592514\pi\)
−0.286568 + 0.958060i \(0.592514\pi\)
\(558\) −51.8074 −2.19318
\(559\) −13.7075 −0.579764
\(560\) 15.0259 0.634960
\(561\) 12.3872 0.522988
\(562\) −28.3852 −1.19736
\(563\) 43.2512 1.82282 0.911410 0.411500i \(-0.134995\pi\)
0.911410 + 0.411500i \(0.134995\pi\)
\(564\) −32.8753 −1.38430
\(565\) −40.7878 −1.71596
\(566\) −31.9000 −1.34086
\(567\) −45.7656 −1.92197
\(568\) 6.46973 0.271464
\(569\) 13.0064 0.545256 0.272628 0.962120i \(-0.412107\pi\)
0.272628 + 0.962120i \(0.412107\pi\)
\(570\) 87.2953 3.65640
\(571\) −13.2514 −0.554552 −0.277276 0.960790i \(-0.589432\pi\)
−0.277276 + 0.960790i \(0.589432\pi\)
\(572\) −1.36790 −0.0571948
\(573\) −6.51188 −0.272038
\(574\) −3.10791 −0.129722
\(575\) −61.9843 −2.58493
\(576\) 6.20023 0.258343
\(577\) −32.4321 −1.35016 −0.675082 0.737742i \(-0.735892\pi\)
−0.675082 + 0.737742i \(0.735892\pi\)
\(578\) 40.2476 1.67408
\(579\) −9.46686 −0.393429
\(580\) −18.9692 −0.787654
\(581\) 13.8750 0.575631
\(582\) −38.4936 −1.59561
\(583\) 2.25688 0.0934703
\(584\) −13.6526 −0.564948
\(585\) 55.9349 2.31262
\(586\) 30.1448 1.24527
\(587\) 4.68966 0.193563 0.0967814 0.995306i \(-0.469145\pi\)
0.0967814 + 0.995306i \(0.469145\pi\)
\(588\) −32.8117 −1.35313
\(589\) −67.5553 −2.78357
\(590\) 10.4986 0.432221
\(591\) 42.3409 1.74167
\(592\) 2.83287 0.116430
\(593\) 5.61726 0.230673 0.115337 0.993326i \(-0.463205\pi\)
0.115337 + 0.993326i \(0.463205\pi\)
\(594\) −5.23933 −0.214972
\(595\) −113.689 −4.66080
\(596\) 11.0189 0.451352
\(597\) −58.9151 −2.41123
\(598\) 20.4764 0.837342
\(599\) −7.25280 −0.296341 −0.148171 0.988962i \(-0.547339\pi\)
−0.148171 + 0.988962i \(0.547339\pi\)
\(600\) −23.2695 −0.949974
\(601\) −2.00906 −0.0819514 −0.0409757 0.999160i \(-0.513047\pi\)
−0.0409757 + 0.999160i \(0.513047\pi\)
\(602\) −22.8309 −0.930517
\(603\) −4.04265 −0.164630
\(604\) 11.2698 0.458562
\(605\) 38.1199 1.54979
\(606\) 35.5896 1.44573
\(607\) 35.9967 1.46106 0.730531 0.682879i \(-0.239272\pi\)
0.730531 + 0.682879i \(0.239272\pi\)
\(608\) 8.08491 0.327886
\(609\) 68.2271 2.76470
\(610\) −41.7098 −1.68878
\(611\) −27.4682 −1.11124
\(612\) −46.9122 −1.89631
\(613\) 7.19977 0.290796 0.145398 0.989373i \(-0.453554\pi\)
0.145398 + 0.989373i \(0.453554\pi\)
\(614\) 5.46963 0.220736
\(615\) 7.94987 0.320570
\(616\) −2.27835 −0.0917971
\(617\) 5.55936 0.223811 0.111906 0.993719i \(-0.464305\pi\)
0.111906 + 0.993719i \(0.464305\pi\)
\(618\) −46.1195 −1.85520
\(619\) 18.6869 0.751088 0.375544 0.926804i \(-0.377456\pi\)
0.375544 + 0.926804i \(0.377456\pi\)
\(620\) 29.7441 1.19455
\(621\) 78.4286 3.14723
\(622\) 22.6979 0.910105
\(623\) 41.8509 1.67672
\(624\) 7.68703 0.307727
\(625\) −4.50420 −0.180168
\(626\) −14.9946 −0.599303
\(627\) −13.2364 −0.528611
\(628\) 8.35931 0.333573
\(629\) −21.4341 −0.854634
\(630\) 93.1640 3.71174
\(631\) 42.8040 1.70400 0.852000 0.523541i \(-0.175389\pi\)
0.852000 + 0.523541i \(0.175389\pi\)
\(632\) 9.44342 0.375639
\(633\) 18.0339 0.716784
\(634\) −15.1517 −0.601751
\(635\) −44.0932 −1.74979
\(636\) −12.6827 −0.502902
\(637\) −27.4150 −1.08622
\(638\) 2.87626 0.113872
\(639\) 40.1138 1.58688
\(640\) −3.55972 −0.140710
\(641\) 23.7728 0.938969 0.469484 0.882941i \(-0.344440\pi\)
0.469484 + 0.882941i \(0.344440\pi\)
\(642\) 10.0188 0.395410
\(643\) −1.50015 −0.0591601 −0.0295800 0.999562i \(-0.509417\pi\)
−0.0295800 + 0.999562i \(0.509417\pi\)
\(644\) 34.1050 1.34393
\(645\) 58.4001 2.29950
\(646\) −61.1722 −2.40679
\(647\) −15.9643 −0.627623 −0.313811 0.949485i \(-0.601606\pi\)
−0.313811 + 0.949485i \(0.601606\pi\)
\(648\) 10.8421 0.425919
\(649\) −1.59188 −0.0624869
\(650\) −19.4423 −0.762589
\(651\) −106.981 −4.19293
\(652\) 8.38009 0.328190
\(653\) −5.55533 −0.217397 −0.108698 0.994075i \(-0.534668\pi\)
−0.108698 + 0.994075i \(0.534668\pi\)
\(654\) −3.28269 −0.128363
\(655\) −42.2711 −1.65167
\(656\) 0.736282 0.0287470
\(657\) −84.6491 −3.30248
\(658\) −45.7504 −1.78354
\(659\) −34.2032 −1.33237 −0.666184 0.745787i \(-0.732074\pi\)
−0.666184 + 0.745787i \(0.732074\pi\)
\(660\) 5.82788 0.226850
\(661\) −40.7184 −1.58376 −0.791880 0.610676i \(-0.790898\pi\)
−0.791880 + 0.610676i \(0.790898\pi\)
\(662\) −21.1767 −0.823055
\(663\) −58.1617 −2.25881
\(664\) −3.28706 −0.127563
\(665\) 121.483 4.71091
\(666\) 17.5645 0.680609
\(667\) −43.0554 −1.66711
\(668\) −16.8416 −0.651621
\(669\) −37.7165 −1.45820
\(670\) 2.32100 0.0896681
\(671\) 6.32436 0.244149
\(672\) 12.8033 0.493900
\(673\) −16.4992 −0.635996 −0.317998 0.948091i \(-0.603011\pi\)
−0.317998 + 0.948091i \(0.603011\pi\)
\(674\) −19.0650 −0.734358
\(675\) −74.4677 −2.86626
\(676\) −6.57729 −0.252973
\(677\) −26.5630 −1.02090 −0.510449 0.859908i \(-0.670521\pi\)
−0.510449 + 0.859908i \(0.670521\pi\)
\(678\) −34.7547 −1.33475
\(679\) −53.5690 −2.05579
\(680\) 26.9336 1.03286
\(681\) 61.8593 2.37045
\(682\) −4.51003 −0.172698
\(683\) 22.5665 0.863484 0.431742 0.901997i \(-0.357899\pi\)
0.431742 + 0.901997i \(0.357899\pi\)
\(684\) 50.1283 1.91670
\(685\) 72.9489 2.78723
\(686\) −16.1143 −0.615247
\(687\) 29.3267 1.11889
\(688\) 5.40877 0.206207
\(689\) −10.5967 −0.403703
\(690\) −87.2388 −3.32112
\(691\) 14.5618 0.553956 0.276978 0.960876i \(-0.410667\pi\)
0.276978 + 0.960876i \(0.410667\pi\)
\(692\) 17.3463 0.659408
\(693\) −14.1263 −0.536612
\(694\) 7.60292 0.288603
\(695\) 39.1917 1.48663
\(696\) −16.1634 −0.612672
\(697\) −5.57087 −0.211012
\(698\) 20.6054 0.779925
\(699\) −53.4860 −2.02302
\(700\) −32.3826 −1.22395
\(701\) −41.4929 −1.56717 −0.783583 0.621287i \(-0.786610\pi\)
−0.783583 + 0.621287i \(0.786610\pi\)
\(702\) 24.6002 0.928476
\(703\) 22.9035 0.863823
\(704\) 0.539753 0.0203427
\(705\) 117.027 4.40749
\(706\) 2.77705 0.104516
\(707\) 49.5277 1.86268
\(708\) 8.94572 0.336201
\(709\) 42.3149 1.58917 0.794584 0.607154i \(-0.207689\pi\)
0.794584 + 0.607154i \(0.207689\pi\)
\(710\) −23.0305 −0.864317
\(711\) 58.5514 2.19585
\(712\) −9.91472 −0.371570
\(713\) 67.5116 2.52833
\(714\) −96.8728 −3.62538
\(715\) 4.86935 0.182103
\(716\) −3.22549 −0.120542
\(717\) −10.9634 −0.409434
\(718\) −21.8966 −0.817172
\(719\) 2.71602 0.101290 0.0506452 0.998717i \(-0.483872\pi\)
0.0506452 + 0.998717i \(0.483872\pi\)
\(720\) −22.0711 −0.822541
\(721\) −64.1815 −2.39024
\(722\) 46.3658 1.72556
\(723\) 16.3454 0.607893
\(724\) −22.3274 −0.829791
\(725\) 40.8810 1.51828
\(726\) 32.4814 1.20550
\(727\) 39.8319 1.47728 0.738642 0.674097i \(-0.235467\pi\)
0.738642 + 0.674097i \(0.235467\pi\)
\(728\) 10.6975 0.396477
\(729\) −21.1048 −0.781657
\(730\) 48.5994 1.79875
\(731\) −40.9239 −1.51362
\(732\) −35.5403 −1.31361
\(733\) −21.4927 −0.793850 −0.396925 0.917851i \(-0.629923\pi\)
−0.396925 + 0.917851i \(0.629923\pi\)
\(734\) 21.9008 0.808372
\(735\) 116.801 4.30826
\(736\) −8.07968 −0.297821
\(737\) −0.351928 −0.0129634
\(738\) 4.56512 0.168044
\(739\) −2.02398 −0.0744533 −0.0372266 0.999307i \(-0.511852\pi\)
−0.0372266 + 0.999307i \(0.511852\pi\)
\(740\) −10.0842 −0.370704
\(741\) 62.1489 2.28310
\(742\) −17.6497 −0.647940
\(743\) −16.5245 −0.606227 −0.303113 0.952955i \(-0.598026\pi\)
−0.303113 + 0.952955i \(0.598026\pi\)
\(744\) 25.3445 0.929174
\(745\) −39.2242 −1.43706
\(746\) −12.2184 −0.447348
\(747\) −20.3805 −0.745685
\(748\) −4.08389 −0.149322
\(749\) 13.9425 0.509447
\(750\) 28.8465 1.05332
\(751\) −13.2289 −0.482729 −0.241365 0.970435i \(-0.577595\pi\)
−0.241365 + 0.970435i \(0.577595\pi\)
\(752\) 10.8385 0.395241
\(753\) 76.3101 2.78089
\(754\) −13.5049 −0.491821
\(755\) −40.1174 −1.46002
\(756\) 40.9736 1.49020
\(757\) −20.0853 −0.730012 −0.365006 0.931005i \(-0.618933\pi\)
−0.365006 + 0.931005i \(0.618933\pi\)
\(758\) 0.908152 0.0329856
\(759\) 13.2278 0.480140
\(760\) −28.7801 −1.04396
\(761\) −21.7953 −0.790078 −0.395039 0.918664i \(-0.629269\pi\)
−0.395039 + 0.918664i \(0.629269\pi\)
\(762\) −37.5712 −1.36106
\(763\) −4.56830 −0.165384
\(764\) 2.14688 0.0776713
\(765\) 166.995 6.03770
\(766\) −24.3990 −0.881572
\(767\) 7.47438 0.269884
\(768\) −3.03319 −0.109451
\(769\) 35.0444 1.26373 0.631867 0.775077i \(-0.282289\pi\)
0.631867 + 0.775077i \(0.282289\pi\)
\(770\) 8.11028 0.292274
\(771\) −47.1372 −1.69761
\(772\) 3.12109 0.112331
\(773\) 21.7085 0.780800 0.390400 0.920645i \(-0.372337\pi\)
0.390400 + 0.920645i \(0.372337\pi\)
\(774\) 33.5356 1.20541
\(775\) −64.1021 −2.30262
\(776\) 12.6908 0.455574
\(777\) 36.2703 1.30119
\(778\) 23.5296 0.843576
\(779\) 5.95278 0.213280
\(780\) −27.3637 −0.979777
\(781\) 3.49206 0.124956
\(782\) 61.1326 2.18610
\(783\) −51.7265 −1.84856
\(784\) 10.8176 0.386342
\(785\) −29.7568 −1.06207
\(786\) −36.0186 −1.28474
\(787\) 3.34765 0.119331 0.0596655 0.998218i \(-0.480997\pi\)
0.0596655 + 0.998218i \(0.480997\pi\)
\(788\) −13.9592 −0.497276
\(789\) 11.0669 0.393993
\(790\) −33.6160 −1.19600
\(791\) −48.3658 −1.71969
\(792\) 3.34659 0.118916
\(793\) −29.6948 −1.05449
\(794\) 8.10906 0.287780
\(795\) 45.1469 1.60120
\(796\) 19.4235 0.688447
\(797\) 37.3341 1.32244 0.661222 0.750191i \(-0.270038\pi\)
0.661222 + 0.750191i \(0.270038\pi\)
\(798\) 103.514 3.66435
\(799\) −82.0067 −2.90119
\(800\) 7.67163 0.271233
\(801\) −61.4735 −2.17206
\(802\) −21.3491 −0.753862
\(803\) −7.36903 −0.260047
\(804\) 1.97769 0.0697477
\(805\) −121.404 −4.27895
\(806\) 21.1760 0.745892
\(807\) 81.8635 2.88173
\(808\) −11.7334 −0.412780
\(809\) −25.1471 −0.884127 −0.442063 0.896984i \(-0.645753\pi\)
−0.442063 + 0.896984i \(0.645753\pi\)
\(810\) −38.5950 −1.35609
\(811\) −33.3245 −1.17018 −0.585091 0.810967i \(-0.698941\pi\)
−0.585091 + 0.810967i \(0.698941\pi\)
\(812\) −22.4935 −0.789368
\(813\) 45.0887 1.58133
\(814\) 1.52905 0.0535933
\(815\) −29.8308 −1.04493
\(816\) 22.9497 0.803402
\(817\) 43.7294 1.52990
\(818\) 14.4921 0.506703
\(819\) 66.3271 2.31766
\(820\) −2.62096 −0.0915279
\(821\) 40.8658 1.42623 0.713113 0.701050i \(-0.247285\pi\)
0.713113 + 0.701050i \(0.247285\pi\)
\(822\) 62.1587 2.16803
\(823\) 12.1096 0.422116 0.211058 0.977474i \(-0.432309\pi\)
0.211058 + 0.977474i \(0.432309\pi\)
\(824\) 15.2050 0.529690
\(825\) −12.5598 −0.437276
\(826\) 12.4492 0.433162
\(827\) 16.7267 0.581644 0.290822 0.956777i \(-0.406071\pi\)
0.290822 + 0.956777i \(0.406071\pi\)
\(828\) −50.0959 −1.74095
\(829\) −28.6371 −0.994607 −0.497304 0.867577i \(-0.665676\pi\)
−0.497304 + 0.867577i \(0.665676\pi\)
\(830\) 11.7010 0.406149
\(831\) 47.7289 1.65570
\(832\) −2.53431 −0.0878613
\(833\) −81.8480 −2.83587
\(834\) 33.3946 1.15636
\(835\) 59.9514 2.07470
\(836\) 4.36386 0.150927
\(837\) 81.1081 2.80351
\(838\) 22.3852 0.773285
\(839\) 22.8471 0.788771 0.394386 0.918945i \(-0.370957\pi\)
0.394386 + 0.918945i \(0.370957\pi\)
\(840\) −45.5764 −1.57253
\(841\) −0.603370 −0.0208059
\(842\) 20.5334 0.707626
\(843\) 86.0977 2.96536
\(844\) −5.94554 −0.204654
\(845\) 23.4133 0.805443
\(846\) 67.2014 2.31043
\(847\) 45.2022 1.55317
\(848\) 4.18131 0.143587
\(849\) 96.7587 3.32075
\(850\) −58.0452 −1.99093
\(851\) −22.8887 −0.784615
\(852\) −19.6239 −0.672304
\(853\) 14.9950 0.513418 0.256709 0.966489i \(-0.417362\pi\)
0.256709 + 0.966489i \(0.417362\pi\)
\(854\) −49.4590 −1.69245
\(855\) −178.443 −6.10262
\(856\) −3.30305 −0.112896
\(857\) −20.8521 −0.712295 −0.356147 0.934430i \(-0.615910\pi\)
−0.356147 + 0.934430i \(0.615910\pi\)
\(858\) 4.14910 0.141648
\(859\) 38.5565 1.31553 0.657766 0.753223i \(-0.271502\pi\)
0.657766 + 0.753223i \(0.271502\pi\)
\(860\) −19.2537 −0.656546
\(861\) 9.42688 0.321267
\(862\) −20.7962 −0.708323
\(863\) 34.8459 1.18617 0.593084 0.805141i \(-0.297910\pi\)
0.593084 + 0.805141i \(0.297910\pi\)
\(864\) −9.70689 −0.330235
\(865\) −61.7481 −2.09950
\(866\) −21.9824 −0.746992
\(867\) −122.078 −4.14600
\(868\) 35.2703 1.19715
\(869\) 5.09712 0.172908
\(870\) 57.5372 1.95069
\(871\) 1.65241 0.0559898
\(872\) 1.08226 0.0366499
\(873\) 78.6860 2.66312
\(874\) −65.3235 −2.20960
\(875\) 40.1437 1.35711
\(876\) 41.4108 1.39914
\(877\) 6.48816 0.219090 0.109545 0.993982i \(-0.465061\pi\)
0.109545 + 0.993982i \(0.465061\pi\)
\(878\) 32.2123 1.08711
\(879\) −91.4347 −3.08402
\(880\) −1.92137 −0.0647695
\(881\) 27.8005 0.936624 0.468312 0.883563i \(-0.344862\pi\)
0.468312 + 0.883563i \(0.344862\pi\)
\(882\) 67.0714 2.25841
\(883\) 12.4166 0.417851 0.208925 0.977932i \(-0.433003\pi\)
0.208925 + 0.977932i \(0.433003\pi\)
\(884\) 19.1751 0.644928
\(885\) −31.8443 −1.07043
\(886\) 32.4274 1.08942
\(887\) −24.4194 −0.819923 −0.409962 0.912103i \(-0.634458\pi\)
−0.409962 + 0.912103i \(0.634458\pi\)
\(888\) −8.59263 −0.288350
\(889\) −52.2853 −1.75359
\(890\) 35.2937 1.18305
\(891\) 5.85208 0.196052
\(892\) 12.4346 0.416342
\(893\) 87.6286 2.93238
\(894\) −33.4224 −1.11781
\(895\) 11.4819 0.383797
\(896\) −4.22109 −0.141017
\(897\) −62.1087 −2.07375
\(898\) 32.9473 1.09947
\(899\) −44.5264 −1.48504
\(900\) 47.5659 1.58553
\(901\) −31.6367 −1.05397
\(902\) 0.397411 0.0132323
\(903\) 69.2503 2.30451
\(904\) 11.4581 0.381092
\(905\) 79.4793 2.64198
\(906\) −34.1835 −1.13567
\(907\) 16.0534 0.533045 0.266522 0.963829i \(-0.414125\pi\)
0.266522 + 0.963829i \(0.414125\pi\)
\(908\) −20.3942 −0.676804
\(909\) −72.7498 −2.41296
\(910\) −38.0802 −1.26235
\(911\) 47.8056 1.58387 0.791935 0.610606i \(-0.209074\pi\)
0.791935 + 0.610606i \(0.209074\pi\)
\(912\) −24.5231 −0.812039
\(913\) −1.77420 −0.0587176
\(914\) −32.8041 −1.08506
\(915\) 126.514 4.18241
\(916\) −9.66862 −0.319460
\(917\) −50.1246 −1.65526
\(918\) 73.4444 2.42403
\(919\) 13.5636 0.447421 0.223710 0.974656i \(-0.428183\pi\)
0.223710 + 0.974656i \(0.428183\pi\)
\(920\) 28.7614 0.948236
\(921\) −16.5904 −0.546672
\(922\) −14.4291 −0.475196
\(923\) −16.3963 −0.539690
\(924\) 6.91065 0.227344
\(925\) 21.7328 0.714569
\(926\) 25.2189 0.828745
\(927\) 94.2743 3.09637
\(928\) 5.32885 0.174928
\(929\) −2.98388 −0.0978981 −0.0489490 0.998801i \(-0.515587\pi\)
−0.0489490 + 0.998801i \(0.515587\pi\)
\(930\) −90.2194 −2.95841
\(931\) 87.4591 2.86636
\(932\) 17.6336 0.577607
\(933\) −68.8471 −2.25395
\(934\) 4.84703 0.158600
\(935\) 14.5375 0.475428
\(936\) −15.7133 −0.513604
\(937\) 17.6311 0.575983 0.287992 0.957633i \(-0.407012\pi\)
0.287992 + 0.957633i \(0.407012\pi\)
\(938\) 2.75222 0.0898632
\(939\) 45.4813 1.48423
\(940\) −38.5822 −1.25841
\(941\) 37.9482 1.23707 0.618537 0.785755i \(-0.287726\pi\)
0.618537 + 0.785755i \(0.287726\pi\)
\(942\) −25.3554 −0.826122
\(943\) −5.94892 −0.193724
\(944\) −2.94928 −0.0959909
\(945\) −145.855 −4.74466
\(946\) 2.91940 0.0949178
\(947\) −23.1013 −0.750692 −0.375346 0.926885i \(-0.622476\pi\)
−0.375346 + 0.926885i \(0.622476\pi\)
\(948\) −28.6437 −0.930303
\(949\) 34.5998 1.12316
\(950\) 62.0245 2.01234
\(951\) 45.9580 1.49029
\(952\) 31.9376 1.03510
\(953\) 1.09712 0.0355392 0.0177696 0.999842i \(-0.494343\pi\)
0.0177696 + 0.999842i \(0.494343\pi\)
\(954\) 25.9251 0.839356
\(955\) −7.64229 −0.247299
\(956\) 3.61447 0.116900
\(957\) −8.72425 −0.282015
\(958\) −1.02461 −0.0331038
\(959\) 86.5021 2.79330
\(960\) 10.7973 0.348482
\(961\) 38.8182 1.25220
\(962\) −7.17937 −0.231472
\(963\) −20.4797 −0.659949
\(964\) −5.38886 −0.173564
\(965\) −11.1102 −0.357651
\(966\) −103.447 −3.32835
\(967\) −48.7805 −1.56868 −0.784338 0.620334i \(-0.786997\pi\)
−0.784338 + 0.620334i \(0.786997\pi\)
\(968\) −10.7087 −0.344190
\(969\) 185.547 5.96062
\(970\) −45.1758 −1.45051
\(971\) 39.5940 1.27063 0.635316 0.772252i \(-0.280870\pi\)
0.635316 + 0.772252i \(0.280870\pi\)
\(972\) −3.76556 −0.120780
\(973\) 46.4731 1.48986
\(974\) −2.65034 −0.0849223
\(975\) 58.9721 1.88862
\(976\) 11.7171 0.375056
\(977\) −19.8300 −0.634419 −0.317209 0.948356i \(-0.602746\pi\)
−0.317209 + 0.948356i \(0.602746\pi\)
\(978\) −25.4184 −0.812790
\(979\) −5.35150 −0.171035
\(980\) −38.5076 −1.23008
\(981\) 6.71024 0.214242
\(982\) −30.7111 −0.980031
\(983\) −39.0525 −1.24558 −0.622791 0.782388i \(-0.714001\pi\)
−0.622791 + 0.782388i \(0.714001\pi\)
\(984\) −2.23328 −0.0711944
\(985\) 49.6909 1.58328
\(986\) −40.3192 −1.28402
\(987\) 138.770 4.41708
\(988\) −20.4896 −0.651862
\(989\) −43.7011 −1.38961
\(990\) −11.9129 −0.378618
\(991\) 37.2256 1.18251 0.591255 0.806485i \(-0.298633\pi\)
0.591255 + 0.806485i \(0.298633\pi\)
\(992\) −8.35573 −0.265295
\(993\) 64.2328 2.03837
\(994\) −27.3093 −0.866198
\(995\) −69.1422 −2.19196
\(996\) 9.97028 0.315921
\(997\) 1.98664 0.0629175 0.0314588 0.999505i \(-0.489985\pi\)
0.0314588 + 0.999505i \(0.489985\pi\)
\(998\) 9.11311 0.288470
\(999\) −27.4984 −0.870010
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 \(a_p\))