Properties

Label 8021.2.a.a.1.17
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

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Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.22845 q^{2}\) \(-2.09787 q^{3}\) \(+2.96601 q^{4}\) \(-1.11575 q^{5}\) \(+4.67502 q^{6}\) \(-1.94623 q^{7}\) \(-2.15271 q^{8}\) \(+1.40108 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.22845 q^{2}\) \(-2.09787 q^{3}\) \(+2.96601 q^{4}\) \(-1.11575 q^{5}\) \(+4.67502 q^{6}\) \(-1.94623 q^{7}\) \(-2.15271 q^{8}\) \(+1.40108 q^{9}\) \(+2.48640 q^{10}\) \(+2.64240 q^{11}\) \(-6.22232 q^{12}\) \(+1.00000 q^{13}\) \(+4.33708 q^{14}\) \(+2.34071 q^{15}\) \(-1.13480 q^{16}\) \(+2.48199 q^{17}\) \(-3.12224 q^{18}\) \(+7.04847 q^{19}\) \(-3.30933 q^{20}\) \(+4.08294 q^{21}\) \(-5.88847 q^{22}\) \(-1.41370 q^{23}\) \(+4.51612 q^{24}\) \(-3.75510 q^{25}\) \(-2.22845 q^{26}\) \(+3.35434 q^{27}\) \(-5.77253 q^{28}\) \(-0.0497420 q^{29}\) \(-5.21616 q^{30}\) \(-1.45582 q^{31}\) \(+6.83428 q^{32}\) \(-5.54343 q^{33}\) \(-5.53100 q^{34}\) \(+2.17151 q^{35}\) \(+4.15561 q^{36}\) \(-5.20017 q^{37}\) \(-15.7072 q^{38}\) \(-2.09787 q^{39}\) \(+2.40189 q^{40}\) \(-4.25711 q^{41}\) \(-9.09866 q^{42}\) \(+6.11301 q^{43}\) \(+7.83739 q^{44}\) \(-1.56326 q^{45}\) \(+3.15037 q^{46}\) \(-1.92576 q^{47}\) \(+2.38067 q^{48}\) \(-3.21219 q^{49}\) \(+8.36807 q^{50}\) \(-5.20690 q^{51}\) \(+2.96601 q^{52}\) \(+2.85538 q^{53}\) \(-7.47499 q^{54}\) \(-2.94826 q^{55}\) \(+4.18967 q^{56}\) \(-14.7868 q^{57}\) \(+0.110848 q^{58}\) \(-12.2273 q^{59}\) \(+6.94256 q^{60}\) \(-2.61160 q^{61}\) \(+3.24423 q^{62}\) \(-2.72682 q^{63}\) \(-12.9603 q^{64}\) \(-1.11575 q^{65}\) \(+12.3533 q^{66}\) \(+11.1248 q^{67}\) \(+7.36160 q^{68}\) \(+2.96577 q^{69}\) \(-4.83911 q^{70}\) \(+0.447967 q^{71}\) \(-3.01612 q^{72}\) \(-6.17299 q^{73}\) \(+11.5883 q^{74}\) \(+7.87773 q^{75}\) \(+20.9058 q^{76}\) \(-5.14272 q^{77}\) \(+4.67502 q^{78}\) \(-2.31526 q^{79}\) \(+1.26616 q^{80}\) \(-11.2402 q^{81}\) \(+9.48677 q^{82}\) \(+0.591891 q^{83}\) \(+12.1101 q^{84}\) \(-2.76928 q^{85}\) \(-13.6226 q^{86}\) \(+0.104353 q^{87}\) \(-5.68833 q^{88}\) \(-14.9607 q^{89}\) \(+3.48364 q^{90}\) \(-1.94623 q^{91}\) \(-4.19305 q^{92}\) \(+3.05413 q^{93}\) \(+4.29146 q^{94}\) \(-7.86434 q^{95}\) \(-14.3375 q^{96}\) \(+10.6926 q^{97}\) \(+7.15823 q^{98}\) \(+3.70221 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 53q^{12} \) \(\mathstrut +\mathstrut 134q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 87q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 52q^{22} \) \(\mathstrut -\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 117q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 21q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 86q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 54q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 57q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 148q^{55} \) \(\mathstrut -\mathstrut 47q^{56} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 64q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut -\mathstrut 58q^{63} \) \(\mathstrut -\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 110q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 150q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 228q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 77q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 62q^{92} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 87q^{94} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 193q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.22845 −1.57576 −0.787878 0.615832i \(-0.788820\pi\)
−0.787878 + 0.615832i \(0.788820\pi\)
\(3\) −2.09787 −1.21121 −0.605604 0.795766i \(-0.707069\pi\)
−0.605604 + 0.795766i \(0.707069\pi\)
\(4\) 2.96601 1.48301
\(5\) −1.11575 −0.498979 −0.249490 0.968377i \(-0.580263\pi\)
−0.249490 + 0.968377i \(0.580263\pi\)
\(6\) 4.67502 1.90857
\(7\) −1.94623 −0.735605 −0.367803 0.929904i \(-0.619890\pi\)
−0.367803 + 0.929904i \(0.619890\pi\)
\(8\) −2.15271 −0.761098
\(9\) 1.40108 0.467026
\(10\) 2.48640 0.786269
\(11\) 2.64240 0.796714 0.398357 0.917230i \(-0.369581\pi\)
0.398357 + 0.917230i \(0.369581\pi\)
\(12\) −6.22232 −1.79623
\(13\) 1.00000 0.277350
\(14\) 4.33708 1.15913
\(15\) 2.34071 0.604368
\(16\) −1.13480 −0.283701
\(17\) 2.48199 0.601971 0.300985 0.953629i \(-0.402684\pi\)
0.300985 + 0.953629i \(0.402684\pi\)
\(18\) −3.12224 −0.735919
\(19\) 7.04847 1.61703 0.808515 0.588475i \(-0.200272\pi\)
0.808515 + 0.588475i \(0.200272\pi\)
\(20\) −3.30933 −0.739989
\(21\) 4.08294 0.890972
\(22\) −5.88847 −1.25543
\(23\) −1.41370 −0.294777 −0.147388 0.989079i \(-0.547087\pi\)
−0.147388 + 0.989079i \(0.547087\pi\)
\(24\) 4.51612 0.921849
\(25\) −3.75510 −0.751020
\(26\) −2.22845 −0.437036
\(27\) 3.35434 0.645542
\(28\) −5.77253 −1.09091
\(29\) −0.0497420 −0.00923687 −0.00461843 0.999989i \(-0.501470\pi\)
−0.00461843 + 0.999989i \(0.501470\pi\)
\(30\) −5.21616 −0.952336
\(31\) −1.45582 −0.261473 −0.130736 0.991417i \(-0.541734\pi\)
−0.130736 + 0.991417i \(0.541734\pi\)
\(32\) 6.83428 1.20814
\(33\) −5.54343 −0.964987
\(34\) −5.53100 −0.948558
\(35\) 2.17151 0.367052
\(36\) 4.15561 0.692602
\(37\) −5.20017 −0.854903 −0.427451 0.904038i \(-0.640588\pi\)
−0.427451 + 0.904038i \(0.640588\pi\)
\(38\) −15.7072 −2.54804
\(39\) −2.09787 −0.335929
\(40\) 2.40189 0.379772
\(41\) −4.25711 −0.664849 −0.332424 0.943130i \(-0.607867\pi\)
−0.332424 + 0.943130i \(0.607867\pi\)
\(42\) −9.09866 −1.40395
\(43\) 6.11301 0.932225 0.466112 0.884726i \(-0.345654\pi\)
0.466112 + 0.884726i \(0.345654\pi\)
\(44\) 7.83739 1.18153
\(45\) −1.56326 −0.233036
\(46\) 3.15037 0.464496
\(47\) −1.92576 −0.280901 −0.140450 0.990088i \(-0.544855\pi\)
−0.140450 + 0.990088i \(0.544855\pi\)
\(48\) 2.38067 0.343621
\(49\) −3.21219 −0.458885
\(50\) 8.36807 1.18342
\(51\) −5.20690 −0.729112
\(52\) 2.96601 0.411312
\(53\) 2.85538 0.392216 0.196108 0.980582i \(-0.437170\pi\)
0.196108 + 0.980582i \(0.437170\pi\)
\(54\) −7.47499 −1.01722
\(55\) −2.94826 −0.397544
\(56\) 4.18967 0.559868
\(57\) −14.7868 −1.95856
\(58\) 0.110848 0.0145550
\(59\) −12.2273 −1.59186 −0.795931 0.605388i \(-0.793018\pi\)
−0.795931 + 0.605388i \(0.793018\pi\)
\(60\) 6.94256 0.896281
\(61\) −2.61160 −0.334381 −0.167190 0.985925i \(-0.553469\pi\)
−0.167190 + 0.985925i \(0.553469\pi\)
\(62\) 3.24423 0.412017
\(63\) −2.72682 −0.343547
\(64\) −12.9603 −1.62003
\(65\) −1.11575 −0.138392
\(66\) 12.3533 1.52058
\(67\) 11.1248 1.35911 0.679553 0.733626i \(-0.262174\pi\)
0.679553 + 0.733626i \(0.262174\pi\)
\(68\) 7.36160 0.892725
\(69\) 2.96577 0.357036
\(70\) −4.83911 −0.578384
\(71\) 0.447967 0.0531639 0.0265820 0.999647i \(-0.491538\pi\)
0.0265820 + 0.999647i \(0.491538\pi\)
\(72\) −3.01612 −0.355453
\(73\) −6.17299 −0.722494 −0.361247 0.932470i \(-0.617649\pi\)
−0.361247 + 0.932470i \(0.617649\pi\)
\(74\) 11.5883 1.34712
\(75\) 7.87773 0.909641
\(76\) 20.9058 2.39806
\(77\) −5.14272 −0.586067
\(78\) 4.67502 0.529342
\(79\) −2.31526 −0.260487 −0.130244 0.991482i \(-0.541576\pi\)
−0.130244 + 0.991482i \(0.541576\pi\)
\(80\) 1.26616 0.141561
\(81\) −11.2402 −1.24891
\(82\) 9.48677 1.04764
\(83\) 0.591891 0.0649684 0.0324842 0.999472i \(-0.489658\pi\)
0.0324842 + 0.999472i \(0.489658\pi\)
\(84\) 12.1101 1.32132
\(85\) −2.76928 −0.300371
\(86\) −13.6226 −1.46896
\(87\) 0.104353 0.0111878
\(88\) −5.68833 −0.606378
\(89\) −14.9607 −1.58583 −0.792913 0.609334i \(-0.791437\pi\)
−0.792913 + 0.609334i \(0.791437\pi\)
\(90\) 3.48364 0.367208
\(91\) −1.94623 −0.204020
\(92\) −4.19305 −0.437156
\(93\) 3.05413 0.316698
\(94\) 4.29146 0.442631
\(95\) −7.86434 −0.806865
\(96\) −14.3375 −1.46331
\(97\) 10.6926 1.08567 0.542834 0.839840i \(-0.317351\pi\)
0.542834 + 0.839840i \(0.317351\pi\)
\(98\) 7.15823 0.723090
\(99\) 3.70221 0.372086
\(100\) −11.1377 −1.11377
\(101\) 5.37155 0.534490 0.267245 0.963629i \(-0.413887\pi\)
0.267245 + 0.963629i \(0.413887\pi\)
\(102\) 11.6033 1.14890
\(103\) 16.2979 1.60588 0.802941 0.596059i \(-0.203268\pi\)
0.802941 + 0.596059i \(0.203268\pi\)
\(104\) −2.15271 −0.211091
\(105\) −4.55555 −0.444576
\(106\) −6.36308 −0.618037
\(107\) 7.87838 0.761632 0.380816 0.924651i \(-0.375643\pi\)
0.380816 + 0.924651i \(0.375643\pi\)
\(108\) 9.94900 0.957343
\(109\) −3.85049 −0.368810 −0.184405 0.982850i \(-0.559036\pi\)
−0.184405 + 0.982850i \(0.559036\pi\)
\(110\) 6.57007 0.626432
\(111\) 10.9093 1.03547
\(112\) 2.20859 0.208692
\(113\) −4.72865 −0.444834 −0.222417 0.974952i \(-0.571395\pi\)
−0.222417 + 0.974952i \(0.571395\pi\)
\(114\) 32.9517 3.08621
\(115\) 1.57734 0.147088
\(116\) −0.147535 −0.0136983
\(117\) 1.40108 0.129530
\(118\) 27.2480 2.50838
\(119\) −4.83052 −0.442813
\(120\) −5.03887 −0.459983
\(121\) −4.01771 −0.365247
\(122\) 5.81982 0.526902
\(123\) 8.93088 0.805270
\(124\) −4.31798 −0.387766
\(125\) 9.76852 0.873723
\(126\) 6.07659 0.541346
\(127\) −10.4416 −0.926539 −0.463270 0.886217i \(-0.653324\pi\)
−0.463270 + 0.886217i \(0.653324\pi\)
\(128\) 15.2128 1.34464
\(129\) −12.8243 −1.12912
\(130\) 2.48640 0.218072
\(131\) −2.67514 −0.233728 −0.116864 0.993148i \(-0.537284\pi\)
−0.116864 + 0.993148i \(0.537284\pi\)
\(132\) −16.4419 −1.43108
\(133\) −13.7179 −1.18950
\(134\) −24.7910 −2.14162
\(135\) −3.74261 −0.322112
\(136\) −5.34300 −0.458159
\(137\) 3.46240 0.295813 0.147906 0.989001i \(-0.452747\pi\)
0.147906 + 0.989001i \(0.452747\pi\)
\(138\) −6.60907 −0.562602
\(139\) −6.09534 −0.517000 −0.258500 0.966011i \(-0.583228\pi\)
−0.258500 + 0.966011i \(0.583228\pi\)
\(140\) 6.44072 0.544340
\(141\) 4.04000 0.340229
\(142\) −0.998274 −0.0837733
\(143\) 2.64240 0.220969
\(144\) −1.58995 −0.132496
\(145\) 0.0554998 0.00460901
\(146\) 13.7562 1.13847
\(147\) 6.73878 0.555805
\(148\) −15.4238 −1.26783
\(149\) 22.7341 1.86245 0.931226 0.364443i \(-0.118741\pi\)
0.931226 + 0.364443i \(0.118741\pi\)
\(150\) −17.5552 −1.43337
\(151\) −9.01595 −0.733708 −0.366854 0.930279i \(-0.619565\pi\)
−0.366854 + 0.930279i \(0.619565\pi\)
\(152\) −15.1733 −1.23072
\(153\) 3.47746 0.281136
\(154\) 11.4603 0.923498
\(155\) 1.62433 0.130470
\(156\) −6.22232 −0.498184
\(157\) 17.9212 1.43027 0.715136 0.698986i \(-0.246365\pi\)
0.715136 + 0.698986i \(0.246365\pi\)
\(158\) 5.15945 0.410464
\(159\) −5.99022 −0.475055
\(160\) −7.62536 −0.602837
\(161\) 2.75138 0.216839
\(162\) 25.0483 1.96798
\(163\) −1.84638 −0.144620 −0.0723098 0.997382i \(-0.523037\pi\)
−0.0723098 + 0.997382i \(0.523037\pi\)
\(164\) −12.6266 −0.985974
\(165\) 6.18509 0.481509
\(166\) −1.31900 −0.102374
\(167\) −1.83493 −0.141991 −0.0709954 0.997477i \(-0.522618\pi\)
−0.0709954 + 0.997477i \(0.522618\pi\)
\(168\) −8.78940 −0.678117
\(169\) 1.00000 0.0769231
\(170\) 6.17122 0.473311
\(171\) 9.87546 0.755195
\(172\) 18.1312 1.38249
\(173\) 15.9279 1.21098 0.605488 0.795854i \(-0.292978\pi\)
0.605488 + 0.795854i \(0.292978\pi\)
\(174\) −0.232545 −0.0176292
\(175\) 7.30828 0.552454
\(176\) −2.99861 −0.226028
\(177\) 25.6514 1.92808
\(178\) 33.3392 2.49887
\(179\) −15.2925 −1.14302 −0.571508 0.820596i \(-0.693642\pi\)
−0.571508 + 0.820596i \(0.693642\pi\)
\(180\) −4.63663 −0.345594
\(181\) −21.3393 −1.58614 −0.793068 0.609133i \(-0.791518\pi\)
−0.793068 + 0.609133i \(0.791518\pi\)
\(182\) 4.33708 0.321486
\(183\) 5.47880 0.405005
\(184\) 3.04329 0.224354
\(185\) 5.80210 0.426579
\(186\) −6.80598 −0.499039
\(187\) 6.55841 0.479598
\(188\) −5.71182 −0.416577
\(189\) −6.52831 −0.474864
\(190\) 17.5253 1.27142
\(191\) −9.65240 −0.698423 −0.349212 0.937044i \(-0.613551\pi\)
−0.349212 + 0.937044i \(0.613551\pi\)
\(192\) 27.1890 1.96220
\(193\) −8.68965 −0.625494 −0.312747 0.949836i \(-0.601249\pi\)
−0.312747 + 0.949836i \(0.601249\pi\)
\(194\) −23.8280 −1.71075
\(195\) 2.34071 0.167622
\(196\) −9.52740 −0.680528
\(197\) 10.0940 0.719171 0.359585 0.933112i \(-0.382918\pi\)
0.359585 + 0.933112i \(0.382918\pi\)
\(198\) −8.25021 −0.586317
\(199\) 3.13931 0.222540 0.111270 0.993790i \(-0.464508\pi\)
0.111270 + 0.993790i \(0.464508\pi\)
\(200\) 8.08364 0.571600
\(201\) −23.3384 −1.64616
\(202\) −11.9703 −0.842225
\(203\) 0.0968094 0.00679469
\(204\) −15.4437 −1.08128
\(205\) 4.74988 0.331746
\(206\) −36.3192 −2.53048
\(207\) −1.98070 −0.137668
\(208\) −1.13480 −0.0786844
\(209\) 18.6249 1.28831
\(210\) 10.1518 0.700544
\(211\) 10.6081 0.730291 0.365145 0.930951i \(-0.381019\pi\)
0.365145 + 0.930951i \(0.381019\pi\)
\(212\) 8.46908 0.581658
\(213\) −0.939779 −0.0643926
\(214\) −17.5566 −1.20015
\(215\) −6.82060 −0.465161
\(216\) −7.22092 −0.491321
\(217\) 2.83336 0.192341
\(218\) 8.58065 0.581155
\(219\) 12.9502 0.875091
\(220\) −8.74458 −0.589560
\(221\) 2.48199 0.166957
\(222\) −24.3109 −1.63164
\(223\) 5.12964 0.343506 0.171753 0.985140i \(-0.445057\pi\)
0.171753 + 0.985140i \(0.445057\pi\)
\(224\) −13.3011 −0.888715
\(225\) −5.26119 −0.350746
\(226\) 10.5376 0.700950
\(227\) 1.50214 0.0997004 0.0498502 0.998757i \(-0.484126\pi\)
0.0498502 + 0.998757i \(0.484126\pi\)
\(228\) −43.8578 −2.90456
\(229\) −12.3290 −0.814721 −0.407360 0.913267i \(-0.633551\pi\)
−0.407360 + 0.913267i \(0.633551\pi\)
\(230\) −3.51503 −0.231774
\(231\) 10.7888 0.709850
\(232\) 0.107080 0.00703016
\(233\) −10.1585 −0.665505 −0.332752 0.943014i \(-0.607977\pi\)
−0.332752 + 0.943014i \(0.607977\pi\)
\(234\) −3.12224 −0.204107
\(235\) 2.14867 0.140164
\(236\) −36.2664 −2.36074
\(237\) 4.85713 0.315504
\(238\) 10.7646 0.697765
\(239\) −12.1406 −0.785308 −0.392654 0.919686i \(-0.628443\pi\)
−0.392654 + 0.919686i \(0.628443\pi\)
\(240\) −2.65624 −0.171460
\(241\) −18.8712 −1.21560 −0.607802 0.794089i \(-0.707948\pi\)
−0.607802 + 0.794089i \(0.707948\pi\)
\(242\) 8.95329 0.575539
\(243\) 13.5176 0.867151
\(244\) −7.74602 −0.495888
\(245\) 3.58401 0.228974
\(246\) −19.9021 −1.26891
\(247\) 7.04847 0.448483
\(248\) 3.13396 0.199007
\(249\) −1.24171 −0.0786903
\(250\) −21.7687 −1.37677
\(251\) 27.2093 1.71744 0.858719 0.512446i \(-0.171261\pi\)
0.858719 + 0.512446i \(0.171261\pi\)
\(252\) −8.08778 −0.509482
\(253\) −3.73556 −0.234853
\(254\) 23.2686 1.46000
\(255\) 5.80961 0.363812
\(256\) −7.98055 −0.498784
\(257\) 11.0090 0.686721 0.343360 0.939204i \(-0.388435\pi\)
0.343360 + 0.939204i \(0.388435\pi\)
\(258\) 28.5784 1.77921
\(259\) 10.1207 0.628871
\(260\) −3.30933 −0.205236
\(261\) −0.0696925 −0.00431386
\(262\) 5.96143 0.368298
\(263\) 30.6146 1.88778 0.943888 0.330264i \(-0.107138\pi\)
0.943888 + 0.330264i \(0.107138\pi\)
\(264\) 11.9334 0.734450
\(265\) −3.18589 −0.195708
\(266\) 30.5698 1.87435
\(267\) 31.3856 1.92077
\(268\) 32.9962 2.01556
\(269\) 20.3110 1.23838 0.619191 0.785240i \(-0.287461\pi\)
0.619191 + 0.785240i \(0.287461\pi\)
\(270\) 8.34023 0.507570
\(271\) −22.2968 −1.35444 −0.677218 0.735782i \(-0.736815\pi\)
−0.677218 + 0.735782i \(0.736815\pi\)
\(272\) −2.81657 −0.170780
\(273\) 4.08294 0.247111
\(274\) −7.71581 −0.466129
\(275\) −9.92248 −0.598348
\(276\) 8.79649 0.529487
\(277\) −10.6369 −0.639107 −0.319554 0.947568i \(-0.603533\pi\)
−0.319554 + 0.947568i \(0.603533\pi\)
\(278\) 13.5832 0.814665
\(279\) −2.03972 −0.122115
\(280\) −4.67463 −0.279362
\(281\) 23.8463 1.42255 0.711275 0.702913i \(-0.248118\pi\)
0.711275 + 0.702913i \(0.248118\pi\)
\(282\) −9.00295 −0.536118
\(283\) 6.52917 0.388119 0.194059 0.980990i \(-0.437835\pi\)
0.194059 + 0.980990i \(0.437835\pi\)
\(284\) 1.32867 0.0788424
\(285\) 16.4984 0.977281
\(286\) −5.88847 −0.348193
\(287\) 8.28531 0.489066
\(288\) 9.57536 0.564234
\(289\) −10.8397 −0.637631
\(290\) −0.123679 −0.00726267
\(291\) −22.4317 −1.31497
\(292\) −18.3092 −1.07146
\(293\) 9.58021 0.559682 0.279841 0.960046i \(-0.409718\pi\)
0.279841 + 0.960046i \(0.409718\pi\)
\(294\) −15.0171 −0.875813
\(295\) 13.6427 0.794306
\(296\) 11.1945 0.650665
\(297\) 8.86351 0.514313
\(298\) −50.6619 −2.93477
\(299\) −1.41370 −0.0817564
\(300\) 23.3654 1.34900
\(301\) −11.8973 −0.685749
\(302\) 20.0916 1.15614
\(303\) −11.2688 −0.647378
\(304\) −7.99863 −0.458753
\(305\) 2.91389 0.166849
\(306\) −7.74936 −0.443002
\(307\) −18.9717 −1.08277 −0.541386 0.840774i \(-0.682100\pi\)
−0.541386 + 0.840774i \(0.682100\pi\)
\(308\) −15.2534 −0.869141
\(309\) −34.1910 −1.94506
\(310\) −3.61975 −0.205588
\(311\) −9.47412 −0.537228 −0.268614 0.963248i \(-0.586566\pi\)
−0.268614 + 0.963248i \(0.586566\pi\)
\(312\) 4.51612 0.255675
\(313\) 1.65050 0.0932920 0.0466460 0.998911i \(-0.485147\pi\)
0.0466460 + 0.998911i \(0.485147\pi\)
\(314\) −39.9367 −2.25376
\(315\) 3.04245 0.171423
\(316\) −6.86709 −0.386304
\(317\) 21.4376 1.20405 0.602026 0.798476i \(-0.294360\pi\)
0.602026 + 0.798476i \(0.294360\pi\)
\(318\) 13.3489 0.748571
\(319\) −0.131438 −0.00735914
\(320\) 14.4604 0.808364
\(321\) −16.5279 −0.922495
\(322\) −6.13133 −0.341686
\(323\) 17.4942 0.973405
\(324\) −33.3386 −1.85214
\(325\) −3.75510 −0.208295
\(326\) 4.11457 0.227885
\(327\) 8.07785 0.446706
\(328\) 9.16432 0.506015
\(329\) 3.74796 0.206632
\(330\) −13.7832 −0.758740
\(331\) 30.5662 1.68007 0.840035 0.542532i \(-0.182534\pi\)
0.840035 + 0.542532i \(0.182534\pi\)
\(332\) 1.75555 0.0963485
\(333\) −7.28585 −0.399262
\(334\) 4.08905 0.223743
\(335\) −12.4125 −0.678166
\(336\) −4.63334 −0.252769
\(337\) 13.0044 0.708397 0.354199 0.935170i \(-0.384754\pi\)
0.354199 + 0.935170i \(0.384754\pi\)
\(338\) −2.22845 −0.121212
\(339\) 9.92011 0.538787
\(340\) −8.21372 −0.445452
\(341\) −3.84686 −0.208319
\(342\) −22.0070 −1.19000
\(343\) 19.8753 1.07316
\(344\) −13.1595 −0.709514
\(345\) −3.30906 −0.178154
\(346\) −35.4946 −1.90820
\(347\) −22.5538 −1.21075 −0.605375 0.795940i \(-0.706977\pi\)
−0.605375 + 0.795940i \(0.706977\pi\)
\(348\) 0.309511 0.0165915
\(349\) 24.0581 1.28780 0.643899 0.765110i \(-0.277316\pi\)
0.643899 + 0.765110i \(0.277316\pi\)
\(350\) −16.2862 −0.870532
\(351\) 3.35434 0.179041
\(352\) 18.0589 0.962543
\(353\) 26.4959 1.41024 0.705118 0.709090i \(-0.250894\pi\)
0.705118 + 0.709090i \(0.250894\pi\)
\(354\) −57.1629 −3.03818
\(355\) −0.499820 −0.0265277
\(356\) −44.3735 −2.35179
\(357\) 10.1338 0.536339
\(358\) 34.0787 1.80112
\(359\) −9.35228 −0.493595 −0.246797 0.969067i \(-0.579378\pi\)
−0.246797 + 0.969067i \(0.579378\pi\)
\(360\) 3.36524 0.177364
\(361\) 30.6809 1.61479
\(362\) 47.5536 2.49936
\(363\) 8.42866 0.442390
\(364\) −5.77253 −0.302563
\(365\) 6.88753 0.360510
\(366\) −12.2093 −0.638188
\(367\) −31.9250 −1.66647 −0.833236 0.552917i \(-0.813515\pi\)
−0.833236 + 0.552917i \(0.813515\pi\)
\(368\) 1.60427 0.0836284
\(369\) −5.96454 −0.310502
\(370\) −12.9297 −0.672184
\(371\) −5.55722 −0.288516
\(372\) 9.05857 0.469665
\(373\) −9.46315 −0.489983 −0.244992 0.969525i \(-0.578785\pi\)
−0.244992 + 0.969525i \(0.578785\pi\)
\(374\) −14.6151 −0.755730
\(375\) −20.4931 −1.05826
\(376\) 4.14560 0.213793
\(377\) −0.0497420 −0.00256185
\(378\) 14.5480 0.748270
\(379\) 14.5747 0.748653 0.374327 0.927297i \(-0.377874\pi\)
0.374327 + 0.927297i \(0.377874\pi\)
\(380\) −23.3257 −1.19658
\(381\) 21.9051 1.12223
\(382\) 21.5099 1.10054
\(383\) −34.1010 −1.74248 −0.871240 0.490857i \(-0.836684\pi\)
−0.871240 + 0.490857i \(0.836684\pi\)
\(384\) −31.9146 −1.62864
\(385\) 5.73800 0.292435
\(386\) 19.3645 0.985626
\(387\) 8.56480 0.435373
\(388\) 31.7144 1.61005
\(389\) 33.1113 1.67881 0.839405 0.543506i \(-0.182903\pi\)
0.839405 + 0.543506i \(0.182903\pi\)
\(390\) −5.21616 −0.264131
\(391\) −3.50879 −0.177447
\(392\) 6.91492 0.349256
\(393\) 5.61211 0.283093
\(394\) −22.4941 −1.13324
\(395\) 2.58326 0.129978
\(396\) 10.9808 0.551806
\(397\) −4.89700 −0.245773 −0.122887 0.992421i \(-0.539215\pi\)
−0.122887 + 0.992421i \(0.539215\pi\)
\(398\) −6.99581 −0.350668
\(399\) 28.7785 1.44073
\(400\) 4.26130 0.213065
\(401\) −15.7321 −0.785623 −0.392812 0.919619i \(-0.628498\pi\)
−0.392812 + 0.919619i \(0.628498\pi\)
\(402\) 52.0085 2.59395
\(403\) −1.45582 −0.0725195
\(404\) 15.9321 0.792651
\(405\) 12.5413 0.623182
\(406\) −0.215735 −0.0107068
\(407\) −13.7409 −0.681113
\(408\) 11.2089 0.554926
\(409\) 5.86652 0.290081 0.145040 0.989426i \(-0.453669\pi\)
0.145040 + 0.989426i \(0.453669\pi\)
\(410\) −10.5849 −0.522750
\(411\) −7.26369 −0.358291
\(412\) 48.3398 2.38153
\(413\) 23.7972 1.17098
\(414\) 4.41391 0.216932
\(415\) −0.660403 −0.0324179
\(416\) 6.83428 0.335078
\(417\) 12.7873 0.626195
\(418\) −41.5047 −2.03006
\(419\) 21.9232 1.07102 0.535509 0.844530i \(-0.320120\pi\)
0.535509 + 0.844530i \(0.320120\pi\)
\(420\) −13.5118 −0.659309
\(421\) −0.274013 −0.0133546 −0.00667729 0.999978i \(-0.502125\pi\)
−0.00667729 + 0.999978i \(0.502125\pi\)
\(422\) −23.6396 −1.15076
\(423\) −2.69814 −0.131188
\(424\) −6.14680 −0.298515
\(425\) −9.32011 −0.452092
\(426\) 2.09425 0.101467
\(427\) 5.08276 0.245972
\(428\) 23.3674 1.12950
\(429\) −5.54343 −0.267639
\(430\) 15.1994 0.732980
\(431\) 37.6269 1.81242 0.906211 0.422826i \(-0.138962\pi\)
0.906211 + 0.422826i \(0.138962\pi\)
\(432\) −3.80651 −0.183141
\(433\) −5.96651 −0.286732 −0.143366 0.989670i \(-0.545793\pi\)
−0.143366 + 0.989670i \(0.545793\pi\)
\(434\) −6.31401 −0.303082
\(435\) −0.116432 −0.00558247
\(436\) −11.4206 −0.546947
\(437\) −9.96442 −0.476663
\(438\) −28.8589 −1.37893
\(439\) −35.9224 −1.71448 −0.857242 0.514913i \(-0.827824\pi\)
−0.857242 + 0.514913i \(0.827824\pi\)
\(440\) 6.34676 0.302570
\(441\) −4.50054 −0.214311
\(442\) −5.53100 −0.263083
\(443\) −0.260570 −0.0123801 −0.00619003 0.999981i \(-0.501970\pi\)
−0.00619003 + 0.999981i \(0.501970\pi\)
\(444\) 32.3571 1.53560
\(445\) 16.6924 0.791295
\(446\) −11.4312 −0.541281
\(447\) −47.6933 −2.25582
\(448\) 25.2237 1.19171
\(449\) 40.2617 1.90007 0.950033 0.312148i \(-0.101049\pi\)
0.950033 + 0.312148i \(0.101049\pi\)
\(450\) 11.7243 0.552690
\(451\) −11.2490 −0.529694
\(452\) −14.0252 −0.659691
\(453\) 18.9143 0.888673
\(454\) −3.34745 −0.157103
\(455\) 2.17151 0.101802
\(456\) 31.8317 1.49066
\(457\) −20.7489 −0.970592 −0.485296 0.874350i \(-0.661288\pi\)
−0.485296 + 0.874350i \(0.661288\pi\)
\(458\) 27.4745 1.28380
\(459\) 8.32542 0.388598
\(460\) 4.67840 0.218132
\(461\) 24.5036 1.14125 0.570624 0.821212i \(-0.306701\pi\)
0.570624 + 0.821212i \(0.306701\pi\)
\(462\) −24.0423 −1.11855
\(463\) −30.0195 −1.39512 −0.697562 0.716524i \(-0.745732\pi\)
−0.697562 + 0.716524i \(0.745732\pi\)
\(464\) 0.0564474 0.00262051
\(465\) −3.40765 −0.158026
\(466\) 22.6377 1.04867
\(467\) −25.0301 −1.15825 −0.579127 0.815237i \(-0.696606\pi\)
−0.579127 + 0.815237i \(0.696606\pi\)
\(468\) 4.15561 0.192093
\(469\) −21.6513 −0.999766
\(470\) −4.78821 −0.220864
\(471\) −37.5965 −1.73236
\(472\) 26.3219 1.21156
\(473\) 16.1530 0.742717
\(474\) −10.8239 −0.497157
\(475\) −26.4677 −1.21442
\(476\) −14.3274 −0.656694
\(477\) 4.00061 0.183175
\(478\) 27.0547 1.23745
\(479\) 35.4518 1.61983 0.809917 0.586544i \(-0.199512\pi\)
0.809917 + 0.586544i \(0.199512\pi\)
\(480\) 15.9970 0.730162
\(481\) −5.20017 −0.237107
\(482\) 42.0537 1.91549
\(483\) −5.77206 −0.262638
\(484\) −11.9166 −0.541663
\(485\) −11.9303 −0.541726
\(486\) −30.1233 −1.36642
\(487\) 10.0093 0.453562 0.226781 0.973946i \(-0.427180\pi\)
0.226781 + 0.973946i \(0.427180\pi\)
\(488\) 5.62201 0.254496
\(489\) 3.87347 0.175165
\(490\) −7.98680 −0.360807
\(491\) −0.753366 −0.0339989 −0.0169995 0.999855i \(-0.505411\pi\)
−0.0169995 + 0.999855i \(0.505411\pi\)
\(492\) 26.4891 1.19422
\(493\) −0.123459 −0.00556032
\(494\) −15.7072 −0.706700
\(495\) −4.13075 −0.185663
\(496\) 1.65207 0.0741801
\(497\) −0.871846 −0.0391077
\(498\) 2.76710 0.123997
\(499\) 4.48053 0.200576 0.100288 0.994958i \(-0.468024\pi\)
0.100288 + 0.994958i \(0.468024\pi\)
\(500\) 28.9735 1.29574
\(501\) 3.84945 0.171981
\(502\) −60.6348 −2.70626
\(503\) −6.18239 −0.275659 −0.137830 0.990456i \(-0.544013\pi\)
−0.137830 + 0.990456i \(0.544013\pi\)
\(504\) 5.87005 0.261473
\(505\) −5.99332 −0.266699
\(506\) 8.32453 0.370071
\(507\) −2.09787 −0.0931699
\(508\) −30.9698 −1.37406
\(509\) 8.33205 0.369312 0.184656 0.982803i \(-0.440883\pi\)
0.184656 + 0.982803i \(0.440883\pi\)
\(510\) −12.9464 −0.573278
\(511\) 12.0141 0.531471
\(512\) −12.6414 −0.558675
\(513\) 23.6429 1.04386
\(514\) −24.5330 −1.08210
\(515\) −18.1844 −0.801302
\(516\) −38.0371 −1.67449
\(517\) −5.08862 −0.223797
\(518\) −22.5536 −0.990947
\(519\) −33.4148 −1.46675
\(520\) 2.40189 0.105330
\(521\) −4.87972 −0.213785 −0.106892 0.994271i \(-0.534090\pi\)
−0.106892 + 0.994271i \(0.534090\pi\)
\(522\) 0.155307 0.00679759
\(523\) −42.1469 −1.84296 −0.921478 0.388431i \(-0.873017\pi\)
−0.921478 + 0.388431i \(0.873017\pi\)
\(524\) −7.93449 −0.346620
\(525\) −15.3319 −0.669137
\(526\) −68.2232 −2.97467
\(527\) −3.61333 −0.157399
\(528\) 6.29070 0.273768
\(529\) −21.0015 −0.913107
\(530\) 7.09961 0.308388
\(531\) −17.1314 −0.743441
\(532\) −40.6875 −1.76403
\(533\) −4.25711 −0.184396
\(534\) −69.9414 −3.02666
\(535\) −8.79032 −0.380039
\(536\) −23.9484 −1.03441
\(537\) 32.0818 1.38443
\(538\) −45.2621 −1.95139
\(539\) −8.48791 −0.365600
\(540\) −11.1006 −0.477694
\(541\) 6.86370 0.295094 0.147547 0.989055i \(-0.452862\pi\)
0.147547 + 0.989055i \(0.452862\pi\)
\(542\) 49.6875 2.13426
\(543\) 44.7671 1.92114
\(544\) 16.9626 0.727265
\(545\) 4.29619 0.184029
\(546\) −9.09866 −0.389387
\(547\) −36.2035 −1.54795 −0.773974 0.633217i \(-0.781734\pi\)
−0.773974 + 0.633217i \(0.781734\pi\)
\(548\) 10.2695 0.438692
\(549\) −3.65905 −0.156164
\(550\) 22.1118 0.942850
\(551\) −0.350605 −0.0149363
\(552\) −6.38443 −0.271740
\(553\) 4.50603 0.191616
\(554\) 23.7038 1.00708
\(555\) −12.1721 −0.516676
\(556\) −18.0788 −0.766714
\(557\) −37.2572 −1.57864 −0.789319 0.613983i \(-0.789566\pi\)
−0.789319 + 0.613983i \(0.789566\pi\)
\(558\) 4.54542 0.192423
\(559\) 6.11301 0.258553
\(560\) −2.46423 −0.104133
\(561\) −13.7587 −0.580894
\(562\) −53.1404 −2.24159
\(563\) −0.183521 −0.00773449 −0.00386724 0.999993i \(-0.501231\pi\)
−0.00386724 + 0.999993i \(0.501231\pi\)
\(564\) 11.9827 0.504562
\(565\) 5.27600 0.221963
\(566\) −14.5499 −0.611580
\(567\) 21.8760 0.918707
\(568\) −0.964343 −0.0404629
\(569\) 3.25164 0.136316 0.0681580 0.997675i \(-0.478288\pi\)
0.0681580 + 0.997675i \(0.478288\pi\)
\(570\) −36.7660 −1.53996
\(571\) 16.1936 0.677681 0.338840 0.940844i \(-0.389965\pi\)
0.338840 + 0.940844i \(0.389965\pi\)
\(572\) 7.83739 0.327698
\(573\) 20.2495 0.845936
\(574\) −18.4634 −0.770649
\(575\) 5.30858 0.221383
\(576\) −18.1584 −0.756598
\(577\) −39.0247 −1.62462 −0.812309 0.583228i \(-0.801790\pi\)
−0.812309 + 0.583228i \(0.801790\pi\)
\(578\) 24.1559 1.00475
\(579\) 18.2298 0.757604
\(580\) 0.164613 0.00683518
\(581\) −1.15195 −0.0477911
\(582\) 49.9881 2.07207
\(583\) 7.54505 0.312484
\(584\) 13.2887 0.549889
\(585\) −1.56326 −0.0646327
\(586\) −21.3491 −0.881922
\(587\) 32.4009 1.33733 0.668663 0.743565i \(-0.266867\pi\)
0.668663 + 0.743565i \(0.266867\pi\)
\(588\) 19.9873 0.824262
\(589\) −10.2613 −0.422810
\(590\) −30.4020 −1.25163
\(591\) −21.1760 −0.871065
\(592\) 5.90117 0.242537
\(593\) −17.6447 −0.724583 −0.362291 0.932065i \(-0.618006\pi\)
−0.362291 + 0.932065i \(0.618006\pi\)
\(594\) −19.7519 −0.810431
\(595\) 5.38966 0.220954
\(596\) 67.4296 2.76203
\(597\) −6.58588 −0.269542
\(598\) 3.15037 0.128828
\(599\) −34.0824 −1.39257 −0.696284 0.717766i \(-0.745165\pi\)
−0.696284 + 0.717766i \(0.745165\pi\)
\(600\) −16.9585 −0.692326
\(601\) 7.30524 0.297987 0.148993 0.988838i \(-0.452397\pi\)
0.148993 + 0.988838i \(0.452397\pi\)
\(602\) 26.5126 1.08057
\(603\) 15.5867 0.634738
\(604\) −26.7414 −1.08809
\(605\) 4.48277 0.182251
\(606\) 25.1121 1.02011
\(607\) 13.5351 0.549374 0.274687 0.961534i \(-0.411426\pi\)
0.274687 + 0.961534i \(0.411426\pi\)
\(608\) 48.1712 1.95360
\(609\) −0.203094 −0.00822978
\(610\) −6.49348 −0.262913
\(611\) −1.92576 −0.0779078
\(612\) 10.3142 0.416926
\(613\) 13.1736 0.532076 0.266038 0.963963i \(-0.414285\pi\)
0.266038 + 0.963963i \(0.414285\pi\)
\(614\) 42.2776 1.70619
\(615\) −9.96465 −0.401813
\(616\) 11.0708 0.446055
\(617\) 1.00000 0.0402585
\(618\) 76.1931 3.06493
\(619\) −15.7170 −0.631720 −0.315860 0.948806i \(-0.602293\pi\)
−0.315860 + 0.948806i \(0.602293\pi\)
\(620\) 4.81779 0.193487
\(621\) −4.74203 −0.190291
\(622\) 21.1127 0.846540
\(623\) 29.1169 1.16654
\(624\) 2.38067 0.0953033
\(625\) 7.87625 0.315050
\(626\) −3.67807 −0.147005
\(627\) −39.0727 −1.56041
\(628\) 53.1546 2.12110
\(629\) −12.9068 −0.514626
\(630\) −6.77997 −0.270120
\(631\) 34.0783 1.35664 0.678319 0.734768i \(-0.262709\pi\)
0.678319 + 0.734768i \(0.262709\pi\)
\(632\) 4.98408 0.198256
\(633\) −22.2544 −0.884534
\(634\) −47.7726 −1.89729
\(635\) 11.6502 0.462324
\(636\) −17.7671 −0.704510
\(637\) −3.21219 −0.127272
\(638\) 0.292905 0.0115962
\(639\) 0.627637 0.0248289
\(640\) −16.9737 −0.670946
\(641\) −49.5871 −1.95857 −0.979286 0.202481i \(-0.935100\pi\)
−0.979286 + 0.202481i \(0.935100\pi\)
\(642\) 36.8316 1.45363
\(643\) −31.2135 −1.23094 −0.615470 0.788160i \(-0.711034\pi\)
−0.615470 + 0.788160i \(0.711034\pi\)
\(644\) 8.16063 0.321574
\(645\) 14.3088 0.563407
\(646\) −38.9851 −1.53385
\(647\) −46.0298 −1.80962 −0.904810 0.425815i \(-0.859987\pi\)
−0.904810 + 0.425815i \(0.859987\pi\)
\(648\) 24.1969 0.950545
\(649\) −32.3095 −1.26826
\(650\) 8.36807 0.328223
\(651\) −5.94403 −0.232965
\(652\) −5.47638 −0.214472
\(653\) −13.4085 −0.524715 −0.262358 0.964971i \(-0.584500\pi\)
−0.262358 + 0.964971i \(0.584500\pi\)
\(654\) −18.0011 −0.703899
\(655\) 2.98479 0.116625
\(656\) 4.83098 0.188618
\(657\) −8.64885 −0.337424
\(658\) −8.35217 −0.325601
\(659\) −21.1462 −0.823739 −0.411870 0.911243i \(-0.635124\pi\)
−0.411870 + 0.911243i \(0.635124\pi\)
\(660\) 18.3450 0.714080
\(661\) 7.83165 0.304616 0.152308 0.988333i \(-0.451329\pi\)
0.152308 + 0.988333i \(0.451329\pi\)
\(662\) −68.1154 −2.64738
\(663\) −5.20690 −0.202219
\(664\) −1.27417 −0.0494474
\(665\) 15.3058 0.593534
\(666\) 16.2362 0.629139
\(667\) 0.0703203 0.00272281
\(668\) −5.44241 −0.210573
\(669\) −10.7613 −0.416057
\(670\) 27.6606 1.06862
\(671\) −6.90088 −0.266406
\(672\) 27.9040 1.07642
\(673\) 0.461437 0.0177871 0.00889354 0.999960i \(-0.497169\pi\)
0.00889354 + 0.999960i \(0.497169\pi\)
\(674\) −28.9798 −1.11626
\(675\) −12.5959 −0.484815
\(676\) 2.96601 0.114077
\(677\) 37.0573 1.42423 0.712113 0.702065i \(-0.247738\pi\)
0.712113 + 0.702065i \(0.247738\pi\)
\(678\) −22.1065 −0.848996
\(679\) −20.8102 −0.798624
\(680\) 5.96146 0.228612
\(681\) −3.15130 −0.120758
\(682\) 8.57255 0.328260
\(683\) 36.0696 1.38016 0.690082 0.723731i \(-0.257574\pi\)
0.690082 + 0.723731i \(0.257574\pi\)
\(684\) 29.2907 1.11996
\(685\) −3.86318 −0.147605
\(686\) −44.2911 −1.69104
\(687\) 25.8646 0.986797
\(688\) −6.93706 −0.264473
\(689\) 2.85538 0.108781
\(690\) 7.37409 0.280727
\(691\) 6.70549 0.255089 0.127544 0.991833i \(-0.459290\pi\)
0.127544 + 0.991833i \(0.459290\pi\)
\(692\) 47.2424 1.79588
\(693\) −7.20535 −0.273709
\(694\) 50.2601 1.90785
\(695\) 6.80089 0.257972
\(696\) −0.224641 −0.00851499
\(697\) −10.5661 −0.400219
\(698\) −53.6123 −2.02926
\(699\) 21.3112 0.806065
\(700\) 21.6764 0.819292
\(701\) −36.7222 −1.38698 −0.693490 0.720466i \(-0.743928\pi\)
−0.693490 + 0.720466i \(0.743928\pi\)
\(702\) −7.47499 −0.282125
\(703\) −36.6533 −1.38240
\(704\) −34.2462 −1.29070
\(705\) −4.50763 −0.169767
\(706\) −59.0450 −2.22219
\(707\) −10.4543 −0.393173
\(708\) 76.0823 2.85935
\(709\) 21.0457 0.790387 0.395193 0.918598i \(-0.370678\pi\)
0.395193 + 0.918598i \(0.370678\pi\)
\(710\) 1.11383 0.0418012
\(711\) −3.24386 −0.121654
\(712\) 32.2060 1.20697
\(713\) 2.05809 0.0770762
\(714\) −22.5828 −0.845138
\(715\) −2.94826 −0.110259
\(716\) −45.3578 −1.69510
\(717\) 25.4694 0.951172
\(718\) 20.8411 0.777784
\(719\) −31.4717 −1.17370 −0.586848 0.809697i \(-0.699631\pi\)
−0.586848 + 0.809697i \(0.699631\pi\)
\(720\) 1.77399 0.0661126
\(721\) −31.7195 −1.18129
\(722\) −68.3711 −2.54451
\(723\) 39.5895 1.47235
\(724\) −63.2925 −2.35225
\(725\) 0.186786 0.00693707
\(726\) −18.7829 −0.697098
\(727\) −1.52070 −0.0563995 −0.0281998 0.999602i \(-0.508977\pi\)
−0.0281998 + 0.999602i \(0.508977\pi\)
\(728\) 4.18967 0.155279
\(729\) 5.36251 0.198612
\(730\) −15.3485 −0.568075
\(731\) 15.1724 0.561172
\(732\) 16.2502 0.600624
\(733\) −18.0405 −0.666342 −0.333171 0.942866i \(-0.608119\pi\)
−0.333171 + 0.942866i \(0.608119\pi\)
\(734\) 71.1435 2.62595
\(735\) −7.51880 −0.277335
\(736\) −9.66162 −0.356132
\(737\) 29.3961 1.08282
\(738\) 13.2917 0.489275
\(739\) −3.86883 −0.142317 −0.0711586 0.997465i \(-0.522670\pi\)
−0.0711586 + 0.997465i \(0.522670\pi\)
\(740\) 17.2091 0.632619
\(741\) −14.7868 −0.543207
\(742\) 12.3840 0.454631
\(743\) −12.7292 −0.466988 −0.233494 0.972358i \(-0.575016\pi\)
−0.233494 + 0.972358i \(0.575016\pi\)
\(744\) −6.57465 −0.241038
\(745\) −25.3656 −0.929325
\(746\) 21.0882 0.772094
\(747\) 0.829285 0.0303420
\(748\) 19.4523 0.711247
\(749\) −15.3331 −0.560260
\(750\) 45.6680 1.66756
\(751\) −13.4646 −0.491330 −0.245665 0.969355i \(-0.579006\pi\)
−0.245665 + 0.969355i \(0.579006\pi\)
\(752\) 2.18536 0.0796917
\(753\) −57.0818 −2.08018
\(754\) 0.110848 0.00403684
\(755\) 10.0596 0.366105
\(756\) −19.3630 −0.704226
\(757\) 20.2729 0.736832 0.368416 0.929661i \(-0.379900\pi\)
0.368416 + 0.929661i \(0.379900\pi\)
\(758\) −32.4791 −1.17969
\(759\) 7.83674 0.284456
\(760\) 16.9297 0.614103
\(761\) −2.48948 −0.0902435 −0.0451218 0.998981i \(-0.514368\pi\)
−0.0451218 + 0.998981i \(0.514368\pi\)
\(762\) −48.8145 −1.76836
\(763\) 7.49394 0.271299
\(764\) −28.6291 −1.03577
\(765\) −3.87998 −0.140281
\(766\) 75.9926 2.74572
\(767\) −12.2273 −0.441503
\(768\) 16.7422 0.604132
\(769\) −12.1961 −0.439803 −0.219902 0.975522i \(-0.570574\pi\)
−0.219902 + 0.975522i \(0.570574\pi\)
\(770\) −12.7869 −0.460807
\(771\) −23.0954 −0.831762
\(772\) −25.7736 −0.927612
\(773\) −5.36128 −0.192832 −0.0964160 0.995341i \(-0.530738\pi\)
−0.0964160 + 0.995341i \(0.530738\pi\)
\(774\) −19.0863 −0.686042
\(775\) 5.46675 0.196371
\(776\) −23.0181 −0.826300
\(777\) −21.2320 −0.761694
\(778\) −73.7871 −2.64540
\(779\) −30.0061 −1.07508
\(780\) 6.94256 0.248584
\(781\) 1.18371 0.0423564
\(782\) 7.81917 0.279613
\(783\) −0.166852 −0.00596279
\(784\) 3.64521 0.130186
\(785\) −19.9957 −0.713676
\(786\) −12.5063 −0.446086
\(787\) −0.227609 −0.00811340 −0.00405670 0.999992i \(-0.501291\pi\)
−0.00405670 + 0.999992i \(0.501291\pi\)
\(788\) 29.9390 1.06653
\(789\) −64.2256 −2.28649
\(790\) −5.75667 −0.204813
\(791\) 9.20303 0.327222
\(792\) −7.96979 −0.283194
\(793\) −2.61160 −0.0927405
\(794\) 10.9127 0.387279
\(795\) 6.68360 0.237043
\(796\) 9.31123 0.330028
\(797\) −0.667487 −0.0236436 −0.0118218 0.999930i \(-0.503763\pi\)
−0.0118218 + 0.999930i \(0.503763\pi\)
\(798\) −64.1316 −2.27023
\(799\) −4.77971 −0.169094
\(800\) −25.6634 −0.907338
\(801\) −20.9611 −0.740623
\(802\) 35.0583 1.23795
\(803\) −16.3115 −0.575621
\(804\) −69.2218 −2.44127
\(805\) −3.06986 −0.108198
\(806\) 3.24423 0.114273
\(807\) −42.6099 −1.49994
\(808\) −11.5634 −0.406799
\(809\) −20.2496 −0.711939 −0.355970 0.934498i \(-0.615849\pi\)
−0.355970 + 0.934498i \(0.615849\pi\)
\(810\) −27.9477 −0.981982
\(811\) −29.6930 −1.04266 −0.521332 0.853354i \(-0.674565\pi\)
−0.521332 + 0.853354i \(0.674565\pi\)
\(812\) 0.287138 0.0100766
\(813\) 46.7760 1.64051
\(814\) 30.6211 1.07327
\(815\) 2.06010 0.0721622
\(816\) 5.90881 0.206850
\(817\) 43.0873 1.50744
\(818\) −13.0733 −0.457096
\(819\) −2.72682 −0.0952828
\(820\) 14.0882 0.491981
\(821\) −24.6566 −0.860520 −0.430260 0.902705i \(-0.641578\pi\)
−0.430260 + 0.902705i \(0.641578\pi\)
\(822\) 16.1868 0.564579
\(823\) 52.6876 1.83657 0.918287 0.395914i \(-0.129572\pi\)
0.918287 + 0.395914i \(0.129572\pi\)
\(824\) −35.0847 −1.22223
\(825\) 20.8161 0.724724
\(826\) −53.0309 −1.84518
\(827\) −26.0073 −0.904362 −0.452181 0.891926i \(-0.649354\pi\)
−0.452181 + 0.891926i \(0.649354\pi\)
\(828\) −5.87479 −0.204163
\(829\) 39.1046 1.35816 0.679080 0.734065i \(-0.262379\pi\)
0.679080 + 0.734065i \(0.262379\pi\)
\(830\) 1.47168 0.0510827
\(831\) 22.3148 0.774092
\(832\) −12.9603 −0.449317
\(833\) −7.97263 −0.276235
\(834\) −28.4958 −0.986730
\(835\) 2.04732 0.0708505
\(836\) 55.2416 1.91057
\(837\) −4.88331 −0.168792
\(838\) −48.8548 −1.68766
\(839\) −8.53239 −0.294571 −0.147285 0.989094i \(-0.547054\pi\)
−0.147285 + 0.989094i \(0.547054\pi\)
\(840\) 9.80679 0.338366
\(841\) −28.9975 −0.999915
\(842\) 0.610626 0.0210436
\(843\) −50.0266 −1.72301
\(844\) 31.4637 1.08302
\(845\) −1.11575 −0.0383830
\(846\) 6.01268 0.206720
\(847\) 7.81939 0.268677
\(848\) −3.24029 −0.111272
\(849\) −13.6974 −0.470093
\(850\) 20.7694 0.712386
\(851\) 7.35148 0.252006
\(852\) −2.78739 −0.0954945
\(853\) 37.3126 1.27756 0.638780 0.769390i \(-0.279440\pi\)
0.638780 + 0.769390i \(0.279440\pi\)
\(854\) −11.3267 −0.387592
\(855\) −11.0186 −0.376827
\(856\) −16.9599 −0.579677
\(857\) −30.7291 −1.04969 −0.524843 0.851199i \(-0.675876\pi\)
−0.524843 + 0.851199i \(0.675876\pi\)
\(858\) 12.3533 0.421734
\(859\) −20.4159 −0.696583 −0.348292 0.937386i \(-0.613238\pi\)
−0.348292 + 0.937386i \(0.613238\pi\)
\(860\) −20.2300 −0.689836
\(861\) −17.3815 −0.592361
\(862\) −83.8497 −2.85593
\(863\) −16.6693 −0.567429 −0.283715 0.958909i \(-0.591567\pi\)
−0.283715 + 0.958909i \(0.591567\pi\)
\(864\) 22.9245 0.779906
\(865\) −17.7716 −0.604252
\(866\) 13.2961 0.451820
\(867\) 22.7404 0.772305
\(868\) 8.40377 0.285243
\(869\) −6.11785 −0.207534
\(870\) 0.259462 0.00879660
\(871\) 11.1248 0.376948
\(872\) 8.28899 0.280701
\(873\) 14.9812 0.507036
\(874\) 22.2053 0.751104
\(875\) −19.0118 −0.642715
\(876\) 38.4103 1.29776
\(877\) −26.1274 −0.882261 −0.441131 0.897443i \(-0.645422\pi\)
−0.441131 + 0.897443i \(0.645422\pi\)
\(878\) 80.0515 2.70161
\(879\) −20.0981 −0.677892
\(880\) 3.34570 0.112784
\(881\) −0.715902 −0.0241194 −0.0120597 0.999927i \(-0.503839\pi\)
−0.0120597 + 0.999927i \(0.503839\pi\)
\(882\) 10.0292 0.337702
\(883\) 8.44911 0.284335 0.142168 0.989843i \(-0.454593\pi\)
0.142168 + 0.989843i \(0.454593\pi\)
\(884\) 7.36160 0.247597
\(885\) −28.6206 −0.962070
\(886\) 0.580669 0.0195080
\(887\) 10.7174 0.359855 0.179928 0.983680i \(-0.442414\pi\)
0.179928 + 0.983680i \(0.442414\pi\)
\(888\) −23.4846 −0.788091
\(889\) 20.3217 0.681567
\(890\) −37.1982 −1.24689
\(891\) −29.7012 −0.995026
\(892\) 15.2146 0.509421
\(893\) −13.5736 −0.454225
\(894\) 106.282 3.55462
\(895\) 17.0627 0.570342
\(896\) −29.6076 −0.989122
\(897\) 2.96577 0.0990240
\(898\) −89.7214 −2.99404
\(899\) 0.0724155 0.00241519
\(900\) −15.6047 −0.520158
\(901\) 7.08701 0.236103
\(902\) 25.0679 0.834669
\(903\) 24.9591 0.830586
\(904\) 10.1794 0.338562
\(905\) 23.8093 0.791449
\(906\) −42.1497 −1.40033
\(907\) −54.7313 −1.81732 −0.908662 0.417532i \(-0.862895\pi\)
−0.908662 + 0.417532i \(0.862895\pi\)
\(908\) 4.45536 0.147856
\(909\) 7.52597 0.249621
\(910\) −4.83911 −0.160415
\(911\) −25.7493 −0.853111 −0.426556 0.904461i \(-0.640273\pi\)
−0.426556 + 0.904461i \(0.640273\pi\)
\(912\) 16.7801 0.555645
\(913\) 1.56401 0.0517613
\(914\) 46.2380 1.52942
\(915\) −6.11298 −0.202089
\(916\) −36.5678 −1.20824
\(917\) 5.20643 0.171932
\(918\) −18.5528 −0.612335
\(919\) −20.9144 −0.689903 −0.344951 0.938621i \(-0.612105\pi\)
−0.344951 + 0.938621i \(0.612105\pi\)
\(920\) −3.39555 −0.111948
\(921\) 39.8003 1.31146
\(922\) −54.6052 −1.79833
\(923\) 0.447967 0.0147450
\(924\) 31.9996 1.05271
\(925\) 19.5272 0.642049
\(926\) 66.8971 2.19838
\(927\) 22.8347 0.749989
\(928\) −0.339951 −0.0111594
\(929\) 31.9503 1.04826 0.524128 0.851640i \(-0.324391\pi\)
0.524128 + 0.851640i \(0.324391\pi\)
\(930\) 7.59379 0.249010
\(931\) −22.6411 −0.742031
\(932\) −30.1302 −0.986947
\(933\) 19.8755 0.650695
\(934\) 55.7784 1.82512
\(935\) −7.31756 −0.239310
\(936\) −3.01612 −0.0985849
\(937\) −20.7257 −0.677079 −0.338540 0.940952i \(-0.609933\pi\)
−0.338540 + 0.940952i \(0.609933\pi\)
\(938\) 48.2490 1.57539
\(939\) −3.46255 −0.112996
\(940\) 6.37297 0.207863
\(941\) −22.7201 −0.740653 −0.370326 0.928902i \(-0.620754\pi\)
−0.370326 + 0.928902i \(0.620754\pi\)
\(942\) 83.7822 2.72977
\(943\) 6.01827 0.195982
\(944\) 13.8756 0.451612
\(945\) 7.28397 0.236948
\(946\) −35.9963 −1.17034
\(947\) 54.4270 1.76864 0.884320 0.466881i \(-0.154622\pi\)
0.884320 + 0.466881i \(0.154622\pi\)
\(948\) 14.4063 0.467894
\(949\) −6.17299 −0.200384
\(950\) 58.9821 1.91363
\(951\) −44.9733 −1.45836
\(952\) 10.3987 0.337024
\(953\) −18.9848 −0.614977 −0.307489 0.951552i \(-0.599489\pi\)
−0.307489 + 0.951552i \(0.599489\pi\)
\(954\) −8.91517 −0.288639
\(955\) 10.7697 0.348499
\(956\) −36.0091 −1.16462
\(957\) 0.275741 0.00891345
\(958\) −79.0028 −2.55246
\(959\) −6.73863 −0.217602
\(960\) −30.3362 −0.979097
\(961\) −28.8806 −0.931632
\(962\) 11.5883 0.373623
\(963\) 11.0382 0.355702
\(964\) −55.9723 −1.80275
\(965\) 9.69549 0.312109
\(966\) 12.8628 0.413853
\(967\) 19.1002 0.614221 0.307111 0.951674i \(-0.400638\pi\)
0.307111 + 0.951674i \(0.400638\pi\)
\(968\) 8.64897 0.277989
\(969\) −36.7007 −1.17900
\(970\) 26.5861 0.853628
\(971\) 8.80471 0.282556 0.141278 0.989970i \(-0.454879\pi\)
0.141278 + 0.989970i \(0.454879\pi\)
\(972\) 40.0932 1.28599
\(973\) 11.8629 0.380308
\(974\) −22.3052 −0.714703
\(975\) 7.87773 0.252289
\(976\) 2.96365 0.0948640
\(977\) 52.1468 1.66832 0.834162 0.551519i \(-0.185952\pi\)
0.834162 + 0.551519i \(0.185952\pi\)
\(978\) −8.63186 −0.276017
\(979\) −39.5321 −1.26345
\(980\) 10.6302 0.339570
\(981\) −5.39484 −0.172244
\(982\) 1.67884 0.0535740
\(983\) −7.98141 −0.254568 −0.127284 0.991866i \(-0.540626\pi\)
−0.127284 + 0.991866i \(0.540626\pi\)
\(984\) −19.2256 −0.612890
\(985\) −11.2624 −0.358851
\(986\) 0.275123 0.00876171
\(987\) −7.86276 −0.250274
\(988\) 20.9058 0.665103
\(989\) −8.64196 −0.274798
\(990\) 9.20519 0.292560
\(991\) −47.0376 −1.49420 −0.747099 0.664713i \(-0.768554\pi\)
−0.747099 + 0.664713i \(0.768554\pi\)
\(992\) −9.94948 −0.315896
\(993\) −64.1241 −2.03492
\(994\) 1.94287 0.0616241
\(995\) −3.50269 −0.111043
\(996\) −3.68293 −0.116698
\(997\) 1.12498 0.0356285 0.0178142 0.999841i \(-0.494329\pi\)
0.0178142 + 0.999841i \(0.494329\pi\)
\(998\) −9.98466 −0.316059
\(999\) −17.4431 −0.551876
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 \(a_p\))