Properties

Label 8021.2.a.a.1.9
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 1.9
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.48308 q^{2}\) \(+1.22996 q^{3}\) \(+4.16571 q^{4}\) \(+3.96003 q^{5}\) \(-3.05409 q^{6}\) \(-1.52214 q^{7}\) \(-5.37763 q^{8}\) \(-1.48721 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.48308 q^{2}\) \(+1.22996 q^{3}\) \(+4.16571 q^{4}\) \(+3.96003 q^{5}\) \(-3.05409 q^{6}\) \(-1.52214 q^{7}\) \(-5.37763 q^{8}\) \(-1.48721 q^{9}\) \(-9.83308 q^{10}\) \(+3.53545 q^{11}\) \(+5.12364 q^{12}\) \(+1.00000 q^{13}\) \(+3.77960 q^{14}\) \(+4.87066 q^{15}\) \(+5.02170 q^{16}\) \(-4.34507 q^{17}\) \(+3.69286 q^{18}\) \(-4.22546 q^{19}\) \(+16.4963 q^{20}\) \(-1.87217 q^{21}\) \(-8.77881 q^{22}\) \(-2.12271 q^{23}\) \(-6.61425 q^{24}\) \(+10.6818 q^{25}\) \(-2.48308 q^{26}\) \(-5.51907 q^{27}\) \(-6.34079 q^{28}\) \(+3.03990 q^{29}\) \(-12.0943 q^{30}\) \(-3.99192 q^{31}\) \(-1.71403 q^{32}\) \(+4.34845 q^{33}\) \(+10.7892 q^{34}\) \(-6.02771 q^{35}\) \(-6.19527 q^{36}\) \(+1.67262 q^{37}\) \(+10.4922 q^{38}\) \(+1.22996 q^{39}\) \(-21.2956 q^{40}\) \(-4.58133 q^{41}\) \(+4.64875 q^{42}\) \(+0.939516 q^{43}\) \(+14.7276 q^{44}\) \(-5.88938 q^{45}\) \(+5.27087 q^{46}\) \(-7.91434 q^{47}\) \(+6.17647 q^{48}\) \(-4.68309 q^{49}\) \(-26.5238 q^{50}\) \(-5.34425 q^{51}\) \(+4.16571 q^{52}\) \(-3.48634 q^{53}\) \(+13.7043 q^{54}\) \(+14.0005 q^{55}\) \(+8.18551 q^{56}\) \(-5.19713 q^{57}\) \(-7.54833 q^{58}\) \(-6.34877 q^{59}\) \(+20.2897 q^{60}\) \(+5.63188 q^{61}\) \(+9.91227 q^{62}\) \(+2.26374 q^{63}\) \(-5.78731 q^{64}\) \(+3.96003 q^{65}\) \(-10.7976 q^{66}\) \(-11.1244 q^{67}\) \(-18.1003 q^{68}\) \(-2.61084 q^{69}\) \(+14.9673 q^{70}\) \(-11.6419 q^{71}\) \(+7.99765 q^{72}\) \(+7.26666 q^{73}\) \(-4.15325 q^{74}\) \(+13.1382 q^{75}\) \(-17.6020 q^{76}\) \(-5.38145 q^{77}\) \(-3.05409 q^{78}\) \(-3.57287 q^{79}\) \(+19.8860 q^{80}\) \(-2.32659 q^{81}\) \(+11.3758 q^{82}\) \(+6.26776 q^{83}\) \(-7.79889 q^{84}\) \(-17.2066 q^{85}\) \(-2.33290 q^{86}\) \(+3.73895 q^{87}\) \(-19.0123 q^{88}\) \(-6.28391 q^{89}\) \(+14.6238 q^{90}\) \(-1.52214 q^{91}\) \(-8.84259 q^{92}\) \(-4.90989 q^{93}\) \(+19.6520 q^{94}\) \(-16.7329 q^{95}\) \(-2.10818 q^{96}\) \(-1.35998 q^{97}\) \(+11.6285 q^{98}\) \(-5.25794 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 53q^{12} \) \(\mathstrut +\mathstrut 134q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 87q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 52q^{22} \) \(\mathstrut -\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 117q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 21q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 86q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 54q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 57q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 148q^{55} \) \(\mathstrut -\mathstrut 47q^{56} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 64q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut -\mathstrut 58q^{63} \) \(\mathstrut -\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 110q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 150q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 228q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 77q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 62q^{92} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 87q^{94} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 193q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.48308 −1.75581 −0.877903 0.478839i \(-0.841058\pi\)
−0.877903 + 0.478839i \(0.841058\pi\)
\(3\) 1.22996 0.710116 0.355058 0.934844i \(-0.384461\pi\)
0.355058 + 0.934844i \(0.384461\pi\)
\(4\) 4.16571 2.08285
\(5\) 3.96003 1.77098 0.885489 0.464661i \(-0.153824\pi\)
0.885489 + 0.464661i \(0.153824\pi\)
\(6\) −3.05409 −1.24683
\(7\) −1.52214 −0.575315 −0.287657 0.957733i \(-0.592876\pi\)
−0.287657 + 0.957733i \(0.592876\pi\)
\(8\) −5.37763 −1.90128
\(9\) −1.48721 −0.495736
\(10\) −9.83308 −3.10949
\(11\) 3.53545 1.06598 0.532989 0.846122i \(-0.321069\pi\)
0.532989 + 0.846122i \(0.321069\pi\)
\(12\) 5.12364 1.47907
\(13\) 1.00000 0.277350
\(14\) 3.77960 1.01014
\(15\) 4.87066 1.25760
\(16\) 5.02170 1.25542
\(17\) −4.34507 −1.05383 −0.526917 0.849917i \(-0.676652\pi\)
−0.526917 + 0.849917i \(0.676652\pi\)
\(18\) 3.69286 0.870416
\(19\) −4.22546 −0.969387 −0.484693 0.874684i \(-0.661069\pi\)
−0.484693 + 0.874684i \(0.661069\pi\)
\(20\) 16.4963 3.68869
\(21\) −1.87217 −0.408540
\(22\) −8.77881 −1.87165
\(23\) −2.12271 −0.442616 −0.221308 0.975204i \(-0.571033\pi\)
−0.221308 + 0.975204i \(0.571033\pi\)
\(24\) −6.61425 −1.35013
\(25\) 10.6818 2.13636
\(26\) −2.48308 −0.486973
\(27\) −5.51907 −1.06215
\(28\) −6.34079 −1.19830
\(29\) 3.03990 0.564496 0.282248 0.959342i \(-0.408920\pi\)
0.282248 + 0.959342i \(0.408920\pi\)
\(30\) −12.0943 −2.20810
\(31\) −3.99192 −0.716970 −0.358485 0.933535i \(-0.616707\pi\)
−0.358485 + 0.933535i \(0.616707\pi\)
\(32\) −1.71403 −0.303001
\(33\) 4.34845 0.756967
\(34\) 10.7892 1.85033
\(35\) −6.02771 −1.01887
\(36\) −6.19527 −1.03254
\(37\) 1.67262 0.274976 0.137488 0.990503i \(-0.456097\pi\)
0.137488 + 0.990503i \(0.456097\pi\)
\(38\) 10.4922 1.70205
\(39\) 1.22996 0.196951
\(40\) −21.2956 −3.36712
\(41\) −4.58133 −0.715484 −0.357742 0.933820i \(-0.616453\pi\)
−0.357742 + 0.933820i \(0.616453\pi\)
\(42\) 4.64875 0.717317
\(43\) 0.939516 0.143275 0.0716375 0.997431i \(-0.477178\pi\)
0.0716375 + 0.997431i \(0.477178\pi\)
\(44\) 14.7276 2.22027
\(45\) −5.88938 −0.877937
\(46\) 5.27087 0.777147
\(47\) −7.91434 −1.15443 −0.577213 0.816594i \(-0.695860\pi\)
−0.577213 + 0.816594i \(0.695860\pi\)
\(48\) 6.17647 0.891496
\(49\) −4.68309 −0.669013
\(50\) −26.5238 −3.75103
\(51\) −5.34425 −0.748344
\(52\) 4.16571 0.577680
\(53\) −3.48634 −0.478885 −0.239443 0.970911i \(-0.576965\pi\)
−0.239443 + 0.970911i \(0.576965\pi\)
\(54\) 13.7043 1.86492
\(55\) 14.0005 1.88782
\(56\) 8.18551 1.09383
\(57\) −5.19713 −0.688377
\(58\) −7.54833 −0.991144
\(59\) −6.34877 −0.826540 −0.413270 0.910609i \(-0.635613\pi\)
−0.413270 + 0.910609i \(0.635613\pi\)
\(60\) 20.2897 2.61939
\(61\) 5.63188 0.721088 0.360544 0.932742i \(-0.382591\pi\)
0.360544 + 0.932742i \(0.382591\pi\)
\(62\) 9.91227 1.25886
\(63\) 2.26374 0.285204
\(64\) −5.78731 −0.723413
\(65\) 3.96003 0.491181
\(66\) −10.7976 −1.32909
\(67\) −11.1244 −1.35907 −0.679534 0.733644i \(-0.737818\pi\)
−0.679534 + 0.733644i \(0.737818\pi\)
\(68\) −18.1003 −2.19498
\(69\) −2.61084 −0.314308
\(70\) 14.9673 1.78894
\(71\) −11.6419 −1.38164 −0.690818 0.723028i \(-0.742750\pi\)
−0.690818 + 0.723028i \(0.742750\pi\)
\(72\) 7.99765 0.942532
\(73\) 7.26666 0.850498 0.425249 0.905076i \(-0.360187\pi\)
0.425249 + 0.905076i \(0.360187\pi\)
\(74\) −4.15325 −0.482805
\(75\) 13.1382 1.51706
\(76\) −17.6020 −2.01909
\(77\) −5.38145 −0.613273
\(78\) −3.05409 −0.345807
\(79\) −3.57287 −0.401980 −0.200990 0.979593i \(-0.564416\pi\)
−0.200990 + 0.979593i \(0.564416\pi\)
\(80\) 19.8860 2.22333
\(81\) −2.32659 −0.258510
\(82\) 11.3758 1.25625
\(83\) 6.26776 0.687976 0.343988 0.938974i \(-0.388222\pi\)
0.343988 + 0.938974i \(0.388222\pi\)
\(84\) −7.79889 −0.850929
\(85\) −17.2066 −1.86632
\(86\) −2.33290 −0.251563
\(87\) 3.73895 0.400857
\(88\) −19.0123 −2.02672
\(89\) −6.28391 −0.666093 −0.333047 0.942910i \(-0.608077\pi\)
−0.333047 + 0.942910i \(0.608077\pi\)
\(90\) 14.6238 1.54149
\(91\) −1.52214 −0.159564
\(92\) −8.84259 −0.921903
\(93\) −4.90989 −0.509132
\(94\) 19.6520 2.02695
\(95\) −16.7329 −1.71676
\(96\) −2.10818 −0.215166
\(97\) −1.35998 −0.138085 −0.0690423 0.997614i \(-0.521994\pi\)
−0.0690423 + 0.997614i \(0.521994\pi\)
\(98\) 11.6285 1.17466
\(99\) −5.25794 −0.528443
\(100\) 44.4973 4.44973
\(101\) 19.3491 1.92530 0.962651 0.270744i \(-0.0872697\pi\)
0.962651 + 0.270744i \(0.0872697\pi\)
\(102\) 13.2702 1.31395
\(103\) 11.3555 1.11889 0.559447 0.828866i \(-0.311013\pi\)
0.559447 + 0.828866i \(0.311013\pi\)
\(104\) −5.37763 −0.527320
\(105\) −7.41383 −0.723515
\(106\) 8.65687 0.840829
\(107\) 3.44688 0.333222 0.166611 0.986023i \(-0.446718\pi\)
0.166611 + 0.986023i \(0.446718\pi\)
\(108\) −22.9908 −2.21229
\(109\) 9.86710 0.945097 0.472548 0.881305i \(-0.343334\pi\)
0.472548 + 0.881305i \(0.343334\pi\)
\(110\) −34.7643 −3.31465
\(111\) 2.05724 0.195265
\(112\) −7.64373 −0.722264
\(113\) −2.66934 −0.251111 −0.125555 0.992087i \(-0.540071\pi\)
−0.125555 + 0.992087i \(0.540071\pi\)
\(114\) 12.9049 1.20866
\(115\) −8.40599 −0.783862
\(116\) 12.6633 1.17576
\(117\) −1.48721 −0.137492
\(118\) 15.7645 1.45124
\(119\) 6.61380 0.606286
\(120\) −26.1926 −2.39105
\(121\) 1.49939 0.136308
\(122\) −13.9844 −1.26609
\(123\) −5.63484 −0.508076
\(124\) −16.6292 −1.49334
\(125\) 22.5001 2.01247
\(126\) −5.62105 −0.500763
\(127\) 5.89144 0.522781 0.261391 0.965233i \(-0.415819\pi\)
0.261391 + 0.965233i \(0.415819\pi\)
\(128\) 17.7984 1.57317
\(129\) 1.15556 0.101742
\(130\) −9.83308 −0.862418
\(131\) −5.59868 −0.489159 −0.244580 0.969629i \(-0.578650\pi\)
−0.244580 + 0.969629i \(0.578650\pi\)
\(132\) 18.1143 1.57665
\(133\) 6.43174 0.557703
\(134\) 27.6229 2.38626
\(135\) −21.8557 −1.88104
\(136\) 23.3662 2.00363
\(137\) −14.2111 −1.21414 −0.607068 0.794650i \(-0.707654\pi\)
−0.607068 + 0.794650i \(0.707654\pi\)
\(138\) 6.48294 0.551864
\(139\) −15.5376 −1.31788 −0.658940 0.752196i \(-0.728995\pi\)
−0.658940 + 0.752196i \(0.728995\pi\)
\(140\) −25.1097 −2.12216
\(141\) −9.73430 −0.819776
\(142\) 28.9078 2.42589
\(143\) 3.53545 0.295649
\(144\) −7.46830 −0.622359
\(145\) 12.0381 0.999709
\(146\) −18.0437 −1.49331
\(147\) −5.76000 −0.475076
\(148\) 6.96763 0.572735
\(149\) −20.7384 −1.69895 −0.849477 0.527625i \(-0.823083\pi\)
−0.849477 + 0.527625i \(0.823083\pi\)
\(150\) −32.6231 −2.66367
\(151\) −10.6197 −0.864218 −0.432109 0.901821i \(-0.642230\pi\)
−0.432109 + 0.901821i \(0.642230\pi\)
\(152\) 22.7230 1.84308
\(153\) 6.46202 0.522423
\(154\) 13.3626 1.07679
\(155\) −15.8081 −1.26974
\(156\) 5.12364 0.410219
\(157\) −24.9115 −1.98815 −0.994077 0.108681i \(-0.965337\pi\)
−0.994077 + 0.108681i \(0.965337\pi\)
\(158\) 8.87175 0.705798
\(159\) −4.28804 −0.340064
\(160\) −6.78761 −0.536608
\(161\) 3.23106 0.254643
\(162\) 5.77713 0.453894
\(163\) 21.7326 1.70223 0.851116 0.524978i \(-0.175926\pi\)
0.851116 + 0.524978i \(0.175926\pi\)
\(164\) −19.0845 −1.49025
\(165\) 17.2200 1.34057
\(166\) −15.5634 −1.20795
\(167\) 10.3024 0.797224 0.398612 0.917120i \(-0.369492\pi\)
0.398612 + 0.917120i \(0.369492\pi\)
\(168\) 10.0678 0.776749
\(169\) 1.00000 0.0769231
\(170\) 42.7254 3.27689
\(171\) 6.28413 0.480560
\(172\) 3.91375 0.298421
\(173\) −16.1482 −1.22773 −0.613863 0.789413i \(-0.710385\pi\)
−0.613863 + 0.789413i \(0.710385\pi\)
\(174\) −9.28412 −0.703827
\(175\) −16.2592 −1.22908
\(176\) 17.7539 1.33825
\(177\) −7.80871 −0.586939
\(178\) 15.6035 1.16953
\(179\) −0.973105 −0.0727333 −0.0363667 0.999339i \(-0.511578\pi\)
−0.0363667 + 0.999339i \(0.511578\pi\)
\(180\) −24.5334 −1.82861
\(181\) −3.35889 −0.249664 −0.124832 0.992178i \(-0.539839\pi\)
−0.124832 + 0.992178i \(0.539839\pi\)
\(182\) 3.77960 0.280163
\(183\) 6.92697 0.512056
\(184\) 11.4152 0.841536
\(185\) 6.62360 0.486977
\(186\) 12.1917 0.893936
\(187\) −15.3618 −1.12336
\(188\) −32.9688 −2.40450
\(189\) 8.40080 0.611068
\(190\) 41.5493 3.01430
\(191\) −1.88438 −0.136349 −0.0681745 0.997673i \(-0.521717\pi\)
−0.0681745 + 0.997673i \(0.521717\pi\)
\(192\) −7.11814 −0.513707
\(193\) 10.4790 0.754292 0.377146 0.926154i \(-0.376905\pi\)
0.377146 + 0.926154i \(0.376905\pi\)
\(194\) 3.37693 0.242450
\(195\) 4.87066 0.348795
\(196\) −19.5084 −1.39346
\(197\) 11.7830 0.839504 0.419752 0.907639i \(-0.362117\pi\)
0.419752 + 0.907639i \(0.362117\pi\)
\(198\) 13.0559 0.927843
\(199\) −19.8094 −1.40425 −0.702126 0.712053i \(-0.747766\pi\)
−0.702126 + 0.712053i \(0.747766\pi\)
\(200\) −57.4428 −4.06182
\(201\) −13.6826 −0.965095
\(202\) −48.0453 −3.38046
\(203\) −4.62716 −0.324763
\(204\) −22.2626 −1.55869
\(205\) −18.1422 −1.26711
\(206\) −28.1968 −1.96456
\(207\) 3.15691 0.219420
\(208\) 5.02170 0.348192
\(209\) −14.9389 −1.03334
\(210\) 18.4092 1.27035
\(211\) −16.4613 −1.13324 −0.566622 0.823978i \(-0.691750\pi\)
−0.566622 + 0.823978i \(0.691750\pi\)
\(212\) −14.5231 −0.997448
\(213\) −14.3190 −0.981122
\(214\) −8.55889 −0.585074
\(215\) 3.72051 0.253737
\(216\) 29.6795 2.01944
\(217\) 6.07626 0.412484
\(218\) −24.5008 −1.65941
\(219\) 8.93767 0.603952
\(220\) 58.3218 3.93206
\(221\) −4.34507 −0.292281
\(222\) −5.10831 −0.342847
\(223\) 8.94287 0.598859 0.299429 0.954118i \(-0.403204\pi\)
0.299429 + 0.954118i \(0.403204\pi\)
\(224\) 2.60900 0.174321
\(225\) −15.8861 −1.05907
\(226\) 6.62820 0.440902
\(227\) −17.1723 −1.13977 −0.569883 0.821726i \(-0.693012\pi\)
−0.569883 + 0.821726i \(0.693012\pi\)
\(228\) −21.6497 −1.43379
\(229\) −7.31679 −0.483507 −0.241754 0.970338i \(-0.577723\pi\)
−0.241754 + 0.970338i \(0.577723\pi\)
\(230\) 20.8728 1.37631
\(231\) −6.61894 −0.435495
\(232\) −16.3475 −1.07326
\(233\) −1.34734 −0.0882669 −0.0441335 0.999026i \(-0.514053\pi\)
−0.0441335 + 0.999026i \(0.514053\pi\)
\(234\) 3.69286 0.241410
\(235\) −31.3410 −2.04446
\(236\) −26.4471 −1.72156
\(237\) −4.39448 −0.285452
\(238\) −16.4226 −1.06452
\(239\) 0.469954 0.0303988 0.0151994 0.999884i \(-0.495162\pi\)
0.0151994 + 0.999884i \(0.495162\pi\)
\(240\) 24.4590 1.57882
\(241\) 28.8992 1.86156 0.930780 0.365580i \(-0.119129\pi\)
0.930780 + 0.365580i \(0.119129\pi\)
\(242\) −3.72310 −0.239330
\(243\) 13.6956 0.878573
\(244\) 23.4608 1.50192
\(245\) −18.5452 −1.18481
\(246\) 13.9918 0.892084
\(247\) −4.22546 −0.268860
\(248\) 21.4671 1.36316
\(249\) 7.70907 0.488543
\(250\) −55.8696 −3.53350
\(251\) 6.52086 0.411593 0.205797 0.978595i \(-0.434021\pi\)
0.205797 + 0.978595i \(0.434021\pi\)
\(252\) 9.43007 0.594038
\(253\) −7.50473 −0.471818
\(254\) −14.6290 −0.917902
\(255\) −21.1633 −1.32530
\(256\) −32.6204 −2.03877
\(257\) 15.2444 0.950918 0.475459 0.879738i \(-0.342282\pi\)
0.475459 + 0.879738i \(0.342282\pi\)
\(258\) −2.86936 −0.178639
\(259\) −2.54596 −0.158198
\(260\) 16.4963 1.02306
\(261\) −4.52096 −0.279841
\(262\) 13.9020 0.858869
\(263\) −31.6443 −1.95127 −0.975637 0.219392i \(-0.929593\pi\)
−0.975637 + 0.219392i \(0.929593\pi\)
\(264\) −23.3843 −1.43921
\(265\) −13.8060 −0.848095
\(266\) −15.9706 −0.979217
\(267\) −7.72894 −0.473003
\(268\) −46.3412 −2.83074
\(269\) −10.7238 −0.653844 −0.326922 0.945051i \(-0.606011\pi\)
−0.326922 + 0.945051i \(0.606011\pi\)
\(270\) 54.2694 3.30273
\(271\) −30.2525 −1.83771 −0.918854 0.394599i \(-0.870884\pi\)
−0.918854 + 0.394599i \(0.870884\pi\)
\(272\) −21.8196 −1.32301
\(273\) −1.87217 −0.113309
\(274\) 35.2874 2.13179
\(275\) 37.7650 2.27731
\(276\) −10.8760 −0.654658
\(277\) −26.2097 −1.57479 −0.787393 0.616452i \(-0.788570\pi\)
−0.787393 + 0.616452i \(0.788570\pi\)
\(278\) 38.5811 2.31394
\(279\) 5.93681 0.355428
\(280\) 32.4148 1.93716
\(281\) −12.6806 −0.756460 −0.378230 0.925712i \(-0.623467\pi\)
−0.378230 + 0.925712i \(0.623467\pi\)
\(282\) 24.1711 1.43937
\(283\) −6.31162 −0.375187 −0.187593 0.982247i \(-0.560069\pi\)
−0.187593 + 0.982247i \(0.560069\pi\)
\(284\) −48.4966 −2.87775
\(285\) −20.5808 −1.21910
\(286\) −8.77881 −0.519102
\(287\) 6.97343 0.411629
\(288\) 2.54912 0.150208
\(289\) 1.87962 0.110566
\(290\) −29.8916 −1.75529
\(291\) −1.67271 −0.0980560
\(292\) 30.2708 1.77146
\(293\) 7.91731 0.462534 0.231267 0.972890i \(-0.425713\pi\)
0.231267 + 0.972890i \(0.425713\pi\)
\(294\) 14.3026 0.834142
\(295\) −25.1413 −1.46378
\(296\) −8.99471 −0.522807
\(297\) −19.5124 −1.13222
\(298\) 51.4952 2.98303
\(299\) −2.12271 −0.122759
\(300\) 54.7297 3.15982
\(301\) −1.43008 −0.0824282
\(302\) 26.3696 1.51740
\(303\) 23.7985 1.36719
\(304\) −21.2190 −1.21699
\(305\) 22.3024 1.27703
\(306\) −16.0457 −0.917273
\(307\) −8.25869 −0.471348 −0.235674 0.971832i \(-0.575730\pi\)
−0.235674 + 0.971832i \(0.575730\pi\)
\(308\) −22.4175 −1.27736
\(309\) 13.9668 0.794545
\(310\) 39.2529 2.22941
\(311\) −11.4474 −0.649125 −0.324562 0.945864i \(-0.605217\pi\)
−0.324562 + 0.945864i \(0.605217\pi\)
\(312\) −6.61425 −0.374458
\(313\) 18.9042 1.06853 0.534264 0.845318i \(-0.320589\pi\)
0.534264 + 0.845318i \(0.320589\pi\)
\(314\) 61.8573 3.49081
\(315\) 8.96446 0.505090
\(316\) −14.8835 −0.837265
\(317\) 31.3944 1.76328 0.881642 0.471919i \(-0.156439\pi\)
0.881642 + 0.471919i \(0.156439\pi\)
\(318\) 10.6476 0.597086
\(319\) 10.7474 0.601739
\(320\) −22.9179 −1.28115
\(321\) 4.23951 0.236626
\(322\) −8.02300 −0.447104
\(323\) 18.3599 1.02157
\(324\) −9.69191 −0.538439
\(325\) 10.6818 0.592520
\(326\) −53.9640 −2.98879
\(327\) 12.1361 0.671128
\(328\) 24.6367 1.36034
\(329\) 12.0467 0.664158
\(330\) −42.7586 −2.35378
\(331\) 23.5685 1.29544 0.647722 0.761877i \(-0.275722\pi\)
0.647722 + 0.761877i \(0.275722\pi\)
\(332\) 26.1097 1.43295
\(333\) −2.48753 −0.136316
\(334\) −25.5817 −1.39977
\(335\) −44.0531 −2.40688
\(336\) −9.40145 −0.512891
\(337\) −34.0654 −1.85566 −0.927832 0.373000i \(-0.878329\pi\)
−0.927832 + 0.373000i \(0.878329\pi\)
\(338\) −2.48308 −0.135062
\(339\) −3.28318 −0.178318
\(340\) −71.6776 −3.88726
\(341\) −14.1132 −0.764274
\(342\) −15.6040 −0.843769
\(343\) 17.7833 0.960208
\(344\) −5.05237 −0.272406
\(345\) −10.3390 −0.556633
\(346\) 40.0974 2.15565
\(347\) 20.1030 1.07919 0.539593 0.841926i \(-0.318578\pi\)
0.539593 + 0.841926i \(0.318578\pi\)
\(348\) 15.5754 0.834927
\(349\) 16.6339 0.890391 0.445195 0.895433i \(-0.353134\pi\)
0.445195 + 0.895433i \(0.353134\pi\)
\(350\) 40.3730 2.15803
\(351\) −5.51907 −0.294586
\(352\) −6.05987 −0.322992
\(353\) 2.56768 0.136664 0.0683320 0.997663i \(-0.478232\pi\)
0.0683320 + 0.997663i \(0.478232\pi\)
\(354\) 19.3897 1.03055
\(355\) −46.1021 −2.44685
\(356\) −26.1769 −1.38737
\(357\) 8.13469 0.430534
\(358\) 2.41630 0.127706
\(359\) −17.9408 −0.946880 −0.473440 0.880826i \(-0.656988\pi\)
−0.473440 + 0.880826i \(0.656988\pi\)
\(360\) 31.6709 1.66920
\(361\) −1.14550 −0.0602894
\(362\) 8.34040 0.438362
\(363\) 1.84418 0.0967943
\(364\) −6.34079 −0.332348
\(365\) 28.7761 1.50621
\(366\) −17.2002 −0.899071
\(367\) 3.44745 0.179955 0.0899777 0.995944i \(-0.471320\pi\)
0.0899777 + 0.995944i \(0.471320\pi\)
\(368\) −10.6596 −0.555670
\(369\) 6.81339 0.354691
\(370\) −16.4470 −0.855037
\(371\) 5.30669 0.275510
\(372\) −20.4532 −1.06045
\(373\) 8.98400 0.465174 0.232587 0.972576i \(-0.425281\pi\)
0.232587 + 0.972576i \(0.425281\pi\)
\(374\) 38.1445 1.97241
\(375\) 27.6741 1.42909
\(376\) 42.5604 2.19489
\(377\) 3.03990 0.156563
\(378\) −20.8599 −1.07292
\(379\) −14.5587 −0.747828 −0.373914 0.927463i \(-0.621984\pi\)
−0.373914 + 0.927463i \(0.621984\pi\)
\(380\) −69.7045 −3.57576
\(381\) 7.24622 0.371235
\(382\) 4.67908 0.239402
\(383\) −4.91235 −0.251010 −0.125505 0.992093i \(-0.540055\pi\)
−0.125505 + 0.992093i \(0.540055\pi\)
\(384\) 21.8913 1.11714
\(385\) −21.3107 −1.08609
\(386\) −26.0201 −1.32439
\(387\) −1.39726 −0.0710265
\(388\) −5.66526 −0.287610
\(389\) 17.5598 0.890315 0.445157 0.895452i \(-0.353148\pi\)
0.445157 + 0.895452i \(0.353148\pi\)
\(390\) −12.0943 −0.612416
\(391\) 9.22332 0.466443
\(392\) 25.1839 1.27198
\(393\) −6.88614 −0.347360
\(394\) −29.2582 −1.47401
\(395\) −14.1487 −0.711897
\(396\) −21.9030 −1.10067
\(397\) −17.6111 −0.883873 −0.441937 0.897046i \(-0.645708\pi\)
−0.441937 + 0.897046i \(0.645708\pi\)
\(398\) 49.1884 2.46559
\(399\) 7.91076 0.396033
\(400\) 53.6408 2.68204
\(401\) 19.4817 0.972872 0.486436 0.873716i \(-0.338297\pi\)
0.486436 + 0.873716i \(0.338297\pi\)
\(402\) 33.9750 1.69452
\(403\) −3.99192 −0.198852
\(404\) 80.6025 4.01012
\(405\) −9.21337 −0.457816
\(406\) 11.4896 0.570220
\(407\) 5.91344 0.293119
\(408\) 28.7394 1.42281
\(409\) 32.4828 1.60617 0.803084 0.595865i \(-0.203191\pi\)
0.803084 + 0.595865i \(0.203191\pi\)
\(410\) 45.0486 2.22479
\(411\) −17.4790 −0.862177
\(412\) 47.3038 2.33049
\(413\) 9.66372 0.475521
\(414\) −7.83887 −0.385260
\(415\) 24.8205 1.21839
\(416\) −1.71403 −0.0840373
\(417\) −19.1105 −0.935847
\(418\) 37.0945 1.81435
\(419\) −14.4814 −0.707461 −0.353730 0.935347i \(-0.615087\pi\)
−0.353730 + 0.935347i \(0.615087\pi\)
\(420\) −30.8838 −1.50698
\(421\) 5.24430 0.255592 0.127796 0.991801i \(-0.459210\pi\)
0.127796 + 0.991801i \(0.459210\pi\)
\(422\) 40.8749 1.98976
\(423\) 11.7703 0.572290
\(424\) 18.7482 0.910495
\(425\) −46.4132 −2.25137
\(426\) 35.5553 1.72266
\(427\) −8.57251 −0.414853
\(428\) 14.3587 0.694053
\(429\) 4.34845 0.209945
\(430\) −9.23834 −0.445512
\(431\) 35.5231 1.71109 0.855544 0.517731i \(-0.173223\pi\)
0.855544 + 0.517731i \(0.173223\pi\)
\(432\) −27.7151 −1.33344
\(433\) −8.67821 −0.417048 −0.208524 0.978017i \(-0.566866\pi\)
−0.208524 + 0.978017i \(0.566866\pi\)
\(434\) −15.0879 −0.724241
\(435\) 14.8063 0.709909
\(436\) 41.1034 1.96850
\(437\) 8.96942 0.429066
\(438\) −22.1930 −1.06042
\(439\) −18.1770 −0.867541 −0.433770 0.901023i \(-0.642817\pi\)
−0.433770 + 0.901023i \(0.642817\pi\)
\(440\) −75.2893 −3.58928
\(441\) 6.96472 0.331654
\(442\) 10.7892 0.513189
\(443\) 21.6124 1.02684 0.513418 0.858138i \(-0.328379\pi\)
0.513418 + 0.858138i \(0.328379\pi\)
\(444\) 8.56988 0.406708
\(445\) −24.8845 −1.17964
\(446\) −22.2059 −1.05148
\(447\) −25.5073 −1.20645
\(448\) 8.80909 0.416190
\(449\) −2.77970 −0.131182 −0.0655910 0.997847i \(-0.520893\pi\)
−0.0655910 + 0.997847i \(0.520893\pi\)
\(450\) 39.4464 1.85952
\(451\) −16.1971 −0.762690
\(452\) −11.1197 −0.523027
\(453\) −13.0618 −0.613695
\(454\) 42.6403 2.00121
\(455\) −6.02771 −0.282584
\(456\) 27.9482 1.30880
\(457\) 2.30183 0.107675 0.0538375 0.998550i \(-0.482855\pi\)
0.0538375 + 0.998550i \(0.482855\pi\)
\(458\) 18.1682 0.848944
\(459\) 23.9807 1.11932
\(460\) −35.0169 −1.63267
\(461\) 27.2955 1.27128 0.635639 0.771987i \(-0.280737\pi\)
0.635639 + 0.771987i \(0.280737\pi\)
\(462\) 16.4354 0.764644
\(463\) 1.07563 0.0499887 0.0249944 0.999688i \(-0.492043\pi\)
0.0249944 + 0.999688i \(0.492043\pi\)
\(464\) 15.2655 0.708681
\(465\) −19.4433 −0.901661
\(466\) 3.34555 0.154980
\(467\) −35.1459 −1.62636 −0.813179 0.582013i \(-0.802265\pi\)
−0.813179 + 0.582013i \(0.802265\pi\)
\(468\) −6.19527 −0.286376
\(469\) 16.9330 0.781892
\(470\) 77.8224 3.58968
\(471\) −30.6400 −1.41182
\(472\) 34.1413 1.57148
\(473\) 3.32161 0.152728
\(474\) 10.9119 0.501198
\(475\) −45.1355 −2.07096
\(476\) 27.5512 1.26281
\(477\) 5.18491 0.237401
\(478\) −1.16694 −0.0533744
\(479\) 20.8085 0.950764 0.475382 0.879779i \(-0.342310\pi\)
0.475382 + 0.879779i \(0.342310\pi\)
\(480\) −8.34847 −0.381054
\(481\) 1.67262 0.0762647
\(482\) −71.7591 −3.26854
\(483\) 3.97407 0.180826
\(484\) 6.24600 0.283909
\(485\) −5.38554 −0.244545
\(486\) −34.0073 −1.54260
\(487\) 26.0142 1.17882 0.589408 0.807835i \(-0.299361\pi\)
0.589408 + 0.807835i \(0.299361\pi\)
\(488\) −30.2862 −1.37099
\(489\) 26.7302 1.20878
\(490\) 46.0492 2.08029
\(491\) 31.6352 1.42767 0.713837 0.700312i \(-0.246956\pi\)
0.713837 + 0.700312i \(0.246956\pi\)
\(492\) −23.4731 −1.05825
\(493\) −13.2086 −0.594885
\(494\) 10.4922 0.472065
\(495\) −20.8216 −0.935861
\(496\) −20.0462 −0.900102
\(497\) 17.7206 0.794876
\(498\) −19.1423 −0.857786
\(499\) −25.9286 −1.16072 −0.580361 0.814359i \(-0.697089\pi\)
−0.580361 + 0.814359i \(0.697089\pi\)
\(500\) 93.7288 4.19168
\(501\) 12.6715 0.566121
\(502\) −16.1918 −0.722677
\(503\) 20.2039 0.900847 0.450424 0.892815i \(-0.351273\pi\)
0.450424 + 0.892815i \(0.351273\pi\)
\(504\) −12.1735 −0.542253
\(505\) 76.6228 3.40967
\(506\) 18.6349 0.828421
\(507\) 1.22996 0.0546243
\(508\) 24.5420 1.08888
\(509\) −35.4402 −1.57086 −0.785430 0.618951i \(-0.787558\pi\)
−0.785430 + 0.618951i \(0.787558\pi\)
\(510\) 52.5504 2.32697
\(511\) −11.0609 −0.489304
\(512\) 45.4023 2.00652
\(513\) 23.3206 1.02963
\(514\) −37.8531 −1.66963
\(515\) 44.9682 1.98154
\(516\) 4.81374 0.211913
\(517\) −27.9807 −1.23059
\(518\) 6.32182 0.277765
\(519\) −19.8616 −0.871827
\(520\) −21.2956 −0.933872
\(521\) 29.2589 1.28186 0.640929 0.767601i \(-0.278549\pi\)
0.640929 + 0.767601i \(0.278549\pi\)
\(522\) 11.2259 0.491346
\(523\) 2.29827 0.100496 0.0502482 0.998737i \(-0.483999\pi\)
0.0502482 + 0.998737i \(0.483999\pi\)
\(524\) −23.3225 −1.01885
\(525\) −19.9981 −0.872789
\(526\) 78.5756 3.42606
\(527\) 17.3452 0.755568
\(528\) 21.8366 0.950315
\(529\) −18.4941 −0.804091
\(530\) 34.2814 1.48909
\(531\) 9.44194 0.409745
\(532\) 26.7927 1.16161
\(533\) −4.58133 −0.198440
\(534\) 19.1916 0.830502
\(535\) 13.6497 0.590129
\(536\) 59.8232 2.58397
\(537\) −1.19688 −0.0516491
\(538\) 26.6282 1.14802
\(539\) −16.5568 −0.713152
\(540\) −91.0442 −3.91792
\(541\) −1.78231 −0.0766275 −0.0383138 0.999266i \(-0.512199\pi\)
−0.0383138 + 0.999266i \(0.512199\pi\)
\(542\) 75.1194 3.22666
\(543\) −4.13129 −0.177290
\(544\) 7.44759 0.319313
\(545\) 39.0740 1.67375
\(546\) 4.64875 0.198948
\(547\) 29.0846 1.24357 0.621785 0.783188i \(-0.286408\pi\)
0.621785 + 0.783188i \(0.286408\pi\)
\(548\) −59.1993 −2.52887
\(549\) −8.37577 −0.357469
\(550\) −93.7735 −3.99852
\(551\) −12.8450 −0.547214
\(552\) 14.0401 0.597588
\(553\) 5.43842 0.231265
\(554\) 65.0808 2.76502
\(555\) 8.14674 0.345810
\(556\) −64.7249 −2.74495
\(557\) 12.9814 0.550039 0.275020 0.961439i \(-0.411316\pi\)
0.275020 + 0.961439i \(0.411316\pi\)
\(558\) −14.7416 −0.624062
\(559\) 0.939516 0.0397373
\(560\) −30.2693 −1.27911
\(561\) −18.8943 −0.797718
\(562\) 31.4869 1.32820
\(563\) −2.69123 −0.113422 −0.0567109 0.998391i \(-0.518061\pi\)
−0.0567109 + 0.998391i \(0.518061\pi\)
\(564\) −40.5502 −1.70747
\(565\) −10.5707 −0.444711
\(566\) 15.6723 0.658755
\(567\) 3.54140 0.148725
\(568\) 62.6057 2.62688
\(569\) 41.6096 1.74436 0.872182 0.489182i \(-0.162705\pi\)
0.872182 + 0.489182i \(0.162705\pi\)
\(570\) 51.1038 2.14050
\(571\) −3.39647 −0.142138 −0.0710690 0.997471i \(-0.522641\pi\)
−0.0710690 + 0.997471i \(0.522641\pi\)
\(572\) 14.7276 0.615793
\(573\) −2.31771 −0.0968236
\(574\) −17.3156 −0.722740
\(575\) −22.6744 −0.945587
\(576\) 8.60692 0.358622
\(577\) 24.7277 1.02943 0.514715 0.857361i \(-0.327898\pi\)
0.514715 + 0.857361i \(0.327898\pi\)
\(578\) −4.66726 −0.194133
\(579\) 12.8887 0.535635
\(580\) 50.1471 2.08225
\(581\) −9.54041 −0.395803
\(582\) 4.15348 0.172167
\(583\) −12.3258 −0.510481
\(584\) −39.0774 −1.61703
\(585\) −5.88938 −0.243496
\(586\) −19.6593 −0.812120
\(587\) 36.8507 1.52099 0.760496 0.649343i \(-0.224956\pi\)
0.760496 + 0.649343i \(0.224956\pi\)
\(588\) −23.9944 −0.989514
\(589\) 16.8677 0.695021
\(590\) 62.4280 2.57012
\(591\) 14.4926 0.596145
\(592\) 8.39937 0.345212
\(593\) −28.5530 −1.17253 −0.586265 0.810119i \(-0.699402\pi\)
−0.586265 + 0.810119i \(0.699402\pi\)
\(594\) 48.4509 1.98796
\(595\) 26.1908 1.07372
\(596\) −86.3900 −3.53867
\(597\) −24.3647 −0.997181
\(598\) 5.27087 0.215542
\(599\) −13.7645 −0.562400 −0.281200 0.959649i \(-0.590732\pi\)
−0.281200 + 0.959649i \(0.590732\pi\)
\(600\) −70.6521 −2.88436
\(601\) −35.5295 −1.44928 −0.724639 0.689129i \(-0.757993\pi\)
−0.724639 + 0.689129i \(0.757993\pi\)
\(602\) 3.55100 0.144728
\(603\) 16.5444 0.673738
\(604\) −44.2385 −1.80004
\(605\) 5.93761 0.241398
\(606\) −59.0937 −2.40052
\(607\) −3.90470 −0.158487 −0.0792434 0.996855i \(-0.525250\pi\)
−0.0792434 + 0.996855i \(0.525250\pi\)
\(608\) 7.24257 0.293725
\(609\) −5.69120 −0.230619
\(610\) −55.3787 −2.24222
\(611\) −7.91434 −0.320180
\(612\) 26.9189 1.08813
\(613\) −21.4663 −0.867015 −0.433507 0.901150i \(-0.642724\pi\)
−0.433507 + 0.901150i \(0.642724\pi\)
\(614\) 20.5070 0.827596
\(615\) −22.3141 −0.899792
\(616\) 28.9394 1.16600
\(617\) 1.00000 0.0402585
\(618\) −34.6808 −1.39507
\(619\) −30.7152 −1.23455 −0.617274 0.786748i \(-0.711763\pi\)
−0.617274 + 0.786748i \(0.711763\pi\)
\(620\) −65.8519 −2.64468
\(621\) 11.7154 0.470122
\(622\) 28.4249 1.13974
\(623\) 9.56499 0.383213
\(624\) 6.17647 0.247257
\(625\) 35.6919 1.42768
\(626\) −46.9407 −1.87613
\(627\) −18.3742 −0.733794
\(628\) −103.774 −4.14103
\(629\) −7.26763 −0.289779
\(630\) −22.2595 −0.886840
\(631\) −10.8137 −0.430486 −0.215243 0.976560i \(-0.569054\pi\)
−0.215243 + 0.976560i \(0.569054\pi\)
\(632\) 19.2136 0.764276
\(633\) −20.2467 −0.804735
\(634\) −77.9549 −3.09598
\(635\) 23.3303 0.925834
\(636\) −17.8627 −0.708303
\(637\) −4.68309 −0.185551
\(638\) −26.6867 −1.05654
\(639\) 17.3139 0.684927
\(640\) 70.4822 2.78606
\(641\) −19.8380 −0.783553 −0.391777 0.920060i \(-0.628139\pi\)
−0.391777 + 0.920060i \(0.628139\pi\)
\(642\) −10.5271 −0.415470
\(643\) −7.91369 −0.312085 −0.156043 0.987750i \(-0.549874\pi\)
−0.156043 + 0.987750i \(0.549874\pi\)
\(644\) 13.4597 0.530385
\(645\) 4.57606 0.180182
\(646\) −45.5892 −1.79368
\(647\) −24.1382 −0.948972 −0.474486 0.880263i \(-0.657366\pi\)
−0.474486 + 0.880263i \(0.657366\pi\)
\(648\) 12.5116 0.491501
\(649\) −22.4457 −0.881073
\(650\) −26.5238 −1.04035
\(651\) 7.47354 0.292911
\(652\) 90.5318 3.54550
\(653\) 17.5062 0.685070 0.342535 0.939505i \(-0.388714\pi\)
0.342535 + 0.939505i \(0.388714\pi\)
\(654\) −30.1350 −1.17837
\(655\) −22.1709 −0.866290
\(656\) −23.0061 −0.898236
\(657\) −10.8070 −0.421622
\(658\) −29.9131 −1.16613
\(659\) −7.67864 −0.299117 −0.149559 0.988753i \(-0.547785\pi\)
−0.149559 + 0.988753i \(0.547785\pi\)
\(660\) 71.7333 2.79221
\(661\) −27.6520 −1.07554 −0.537769 0.843092i \(-0.680733\pi\)
−0.537769 + 0.843092i \(0.680733\pi\)
\(662\) −58.5227 −2.27455
\(663\) −5.34425 −0.207553
\(664\) −33.7057 −1.30804
\(665\) 25.4699 0.987679
\(666\) 6.17674 0.239344
\(667\) −6.45283 −0.249855
\(668\) 42.9168 1.66050
\(669\) 10.9993 0.425259
\(670\) 109.388 4.22601
\(671\) 19.9112 0.768664
\(672\) 3.20895 0.123788
\(673\) 0.863984 0.0333041 0.0166521 0.999861i \(-0.494699\pi\)
0.0166521 + 0.999861i \(0.494699\pi\)
\(674\) 84.5874 3.25818
\(675\) −58.9536 −2.26913
\(676\) 4.16571 0.160219
\(677\) −35.4038 −1.36068 −0.680340 0.732897i \(-0.738168\pi\)
−0.680340 + 0.732897i \(0.738168\pi\)
\(678\) 8.15240 0.313091
\(679\) 2.07007 0.0794421
\(680\) 92.5307 3.54839
\(681\) −21.1212 −0.809366
\(682\) 35.0443 1.34192
\(683\) 18.2982 0.700160 0.350080 0.936720i \(-0.386154\pi\)
0.350080 + 0.936720i \(0.386154\pi\)
\(684\) 26.1778 1.00094
\(685\) −56.2763 −2.15021
\(686\) −44.1574 −1.68594
\(687\) −8.99933 −0.343346
\(688\) 4.71797 0.179871
\(689\) −3.48634 −0.132819
\(690\) 25.6726 0.977339
\(691\) 17.0566 0.648865 0.324433 0.945909i \(-0.394827\pi\)
0.324433 + 0.945909i \(0.394827\pi\)
\(692\) −67.2687 −2.55717
\(693\) 8.00333 0.304021
\(694\) −49.9174 −1.89484
\(695\) −61.5292 −2.33393
\(696\) −20.1067 −0.762141
\(697\) 19.9062 0.754001
\(698\) −41.3033 −1.56335
\(699\) −1.65716 −0.0626797
\(700\) −67.7311 −2.55999
\(701\) −0.324257 −0.0122470 −0.00612351 0.999981i \(-0.501949\pi\)
−0.00612351 + 0.999981i \(0.501949\pi\)
\(702\) 13.7043 0.517236
\(703\) −7.06757 −0.266558
\(704\) −20.4607 −0.771142
\(705\) −38.5481 −1.45180
\(706\) −6.37577 −0.239955
\(707\) −29.4520 −1.10766
\(708\) −32.5288 −1.22251
\(709\) 16.7721 0.629888 0.314944 0.949110i \(-0.398014\pi\)
0.314944 + 0.949110i \(0.398014\pi\)
\(710\) 114.475 4.29619
\(711\) 5.31360 0.199276
\(712\) 33.7926 1.26643
\(713\) 8.47369 0.317342
\(714\) −20.1991 −0.755933
\(715\) 14.0005 0.523588
\(716\) −4.05367 −0.151493
\(717\) 0.578023 0.0215867
\(718\) 44.5486 1.66254
\(719\) −10.7300 −0.400160 −0.200080 0.979780i \(-0.564120\pi\)
−0.200080 + 0.979780i \(0.564120\pi\)
\(720\) −29.5747 −1.10218
\(721\) −17.2847 −0.643717
\(722\) 2.84437 0.105856
\(723\) 35.5447 1.32192
\(724\) −13.9921 −0.520014
\(725\) 32.4716 1.20597
\(726\) −4.57925 −0.169952
\(727\) 33.4686 1.24128 0.620641 0.784095i \(-0.286872\pi\)
0.620641 + 0.784095i \(0.286872\pi\)
\(728\) 8.18551 0.303375
\(729\) 23.8248 0.882399
\(730\) −71.4536 −2.64462
\(731\) −4.08226 −0.150988
\(732\) 28.8557 1.06654
\(733\) 30.5277 1.12757 0.563784 0.825922i \(-0.309345\pi\)
0.563784 + 0.825922i \(0.309345\pi\)
\(734\) −8.56031 −0.315967
\(735\) −22.8097 −0.841350
\(736\) 3.63839 0.134113
\(737\) −39.3299 −1.44874
\(738\) −16.9182 −0.622768
\(739\) −42.5417 −1.56492 −0.782461 0.622700i \(-0.786036\pi\)
−0.782461 + 0.622700i \(0.786036\pi\)
\(740\) 27.5920 1.01430
\(741\) −5.19713 −0.190921
\(742\) −13.1770 −0.483742
\(743\) 31.0324 1.13847 0.569235 0.822175i \(-0.307240\pi\)
0.569235 + 0.822175i \(0.307240\pi\)
\(744\) 26.4036 0.968002
\(745\) −82.1245 −3.00881
\(746\) −22.3080 −0.816755
\(747\) −9.32146 −0.341054
\(748\) −63.9926 −2.33980
\(749\) −5.24663 −0.191708
\(750\) −68.7172 −2.50920
\(751\) −9.39012 −0.342651 −0.171325 0.985215i \(-0.554805\pi\)
−0.171325 + 0.985215i \(0.554805\pi\)
\(752\) −39.7434 −1.44929
\(753\) 8.02038 0.292279
\(754\) −7.54833 −0.274894
\(755\) −42.0542 −1.53051
\(756\) 34.9953 1.27277
\(757\) −5.33256 −0.193815 −0.0969077 0.995293i \(-0.530895\pi\)
−0.0969077 + 0.995293i \(0.530895\pi\)
\(758\) 36.1504 1.31304
\(759\) −9.23049 −0.335046
\(760\) 89.9835 3.26404
\(761\) 21.0320 0.762411 0.381205 0.924490i \(-0.375509\pi\)
0.381205 + 0.924490i \(0.375509\pi\)
\(762\) −17.9930 −0.651817
\(763\) −15.0191 −0.543728
\(764\) −7.84978 −0.283995
\(765\) 25.5898 0.925200
\(766\) 12.1978 0.440724
\(767\) −6.34877 −0.229241
\(768\) −40.1217 −1.44777
\(769\) 4.86203 0.175329 0.0876646 0.996150i \(-0.472060\pi\)
0.0876646 + 0.996150i \(0.472060\pi\)
\(770\) 52.9162 1.90697
\(771\) 18.7499 0.675262
\(772\) 43.6523 1.57108
\(773\) −20.8518 −0.749988 −0.374994 0.927027i \(-0.622355\pi\)
−0.374994 + 0.927027i \(0.622355\pi\)
\(774\) 3.46950 0.124709
\(775\) −42.6409 −1.53171
\(776\) 7.31344 0.262537
\(777\) −3.13141 −0.112339
\(778\) −43.6023 −1.56322
\(779\) 19.3582 0.693581
\(780\) 20.2897 0.726489
\(781\) −41.1592 −1.47279
\(782\) −22.9023 −0.818984
\(783\) −16.7774 −0.599576
\(784\) −23.5170 −0.839895
\(785\) −98.6501 −3.52097
\(786\) 17.0989 0.609896
\(787\) −3.99080 −0.142257 −0.0711284 0.997467i \(-0.522660\pi\)
−0.0711284 + 0.997467i \(0.522660\pi\)
\(788\) 49.0845 1.74856
\(789\) −38.9212 −1.38563
\(790\) 35.1323 1.24995
\(791\) 4.06311 0.144468
\(792\) 28.2753 1.00472
\(793\) 5.63188 0.199994
\(794\) 43.7297 1.55191
\(795\) −16.9808 −0.602246
\(796\) −82.5202 −2.92485
\(797\) 3.98593 0.141189 0.0705944 0.997505i \(-0.477510\pi\)
0.0705944 + 0.997505i \(0.477510\pi\)
\(798\) −19.6431 −0.695358
\(799\) 34.3884 1.21657
\(800\) −18.3090 −0.647319
\(801\) 9.34548 0.330206
\(802\) −48.3748 −1.70817
\(803\) 25.6909 0.906611
\(804\) −56.9976 −2.01015
\(805\) 12.7951 0.450968
\(806\) 9.91227 0.349145
\(807\) −13.1899 −0.464305
\(808\) −104.052 −3.66054
\(809\) −15.8877 −0.558581 −0.279291 0.960207i \(-0.590099\pi\)
−0.279291 + 0.960207i \(0.590099\pi\)
\(810\) 22.8776 0.803836
\(811\) 22.1132 0.776501 0.388251 0.921554i \(-0.373080\pi\)
0.388251 + 0.921554i \(0.373080\pi\)
\(812\) −19.2754 −0.676433
\(813\) −37.2092 −1.30498
\(814\) −14.6836 −0.514659
\(815\) 86.0618 3.01461
\(816\) −26.8372 −0.939489
\(817\) −3.96989 −0.138889
\(818\) −80.6574 −2.82012
\(819\) 2.26374 0.0791014
\(820\) −75.5751 −2.63920
\(821\) 37.4035 1.30539 0.652696 0.757620i \(-0.273638\pi\)
0.652696 + 0.757620i \(0.273638\pi\)
\(822\) 43.4019 1.51382
\(823\) −3.04770 −0.106236 −0.0531181 0.998588i \(-0.516916\pi\)
−0.0531181 + 0.998588i \(0.516916\pi\)
\(824\) −61.0659 −2.12733
\(825\) 46.4492 1.61716
\(826\) −23.9958 −0.834922
\(827\) 25.5190 0.887381 0.443691 0.896180i \(-0.353669\pi\)
0.443691 + 0.896180i \(0.353669\pi\)
\(828\) 13.1508 0.457020
\(829\) −34.0425 −1.18235 −0.591173 0.806545i \(-0.701335\pi\)
−0.591173 + 0.806545i \(0.701335\pi\)
\(830\) −61.6314 −2.13926
\(831\) −32.2367 −1.11828
\(832\) −5.78731 −0.200639
\(833\) 20.3483 0.705028
\(834\) 47.4531 1.64316
\(835\) 40.7978 1.41186
\(836\) −62.2310 −2.15230
\(837\) 22.0317 0.761527
\(838\) 35.9584 1.24216
\(839\) −23.1980 −0.800882 −0.400441 0.916322i \(-0.631143\pi\)
−0.400441 + 0.916322i \(0.631143\pi\)
\(840\) 39.8688 1.37560
\(841\) −19.7590 −0.681345
\(842\) −13.0220 −0.448769
\(843\) −15.5966 −0.537174
\(844\) −68.5731 −2.36038
\(845\) 3.96003 0.136229
\(846\) −29.2266 −1.00483
\(847\) −2.28228 −0.0784199
\(848\) −17.5073 −0.601204
\(849\) −7.76301 −0.266426
\(850\) 115.248 3.95297
\(851\) −3.55048 −0.121709
\(852\) −59.6488 −2.04353
\(853\) −44.9518 −1.53912 −0.769560 0.638575i \(-0.779524\pi\)
−0.769560 + 0.638575i \(0.779524\pi\)
\(854\) 21.2863 0.728401
\(855\) 24.8853 0.851060
\(856\) −18.5360 −0.633549
\(857\) 23.5718 0.805198 0.402599 0.915376i \(-0.368107\pi\)
0.402599 + 0.915376i \(0.368107\pi\)
\(858\) −10.7976 −0.368623
\(859\) −32.1256 −1.09611 −0.548056 0.836442i \(-0.684632\pi\)
−0.548056 + 0.836442i \(0.684632\pi\)
\(860\) 15.4985 0.528496
\(861\) 8.57702 0.292304
\(862\) −88.2068 −3.00434
\(863\) −0.0589951 −0.00200821 −0.00100411 0.999999i \(-0.500320\pi\)
−0.00100411 + 0.999999i \(0.500320\pi\)
\(864\) 9.45986 0.321831
\(865\) −63.9473 −2.17427
\(866\) 21.5487 0.732256
\(867\) 2.31186 0.0785147
\(868\) 25.3119 0.859143
\(869\) −12.6317 −0.428501
\(870\) −36.7653 −1.24646
\(871\) −11.1244 −0.376938
\(872\) −53.0616 −1.79689
\(873\) 2.02257 0.0684535
\(874\) −22.2718 −0.753356
\(875\) −34.2483 −1.15780
\(876\) 37.2317 1.25794
\(877\) −37.4177 −1.26350 −0.631752 0.775170i \(-0.717664\pi\)
−0.631752 + 0.775170i \(0.717664\pi\)
\(878\) 45.1350 1.52323
\(879\) 9.73794 0.328453
\(880\) 70.3061 2.37002
\(881\) 25.2264 0.849899 0.424949 0.905217i \(-0.360292\pi\)
0.424949 + 0.905217i \(0.360292\pi\)
\(882\) −17.2940 −0.582319
\(883\) −12.8827 −0.433539 −0.216769 0.976223i \(-0.569552\pi\)
−0.216769 + 0.976223i \(0.569552\pi\)
\(884\) −18.1003 −0.608778
\(885\) −30.9227 −1.03946
\(886\) −53.6655 −1.80293
\(887\) 35.8572 1.20397 0.601983 0.798509i \(-0.294377\pi\)
0.601983 + 0.798509i \(0.294377\pi\)
\(888\) −11.0631 −0.371253
\(889\) −8.96760 −0.300764
\(890\) 61.7902 2.07121
\(891\) −8.22555 −0.275566
\(892\) 37.2534 1.24734
\(893\) 33.4417 1.11909
\(894\) 63.3368 2.11830
\(895\) −3.85352 −0.128809
\(896\) −27.0917 −0.905071
\(897\) −2.61084 −0.0871734
\(898\) 6.90222 0.230330
\(899\) −12.1350 −0.404726
\(900\) −66.1766 −2.20589
\(901\) 15.1484 0.504666
\(902\) 40.2187 1.33914
\(903\) −1.75893 −0.0585336
\(904\) 14.3547 0.477432
\(905\) −13.3013 −0.442150
\(906\) 32.4334 1.07753
\(907\) −5.40074 −0.179329 −0.0896643 0.995972i \(-0.528579\pi\)
−0.0896643 + 0.995972i \(0.528579\pi\)
\(908\) −71.5348 −2.37397
\(909\) −28.7761 −0.954441
\(910\) 14.9673 0.496162
\(911\) −11.6188 −0.384947 −0.192473 0.981302i \(-0.561651\pi\)
−0.192473 + 0.981302i \(0.561651\pi\)
\(912\) −26.0984 −0.864205
\(913\) 22.1593 0.733367
\(914\) −5.71564 −0.189056
\(915\) 27.4310 0.906840
\(916\) −30.4796 −1.00707
\(917\) 8.52198 0.281421
\(918\) −59.5462 −1.96532
\(919\) 4.53266 0.149519 0.0747593 0.997202i \(-0.476181\pi\)
0.0747593 + 0.997202i \(0.476181\pi\)
\(920\) 45.2043 1.49034
\(921\) −10.1578 −0.334712
\(922\) −67.7770 −2.23212
\(923\) −11.6419 −0.383197
\(924\) −27.5726 −0.907071
\(925\) 17.8666 0.587449
\(926\) −2.67088 −0.0877705
\(927\) −16.8880 −0.554676
\(928\) −5.21049 −0.171043
\(929\) −2.49965 −0.0820110 −0.0410055 0.999159i \(-0.513056\pi\)
−0.0410055 + 0.999159i \(0.513056\pi\)
\(930\) 48.2793 1.58314
\(931\) 19.7882 0.648532
\(932\) −5.61261 −0.183847
\(933\) −14.0798 −0.460954
\(934\) 87.2702 2.85557
\(935\) −60.8330 −1.98945
\(936\) 7.99765 0.261411
\(937\) −38.7035 −1.26439 −0.632193 0.774811i \(-0.717845\pi\)
−0.632193 + 0.774811i \(0.717845\pi\)
\(938\) −42.0460 −1.37285
\(939\) 23.2513 0.758779
\(940\) −130.557 −4.25831
\(941\) 30.2123 0.984893 0.492447 0.870343i \(-0.336103\pi\)
0.492447 + 0.870343i \(0.336103\pi\)
\(942\) 76.0818 2.47888
\(943\) 9.72484 0.316684
\(944\) −31.8816 −1.03766
\(945\) 33.2674 1.08219
\(946\) −8.24784 −0.268160
\(947\) 47.4280 1.54120 0.770601 0.637318i \(-0.219956\pi\)
0.770601 + 0.637318i \(0.219956\pi\)
\(948\) −18.3061 −0.594555
\(949\) 7.26666 0.235886
\(950\) 112.075 3.63620
\(951\) 38.6137 1.25214
\(952\) −35.5666 −1.15272
\(953\) −6.24219 −0.202204 −0.101102 0.994876i \(-0.532237\pi\)
−0.101102 + 0.994876i \(0.532237\pi\)
\(954\) −12.8746 −0.416829
\(955\) −7.46220 −0.241471
\(956\) 1.95769 0.0633163
\(957\) 13.2188 0.427305
\(958\) −51.6692 −1.66936
\(959\) 21.6313 0.698511
\(960\) −28.1880 −0.909764
\(961\) −15.0646 −0.485954
\(962\) −4.15325 −0.133906
\(963\) −5.12622 −0.165190
\(964\) 120.386 3.87736
\(965\) 41.4970 1.33583
\(966\) −9.86794 −0.317496
\(967\) −29.5912 −0.951588 −0.475794 0.879557i \(-0.657839\pi\)
−0.475794 + 0.879557i \(0.657839\pi\)
\(968\) −8.06315 −0.259159
\(969\) 22.5819 0.725435
\(970\) 13.3727 0.429373
\(971\) 52.9660 1.69976 0.849879 0.526978i \(-0.176675\pi\)
0.849879 + 0.526978i \(0.176675\pi\)
\(972\) 57.0518 1.82994
\(973\) 23.6504 0.758196
\(974\) −64.5955 −2.06977
\(975\) 13.1382 0.420758
\(976\) 28.2816 0.905271
\(977\) −57.4832 −1.83905 −0.919525 0.393031i \(-0.871426\pi\)
−0.919525 + 0.393031i \(0.871426\pi\)
\(978\) −66.3734 −2.12239
\(979\) −22.2164 −0.710040
\(980\) −77.2537 −2.46778
\(981\) −14.6744 −0.468518
\(982\) −78.5527 −2.50672
\(983\) 10.4191 0.332317 0.166159 0.986099i \(-0.446864\pi\)
0.166159 + 0.986099i \(0.446864\pi\)
\(984\) 30.3021 0.965995
\(985\) 46.6610 1.48674
\(986\) 32.7980 1.04450
\(987\) 14.8170 0.471629
\(988\) −17.6020 −0.559995
\(989\) −1.99432 −0.0634157
\(990\) 51.7017 1.64319
\(991\) −26.4505 −0.840226 −0.420113 0.907472i \(-0.638010\pi\)
−0.420113 + 0.907472i \(0.638010\pi\)
\(992\) 6.84228 0.217243
\(993\) 28.9883 0.919915
\(994\) −44.0017 −1.39565
\(995\) −78.4458 −2.48690
\(996\) 32.1137 1.01756
\(997\) 34.8309 1.10311 0.551553 0.834140i \(-0.314035\pi\)
0.551553 + 0.834140i \(0.314035\pi\)
\(998\) 64.3828 2.03800
\(999\) −9.23128 −0.292065
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 \(a_p\))