Properties

Label 6019.2.a.c.1.16
Level 6019
Weight 2
Character 6019.1
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM No

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Newspace parameters

Level: \( N \) = \( 6019 = 13 \cdot 463 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(108\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.23728 q^{2}\) \(+2.31482 q^{3}\) \(+3.00542 q^{4}\) \(-4.05108 q^{5}\) \(-5.17891 q^{6}\) \(-5.18040 q^{7}\) \(-2.24940 q^{8}\) \(+2.35841 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.23728 q^{2}\) \(+2.31482 q^{3}\) \(+3.00542 q^{4}\) \(-4.05108 q^{5}\) \(-5.17891 q^{6}\) \(-5.18040 q^{7}\) \(-2.24940 q^{8}\) \(+2.35841 q^{9}\) \(+9.06339 q^{10}\) \(+4.76756 q^{11}\) \(+6.95701 q^{12}\) \(-1.00000 q^{13}\) \(+11.5900 q^{14}\) \(-9.37753 q^{15}\) \(-0.978307 q^{16}\) \(+2.33346 q^{17}\) \(-5.27643 q^{18}\) \(-4.10318 q^{19}\) \(-12.1752 q^{20}\) \(-11.9917 q^{21}\) \(-10.6664 q^{22}\) \(-4.26438 q^{23}\) \(-5.20696 q^{24}\) \(+11.4112 q^{25}\) \(+2.23728 q^{26}\) \(-1.48516 q^{27}\) \(-15.5693 q^{28}\) \(+3.99786 q^{29}\) \(+20.9802 q^{30}\) \(-2.65455 q^{31}\) \(+6.68754 q^{32}\) \(+11.0361 q^{33}\) \(-5.22060 q^{34}\) \(+20.9862 q^{35}\) \(+7.08801 q^{36}\) \(+10.7176 q^{37}\) \(+9.17996 q^{38}\) \(-2.31482 q^{39}\) \(+9.11248 q^{40}\) \(-4.21707 q^{41}\) \(+26.8288 q^{42}\) \(+4.21943 q^{43}\) \(+14.3285 q^{44}\) \(-9.55411 q^{45}\) \(+9.54060 q^{46}\) \(+2.37423 q^{47}\) \(-2.26461 q^{48}\) \(+19.8366 q^{49}\) \(-25.5301 q^{50}\) \(+5.40155 q^{51}\) \(-3.00542 q^{52}\) \(+9.09971 q^{53}\) \(+3.32272 q^{54}\) \(-19.3138 q^{55}\) \(+11.6528 q^{56}\) \(-9.49814 q^{57}\) \(-8.94432 q^{58}\) \(+2.78313 q^{59}\) \(-28.1834 q^{60}\) \(+4.15230 q^{61}\) \(+5.93897 q^{62}\) \(-12.2175 q^{63}\) \(-13.0053 q^{64}\) \(+4.05108 q^{65}\) \(-24.6908 q^{66}\) \(-4.83531 q^{67}\) \(+7.01302 q^{68}\) \(-9.87128 q^{69}\) \(-46.9520 q^{70}\) \(-12.3965 q^{71}\) \(-5.30500 q^{72}\) \(+5.46936 q^{73}\) \(-23.9783 q^{74}\) \(+26.4150 q^{75}\) \(-12.3318 q^{76}\) \(-24.6979 q^{77}\) \(+5.17891 q^{78}\) \(-1.71267 q^{79}\) \(+3.96320 q^{80}\) \(-10.5131 q^{81}\) \(+9.43475 q^{82}\) \(+7.89643 q^{83}\) \(-36.0401 q^{84}\) \(-9.45303 q^{85}\) \(-9.44005 q^{86}\) \(+9.25434 q^{87}\) \(-10.7241 q^{88}\) \(+12.6072 q^{89}\) \(+21.3752 q^{90}\) \(+5.18040 q^{91}\) \(-12.8162 q^{92}\) \(-6.14482 q^{93}\) \(-5.31181 q^{94}\) \(+16.6223 q^{95}\) \(+15.4805 q^{96}\) \(-4.61728 q^{97}\) \(-44.3799 q^{98}\) \(+11.2439 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.23728 −1.58199 −0.790997 0.611819i \(-0.790438\pi\)
−0.790997 + 0.611819i \(0.790438\pi\)
\(3\) 2.31482 1.33646 0.668232 0.743953i \(-0.267051\pi\)
0.668232 + 0.743953i \(0.267051\pi\)
\(4\) 3.00542 1.50271
\(5\) −4.05108 −1.81170 −0.905848 0.423602i \(-0.860766\pi\)
−0.905848 + 0.423602i \(0.860766\pi\)
\(6\) −5.17891 −2.11428
\(7\) −5.18040 −1.95801 −0.979004 0.203841i \(-0.934657\pi\)
−0.979004 + 0.203841i \(0.934657\pi\)
\(8\) −2.24940 −0.795281
\(9\) 2.35841 0.786138
\(10\) 9.06339 2.86610
\(11\) 4.76756 1.43747 0.718737 0.695282i \(-0.244720\pi\)
0.718737 + 0.695282i \(0.244720\pi\)
\(12\) 6.95701 2.00832
\(13\) −1.00000 −0.277350
\(14\) 11.5900 3.09756
\(15\) −9.37753 −2.42127
\(16\) −0.978307 −0.244577
\(17\) 2.33346 0.565947 0.282974 0.959128i \(-0.408679\pi\)
0.282974 + 0.959128i \(0.408679\pi\)
\(18\) −5.27643 −1.24367
\(19\) −4.10318 −0.941334 −0.470667 0.882311i \(-0.655987\pi\)
−0.470667 + 0.882311i \(0.655987\pi\)
\(20\) −12.1752 −2.72245
\(21\) −11.9917 −2.61681
\(22\) −10.6664 −2.27408
\(23\) −4.26438 −0.889184 −0.444592 0.895733i \(-0.646651\pi\)
−0.444592 + 0.895733i \(0.646651\pi\)
\(24\) −5.20696 −1.06287
\(25\) 11.4112 2.28225
\(26\) 2.23728 0.438766
\(27\) −1.48516 −0.285820
\(28\) −15.5693 −2.94231
\(29\) 3.99786 0.742383 0.371192 0.928556i \(-0.378949\pi\)
0.371192 + 0.928556i \(0.378949\pi\)
\(30\) 20.9802 3.83043
\(31\) −2.65455 −0.476772 −0.238386 0.971171i \(-0.576618\pi\)
−0.238386 + 0.971171i \(0.576618\pi\)
\(32\) 6.68754 1.18220
\(33\) 11.0361 1.92113
\(34\) −5.22060 −0.895326
\(35\) 20.9862 3.54732
\(36\) 7.08801 1.18134
\(37\) 10.7176 1.76197 0.880983 0.473148i \(-0.156882\pi\)
0.880983 + 0.473148i \(0.156882\pi\)
\(38\) 9.17996 1.48919
\(39\) −2.31482 −0.370669
\(40\) 9.11248 1.44081
\(41\) −4.21707 −0.658595 −0.329298 0.944226i \(-0.606812\pi\)
−0.329298 + 0.944226i \(0.606812\pi\)
\(42\) 26.8288 4.13978
\(43\) 4.21943 0.643458 0.321729 0.946832i \(-0.395736\pi\)
0.321729 + 0.946832i \(0.395736\pi\)
\(44\) 14.3285 2.16010
\(45\) −9.55411 −1.42424
\(46\) 9.54060 1.40668
\(47\) 2.37423 0.346317 0.173158 0.984894i \(-0.444603\pi\)
0.173158 + 0.984894i \(0.444603\pi\)
\(48\) −2.26461 −0.326868
\(49\) 19.8366 2.83380
\(50\) −25.5301 −3.61050
\(51\) 5.40155 0.756368
\(52\) −3.00542 −0.416776
\(53\) 9.09971 1.24994 0.624970 0.780648i \(-0.285111\pi\)
0.624970 + 0.780648i \(0.285111\pi\)
\(54\) 3.32272 0.452165
\(55\) −19.3138 −2.60427
\(56\) 11.6528 1.55717
\(57\) −9.49814 −1.25806
\(58\) −8.94432 −1.17445
\(59\) 2.78313 0.362333 0.181167 0.983452i \(-0.442013\pi\)
0.181167 + 0.983452i \(0.442013\pi\)
\(60\) −28.1834 −3.63846
\(61\) 4.15230 0.531648 0.265824 0.964022i \(-0.414356\pi\)
0.265824 + 0.964022i \(0.414356\pi\)
\(62\) 5.93897 0.754250
\(63\) −12.2175 −1.53926
\(64\) −13.0053 −1.62566
\(65\) 4.05108 0.502474
\(66\) −24.6908 −3.03922
\(67\) −4.83531 −0.590727 −0.295364 0.955385i \(-0.595441\pi\)
−0.295364 + 0.955385i \(0.595441\pi\)
\(68\) 7.01302 0.850453
\(69\) −9.87128 −1.18836
\(70\) −46.9520 −5.61184
\(71\) −12.3965 −1.47119 −0.735596 0.677421i \(-0.763098\pi\)
−0.735596 + 0.677421i \(0.763098\pi\)
\(72\) −5.30500 −0.625201
\(73\) 5.46936 0.640141 0.320070 0.947394i \(-0.396293\pi\)
0.320070 + 0.947394i \(0.396293\pi\)
\(74\) −23.9783 −2.78742
\(75\) 26.4150 3.05014
\(76\) −12.3318 −1.41455
\(77\) −24.6979 −2.81459
\(78\) 5.17891 0.586396
\(79\) −1.71267 −0.192691 −0.0963454 0.995348i \(-0.530715\pi\)
−0.0963454 + 0.995348i \(0.530715\pi\)
\(80\) 3.96320 0.443099
\(81\) −10.5131 −1.16813
\(82\) 9.43475 1.04189
\(83\) 7.89643 0.866746 0.433373 0.901215i \(-0.357323\pi\)
0.433373 + 0.901215i \(0.357323\pi\)
\(84\) −36.0401 −3.93230
\(85\) −9.45303 −1.02532
\(86\) −9.44005 −1.01795
\(87\) 9.25434 0.992169
\(88\) −10.7241 −1.14320
\(89\) 12.6072 1.33636 0.668181 0.743999i \(-0.267073\pi\)
0.668181 + 0.743999i \(0.267073\pi\)
\(90\) 21.3752 2.25315
\(91\) 5.18040 0.543054
\(92\) −12.8162 −1.33618
\(93\) −6.14482 −0.637188
\(94\) −5.31181 −0.547871
\(95\) 16.6223 1.70541
\(96\) 15.4805 1.57997
\(97\) −4.61728 −0.468814 −0.234407 0.972139i \(-0.575315\pi\)
−0.234407 + 0.972139i \(0.575315\pi\)
\(98\) −44.3799 −4.48305
\(99\) 11.2439 1.13005
\(100\) 34.2955 3.42955
\(101\) −13.4320 −1.33654 −0.668268 0.743921i \(-0.732964\pi\)
−0.668268 + 0.743921i \(0.732964\pi\)
\(102\) −12.0848 −1.19657
\(103\) −2.27315 −0.223980 −0.111990 0.993709i \(-0.535722\pi\)
−0.111990 + 0.993709i \(0.535722\pi\)
\(104\) 2.24940 0.220571
\(105\) 48.5794 4.74086
\(106\) −20.3586 −1.97740
\(107\) 4.41560 0.426872 0.213436 0.976957i \(-0.431534\pi\)
0.213436 + 0.976957i \(0.431534\pi\)
\(108\) −4.46353 −0.429503
\(109\) −10.1279 −0.970078 −0.485039 0.874492i \(-0.661195\pi\)
−0.485039 + 0.874492i \(0.661195\pi\)
\(110\) 43.2103 4.11994
\(111\) 24.8094 2.35481
\(112\) 5.06802 0.478883
\(113\) −7.44268 −0.700148 −0.350074 0.936722i \(-0.613844\pi\)
−0.350074 + 0.936722i \(0.613844\pi\)
\(114\) 21.2500 1.99024
\(115\) 17.2753 1.61093
\(116\) 12.0152 1.11559
\(117\) −2.35841 −0.218035
\(118\) −6.22665 −0.573209
\(119\) −12.0883 −1.10813
\(120\) 21.0938 1.92559
\(121\) 11.7297 1.06633
\(122\) −9.28986 −0.841064
\(123\) −9.76177 −0.880189
\(124\) −7.97803 −0.716449
\(125\) −25.9724 −2.32304
\(126\) 27.3340 2.43511
\(127\) −13.7762 −1.22244 −0.611222 0.791459i \(-0.709322\pi\)
−0.611222 + 0.791459i \(0.709322\pi\)
\(128\) 15.7213 1.38958
\(129\) 9.76725 0.859959
\(130\) −9.06339 −0.794912
\(131\) 1.68587 0.147295 0.0736477 0.997284i \(-0.476536\pi\)
0.0736477 + 0.997284i \(0.476536\pi\)
\(132\) 33.1680 2.88690
\(133\) 21.2561 1.84314
\(134\) 10.8179 0.934528
\(135\) 6.01651 0.517818
\(136\) −5.24887 −0.450087
\(137\) −21.2511 −1.81560 −0.907800 0.419402i \(-0.862240\pi\)
−0.907800 + 0.419402i \(0.862240\pi\)
\(138\) 22.0848 1.87998
\(139\) 17.6191 1.49444 0.747218 0.664579i \(-0.231389\pi\)
0.747218 + 0.664579i \(0.231389\pi\)
\(140\) 63.0723 5.33058
\(141\) 5.49592 0.462840
\(142\) 27.7344 2.32742
\(143\) −4.76756 −0.398684
\(144\) −2.30725 −0.192271
\(145\) −16.1956 −1.34497
\(146\) −12.2365 −1.01270
\(147\) 45.9182 3.78727
\(148\) 32.2109 2.64772
\(149\) −15.4843 −1.26852 −0.634262 0.773118i \(-0.718696\pi\)
−0.634262 + 0.773118i \(0.718696\pi\)
\(150\) −59.0977 −4.82531
\(151\) 13.7230 1.11676 0.558381 0.829585i \(-0.311423\pi\)
0.558381 + 0.829585i \(0.311423\pi\)
\(152\) 9.22968 0.748626
\(153\) 5.50326 0.444912
\(154\) 55.2561 4.45266
\(155\) 10.7538 0.863766
\(156\) −6.95701 −0.557007
\(157\) 16.4529 1.31309 0.656543 0.754288i \(-0.272018\pi\)
0.656543 + 0.754288i \(0.272018\pi\)
\(158\) 3.83173 0.304836
\(159\) 21.0642 1.67050
\(160\) −27.0917 −2.14179
\(161\) 22.0912 1.74103
\(162\) 23.5208 1.84797
\(163\) 9.61840 0.753371 0.376686 0.926341i \(-0.377064\pi\)
0.376686 + 0.926341i \(0.377064\pi\)
\(164\) −12.6740 −0.989676
\(165\) −44.7080 −3.48051
\(166\) −17.6665 −1.37119
\(167\) 5.90000 0.456556 0.228278 0.973596i \(-0.426690\pi\)
0.228278 + 0.973596i \(0.426690\pi\)
\(168\) 26.9741 2.08110
\(169\) 1.00000 0.0769231
\(170\) 21.1491 1.62206
\(171\) −9.67699 −0.740018
\(172\) 12.6812 0.966929
\(173\) 10.1804 0.774001 0.387000 0.922080i \(-0.373511\pi\)
0.387000 + 0.922080i \(0.373511\pi\)
\(174\) −20.7045 −1.56961
\(175\) −59.1148 −4.46866
\(176\) −4.66414 −0.351573
\(177\) 6.44247 0.484246
\(178\) −28.2058 −2.11412
\(179\) −23.8854 −1.78528 −0.892639 0.450773i \(-0.851149\pi\)
−0.892639 + 0.450773i \(0.851149\pi\)
\(180\) −28.7141 −2.14022
\(181\) −2.16112 −0.160635 −0.0803173 0.996769i \(-0.525593\pi\)
−0.0803173 + 0.996769i \(0.525593\pi\)
\(182\) −11.5900 −0.859108
\(183\) 9.61185 0.710529
\(184\) 9.59227 0.707151
\(185\) −43.4179 −3.19215
\(186\) 13.7477 1.00803
\(187\) 11.1249 0.813535
\(188\) 7.13554 0.520413
\(189\) 7.69374 0.559637
\(190\) −37.1887 −2.69795
\(191\) −13.9001 −1.00578 −0.502888 0.864352i \(-0.667729\pi\)
−0.502888 + 0.864352i \(0.667729\pi\)
\(192\) −30.1049 −2.17264
\(193\) −19.8790 −1.43092 −0.715461 0.698653i \(-0.753783\pi\)
−0.715461 + 0.698653i \(0.753783\pi\)
\(194\) 10.3302 0.741662
\(195\) 9.37753 0.671539
\(196\) 59.6171 4.25837
\(197\) −5.78525 −0.412182 −0.206091 0.978533i \(-0.566074\pi\)
−0.206091 + 0.978533i \(0.566074\pi\)
\(198\) −25.1557 −1.78774
\(199\) 23.9044 1.69454 0.847268 0.531166i \(-0.178246\pi\)
0.847268 + 0.531166i \(0.178246\pi\)
\(200\) −25.6684 −1.81503
\(201\) −11.1929 −0.789486
\(202\) 30.0512 2.11439
\(203\) −20.7105 −1.45359
\(204\) 16.2339 1.13660
\(205\) 17.0837 1.19317
\(206\) 5.08566 0.354335
\(207\) −10.0572 −0.699021
\(208\) 0.978307 0.0678334
\(209\) −19.5622 −1.35314
\(210\) −108.686 −7.50002
\(211\) −22.8017 −1.56974 −0.784868 0.619663i \(-0.787269\pi\)
−0.784868 + 0.619663i \(0.787269\pi\)
\(212\) 27.3484 1.87830
\(213\) −28.6957 −1.96620
\(214\) −9.87893 −0.675310
\(215\) −17.0933 −1.16575
\(216\) 3.34072 0.227307
\(217\) 13.7516 0.933523
\(218\) 22.6590 1.53466
\(219\) 12.6606 0.855525
\(220\) −58.0459 −3.91346
\(221\) −2.33346 −0.156965
\(222\) −55.5056 −3.72529
\(223\) −9.12272 −0.610903 −0.305451 0.952208i \(-0.598807\pi\)
−0.305451 + 0.952208i \(0.598807\pi\)
\(224\) −34.6441 −2.31476
\(225\) 26.9124 1.79416
\(226\) 16.6513 1.10763
\(227\) 18.0198 1.19602 0.598008 0.801490i \(-0.295959\pi\)
0.598008 + 0.801490i \(0.295959\pi\)
\(228\) −28.5459 −1.89050
\(229\) −19.7012 −1.30189 −0.650946 0.759124i \(-0.725628\pi\)
−0.650946 + 0.759124i \(0.725628\pi\)
\(230\) −38.6497 −2.54849
\(231\) −57.1713 −3.76160
\(232\) −8.99276 −0.590404
\(233\) −5.44325 −0.356599 −0.178300 0.983976i \(-0.557060\pi\)
−0.178300 + 0.983976i \(0.557060\pi\)
\(234\) 5.27643 0.344931
\(235\) −9.61818 −0.627421
\(236\) 8.36448 0.544481
\(237\) −3.96454 −0.257524
\(238\) 27.0448 1.75305
\(239\) 20.7066 1.33940 0.669701 0.742631i \(-0.266422\pi\)
0.669701 + 0.742631i \(0.266422\pi\)
\(240\) 9.17411 0.592186
\(241\) 17.3696 1.11887 0.559437 0.828873i \(-0.311017\pi\)
0.559437 + 0.828873i \(0.311017\pi\)
\(242\) −26.2425 −1.68693
\(243\) −19.8806 −1.27534
\(244\) 12.4794 0.798912
\(245\) −80.3595 −5.13398
\(246\) 21.8398 1.39245
\(247\) 4.10318 0.261079
\(248\) 5.97114 0.379168
\(249\) 18.2789 1.15838
\(250\) 58.1075 3.67504
\(251\) 0.151593 0.00956849 0.00478424 0.999989i \(-0.498477\pi\)
0.00478424 + 0.999989i \(0.498477\pi\)
\(252\) −36.7187 −2.31306
\(253\) −20.3307 −1.27818
\(254\) 30.8213 1.93390
\(255\) −21.8821 −1.37031
\(256\) −9.16248 −0.572655
\(257\) −12.2224 −0.762414 −0.381207 0.924490i \(-0.624492\pi\)
−0.381207 + 0.924490i \(0.624492\pi\)
\(258\) −21.8521 −1.36045
\(259\) −55.5216 −3.44994
\(260\) 12.1752 0.755072
\(261\) 9.42860 0.583615
\(262\) −3.77177 −0.233020
\(263\) 14.9432 0.921438 0.460719 0.887546i \(-0.347592\pi\)
0.460719 + 0.887546i \(0.347592\pi\)
\(264\) −24.8245 −1.52784
\(265\) −36.8636 −2.26451
\(266\) −47.5559 −2.91584
\(267\) 29.1835 1.78600
\(268\) −14.5321 −0.887691
\(269\) −6.31809 −0.385221 −0.192610 0.981275i \(-0.561695\pi\)
−0.192610 + 0.981275i \(0.561695\pi\)
\(270\) −13.4606 −0.819186
\(271\) 4.57214 0.277738 0.138869 0.990311i \(-0.455653\pi\)
0.138869 + 0.990311i \(0.455653\pi\)
\(272\) −2.28284 −0.138418
\(273\) 11.9917 0.725772
\(274\) 47.5446 2.87227
\(275\) 54.4038 3.28067
\(276\) −29.6673 −1.78576
\(277\) 19.6717 1.18196 0.590978 0.806688i \(-0.298742\pi\)
0.590978 + 0.806688i \(0.298742\pi\)
\(278\) −39.4189 −2.36419
\(279\) −6.26053 −0.374808
\(280\) −47.2063 −2.82112
\(281\) −14.7252 −0.878431 −0.439216 0.898382i \(-0.644744\pi\)
−0.439216 + 0.898382i \(0.644744\pi\)
\(282\) −12.2959 −0.732211
\(283\) −12.9654 −0.770713 −0.385357 0.922768i \(-0.625922\pi\)
−0.385357 + 0.922768i \(0.625922\pi\)
\(284\) −37.2566 −2.21077
\(285\) 38.4777 2.27922
\(286\) 10.6664 0.630716
\(287\) 21.8461 1.28953
\(288\) 15.7720 0.929372
\(289\) −11.5550 −0.679704
\(290\) 36.2341 2.12774
\(291\) −10.6882 −0.626554
\(292\) 16.4377 0.961945
\(293\) 7.55562 0.441404 0.220702 0.975341i \(-0.429165\pi\)
0.220702 + 0.975341i \(0.429165\pi\)
\(294\) −102.732 −5.99144
\(295\) −11.2747 −0.656438
\(296\) −24.1082 −1.40126
\(297\) −7.08060 −0.410858
\(298\) 34.6427 2.00680
\(299\) 4.26438 0.246615
\(300\) 79.3880 4.58347
\(301\) −21.8584 −1.25990
\(302\) −30.7022 −1.76671
\(303\) −31.0927 −1.78623
\(304\) 4.01417 0.230228
\(305\) −16.8213 −0.963185
\(306\) −12.3123 −0.703849
\(307\) 25.8501 1.47534 0.737671 0.675160i \(-0.235925\pi\)
0.737671 + 0.675160i \(0.235925\pi\)
\(308\) −74.2275 −4.22950
\(309\) −5.26194 −0.299341
\(310\) −24.0592 −1.36647
\(311\) −31.8760 −1.80752 −0.903761 0.428037i \(-0.859205\pi\)
−0.903761 + 0.428037i \(0.859205\pi\)
\(312\) 5.20696 0.294786
\(313\) 14.2861 0.807498 0.403749 0.914870i \(-0.367707\pi\)
0.403749 + 0.914870i \(0.367707\pi\)
\(314\) −36.8098 −2.07730
\(315\) 49.4941 2.78868
\(316\) −5.14730 −0.289558
\(317\) −19.0659 −1.07085 −0.535424 0.844583i \(-0.679848\pi\)
−0.535424 + 0.844583i \(0.679848\pi\)
\(318\) −47.1265 −2.64273
\(319\) 19.0600 1.06716
\(320\) 52.6854 2.94520
\(321\) 10.2213 0.570500
\(322\) −49.4241 −2.75430
\(323\) −9.57461 −0.532745
\(324\) −31.5963 −1.75535
\(325\) −11.4112 −0.632981
\(326\) −21.5190 −1.19183
\(327\) −23.4443 −1.29648
\(328\) 9.48585 0.523769
\(329\) −12.2995 −0.678091
\(330\) 100.024 5.50615
\(331\) 32.3698 1.77921 0.889604 0.456733i \(-0.150981\pi\)
0.889604 + 0.456733i \(0.150981\pi\)
\(332\) 23.7321 1.30247
\(333\) 25.2766 1.38515
\(334\) −13.2000 −0.722269
\(335\) 19.5882 1.07022
\(336\) 11.7316 0.640010
\(337\) 0.342077 0.0186341 0.00931705 0.999957i \(-0.497034\pi\)
0.00931705 + 0.999957i \(0.497034\pi\)
\(338\) −2.23728 −0.121692
\(339\) −17.2285 −0.935723
\(340\) −28.4103 −1.54076
\(341\) −12.6557 −0.685347
\(342\) 21.6501 1.17070
\(343\) −66.4986 −3.59059
\(344\) −9.49118 −0.511730
\(345\) 39.9893 2.15295
\(346\) −22.7764 −1.22446
\(347\) 27.2775 1.46434 0.732168 0.681124i \(-0.238509\pi\)
0.732168 + 0.681124i \(0.238509\pi\)
\(348\) 27.8131 1.49094
\(349\) −12.9125 −0.691188 −0.345594 0.938384i \(-0.612322\pi\)
−0.345594 + 0.938384i \(0.612322\pi\)
\(350\) 132.256 7.06939
\(351\) 1.48516 0.0792721
\(352\) 31.8833 1.69938
\(353\) −3.34223 −0.177889 −0.0889446 0.996037i \(-0.528349\pi\)
−0.0889446 + 0.996037i \(0.528349\pi\)
\(354\) −14.4136 −0.766074
\(355\) 50.2191 2.66535
\(356\) 37.8899 2.00816
\(357\) −27.9822 −1.48098
\(358\) 53.4383 2.82430
\(359\) 4.65572 0.245720 0.122860 0.992424i \(-0.460793\pi\)
0.122860 + 0.992424i \(0.460793\pi\)
\(360\) 21.4910 1.13267
\(361\) −2.16391 −0.113890
\(362\) 4.83502 0.254123
\(363\) 27.1521 1.42512
\(364\) 15.5693 0.816051
\(365\) −22.1568 −1.15974
\(366\) −21.5044 −1.12405
\(367\) −30.3387 −1.58366 −0.791832 0.610738i \(-0.790873\pi\)
−0.791832 + 0.610738i \(0.790873\pi\)
\(368\) 4.17187 0.217474
\(369\) −9.94558 −0.517746
\(370\) 97.1380 5.04996
\(371\) −47.1401 −2.44739
\(372\) −18.4677 −0.957508
\(373\) −6.25855 −0.324055 −0.162028 0.986786i \(-0.551803\pi\)
−0.162028 + 0.986786i \(0.551803\pi\)
\(374\) −24.8895 −1.28701
\(375\) −60.1215 −3.10466
\(376\) −5.34058 −0.275419
\(377\) −3.99786 −0.205900
\(378\) −17.2130 −0.885343
\(379\) 33.5344 1.72254 0.861272 0.508144i \(-0.169668\pi\)
0.861272 + 0.508144i \(0.169668\pi\)
\(380\) 49.9569 2.56274
\(381\) −31.8896 −1.63375
\(382\) 31.0984 1.59113
\(383\) −18.7163 −0.956356 −0.478178 0.878263i \(-0.658703\pi\)
−0.478178 + 0.878263i \(0.658703\pi\)
\(384\) 36.3921 1.85713
\(385\) 100.053 5.09918
\(386\) 44.4749 2.26371
\(387\) 9.95117 0.505846
\(388\) −13.8769 −0.704491
\(389\) −6.80394 −0.344974 −0.172487 0.985012i \(-0.555180\pi\)
−0.172487 + 0.985012i \(0.555180\pi\)
\(390\) −20.9802 −1.06237
\(391\) −9.95075 −0.503231
\(392\) −44.6203 −2.25366
\(393\) 3.90250 0.196855
\(394\) 12.9432 0.652069
\(395\) 6.93817 0.349097
\(396\) 33.7926 1.69814
\(397\) −3.70357 −0.185877 −0.0929385 0.995672i \(-0.529626\pi\)
−0.0929385 + 0.995672i \(0.529626\pi\)
\(398\) −53.4807 −2.68075
\(399\) 49.2042 2.46329
\(400\) −11.1637 −0.558184
\(401\) −37.5645 −1.87588 −0.937942 0.346793i \(-0.887271\pi\)
−0.937942 + 0.346793i \(0.887271\pi\)
\(402\) 25.0416 1.24896
\(403\) 2.65455 0.132233
\(404\) −40.3688 −2.00842
\(405\) 42.5895 2.11629
\(406\) 46.3352 2.29958
\(407\) 51.0970 2.53278
\(408\) −12.1502 −0.601526
\(409\) −16.5389 −0.817798 −0.408899 0.912580i \(-0.634087\pi\)
−0.408899 + 0.912580i \(0.634087\pi\)
\(410\) −38.2209 −1.88760
\(411\) −49.1925 −2.42649
\(412\) −6.83175 −0.336576
\(413\) −14.4178 −0.709451
\(414\) 22.5007 1.10585
\(415\) −31.9891 −1.57028
\(416\) −6.68754 −0.327883
\(417\) 40.7852 1.99726
\(418\) 43.7660 2.14067
\(419\) −22.4658 −1.09752 −0.548762 0.835979i \(-0.684901\pi\)
−0.548762 + 0.835979i \(0.684901\pi\)
\(420\) 146.001 7.12413
\(421\) 4.90331 0.238973 0.119486 0.992836i \(-0.461875\pi\)
0.119486 + 0.992836i \(0.461875\pi\)
\(422\) 51.0138 2.48331
\(423\) 5.59941 0.272253
\(424\) −20.4688 −0.994055
\(425\) 26.6276 1.29163
\(426\) 64.2002 3.11051
\(427\) −21.5106 −1.04097
\(428\) 13.2707 0.641464
\(429\) −11.0361 −0.532827
\(430\) 38.2424 1.84421
\(431\) −24.0006 −1.15607 −0.578034 0.816013i \(-0.696180\pi\)
−0.578034 + 0.816013i \(0.696180\pi\)
\(432\) 1.45294 0.0699048
\(433\) −35.1582 −1.68960 −0.844798 0.535085i \(-0.820279\pi\)
−0.844798 + 0.535085i \(0.820279\pi\)
\(434\) −30.7663 −1.47683
\(435\) −37.4900 −1.79751
\(436\) −30.4386 −1.45774
\(437\) 17.4975 0.837019
\(438\) −28.3253 −1.35344
\(439\) 4.02707 0.192201 0.0961007 0.995372i \(-0.469363\pi\)
0.0961007 + 0.995372i \(0.469363\pi\)
\(440\) 43.4443 2.07113
\(441\) 46.7828 2.22775
\(442\) 5.22060 0.248319
\(443\) −13.3329 −0.633465 −0.316733 0.948515i \(-0.602586\pi\)
−0.316733 + 0.948515i \(0.602586\pi\)
\(444\) 74.5626 3.53859
\(445\) −51.0728 −2.42108
\(446\) 20.4101 0.966445
\(447\) −35.8434 −1.69534
\(448\) 67.3725 3.18305
\(449\) −11.7911 −0.556455 −0.278228 0.960515i \(-0.589747\pi\)
−0.278228 + 0.960515i \(0.589747\pi\)
\(450\) −60.2105 −2.83835
\(451\) −20.1051 −0.946714
\(452\) −22.3683 −1.05212
\(453\) 31.7663 1.49251
\(454\) −40.3153 −1.89209
\(455\) −20.9862 −0.983849
\(456\) 21.3651 1.00051
\(457\) 34.4444 1.61124 0.805621 0.592431i \(-0.201832\pi\)
0.805621 + 0.592431i \(0.201832\pi\)
\(458\) 44.0771 2.05959
\(459\) −3.46557 −0.161759
\(460\) 51.9195 2.42076
\(461\) −1.82312 −0.0849112 −0.0424556 0.999098i \(-0.513518\pi\)
−0.0424556 + 0.999098i \(0.513518\pi\)
\(462\) 127.908 5.95083
\(463\) −1.00000 −0.0464739
\(464\) −3.91113 −0.181570
\(465\) 24.8932 1.15439
\(466\) 12.1781 0.564138
\(467\) 24.6044 1.13856 0.569278 0.822145i \(-0.307223\pi\)
0.569278 + 0.822145i \(0.307223\pi\)
\(468\) −7.08801 −0.327643
\(469\) 25.0489 1.15665
\(470\) 21.5185 0.992577
\(471\) 38.0857 1.75489
\(472\) −6.26037 −0.288157
\(473\) 20.1164 0.924954
\(474\) 8.86978 0.407402
\(475\) −46.8223 −2.14836
\(476\) −36.3302 −1.66519
\(477\) 21.4609 0.982626
\(478\) −46.3265 −2.11893
\(479\) −26.1509 −1.19486 −0.597432 0.801920i \(-0.703812\pi\)
−0.597432 + 0.801920i \(0.703812\pi\)
\(480\) −62.7126 −2.86243
\(481\) −10.7176 −0.488682
\(482\) −38.8606 −1.77005
\(483\) 51.1372 2.32682
\(484\) 35.2525 1.60239
\(485\) 18.7050 0.849349
\(486\) 44.4784 2.01758
\(487\) 24.7109 1.11976 0.559879 0.828575i \(-0.310848\pi\)
0.559879 + 0.828575i \(0.310848\pi\)
\(488\) −9.34017 −0.422810
\(489\) 22.2649 1.00685
\(490\) 179.787 8.12193
\(491\) 4.13862 0.186774 0.0933868 0.995630i \(-0.470231\pi\)
0.0933868 + 0.995630i \(0.470231\pi\)
\(492\) −29.3382 −1.32267
\(493\) 9.32884 0.420150
\(494\) −9.17996 −0.413026
\(495\) −45.5499 −2.04731
\(496\) 2.59697 0.116607
\(497\) 64.2188 2.88060
\(498\) −40.8949 −1.83254
\(499\) 13.5710 0.607523 0.303761 0.952748i \(-0.401757\pi\)
0.303761 + 0.952748i \(0.401757\pi\)
\(500\) −78.0578 −3.49085
\(501\) 13.6575 0.610171
\(502\) −0.339157 −0.0151373
\(503\) −34.9153 −1.55679 −0.778397 0.627772i \(-0.783967\pi\)
−0.778397 + 0.627772i \(0.783967\pi\)
\(504\) 27.4821 1.22415
\(505\) 54.4141 2.42140
\(506\) 45.4854 2.02207
\(507\) 2.31482 0.102805
\(508\) −41.4033 −1.83698
\(509\) −29.2652 −1.29716 −0.648579 0.761147i \(-0.724636\pi\)
−0.648579 + 0.761147i \(0.724636\pi\)
\(510\) 48.9564 2.16782
\(511\) −28.3335 −1.25340
\(512\) −10.9437 −0.483646
\(513\) 6.09389 0.269052
\(514\) 27.3450 1.20614
\(515\) 9.20870 0.405784
\(516\) 29.3547 1.29227
\(517\) 11.3193 0.497822
\(518\) 124.217 5.45779
\(519\) 23.5658 1.03442
\(520\) −9.11248 −0.399608
\(521\) 16.7702 0.734716 0.367358 0.930080i \(-0.380262\pi\)
0.367358 + 0.930080i \(0.380262\pi\)
\(522\) −21.0944 −0.923277
\(523\) −29.9038 −1.30760 −0.653800 0.756667i \(-0.726826\pi\)
−0.653800 + 0.756667i \(0.726826\pi\)
\(524\) 5.06675 0.221342
\(525\) −136.840 −5.97220
\(526\) −33.4321 −1.45771
\(527\) −6.19429 −0.269828
\(528\) −10.7967 −0.469865
\(529\) −4.81510 −0.209352
\(530\) 82.4742 3.58245
\(531\) 6.56378 0.284844
\(532\) 63.8835 2.76970
\(533\) 4.21707 0.182661
\(534\) −65.2916 −2.82544
\(535\) −17.8879 −0.773363
\(536\) 10.8765 0.469795
\(537\) −55.2905 −2.38596
\(538\) 14.1353 0.609417
\(539\) 94.5721 4.07351
\(540\) 18.0821 0.778130
\(541\) −45.8945 −1.97316 −0.986580 0.163280i \(-0.947793\pi\)
−0.986580 + 0.163280i \(0.947793\pi\)
\(542\) −10.2292 −0.439380
\(543\) −5.00261 −0.214682
\(544\) 15.6051 0.669063
\(545\) 41.0290 1.75749
\(546\) −26.8288 −1.14817
\(547\) −1.25473 −0.0536485 −0.0268242 0.999640i \(-0.508539\pi\)
−0.0268242 + 0.999640i \(0.508539\pi\)
\(548\) −63.8683 −2.72832
\(549\) 9.79284 0.417948
\(550\) −121.716 −5.19000
\(551\) −16.4039 −0.698831
\(552\) 22.2044 0.945083
\(553\) 8.87234 0.377290
\(554\) −44.0110 −1.86985
\(555\) −100.505 −4.26619
\(556\) 52.9529 2.24570
\(557\) −14.6619 −0.621246 −0.310623 0.950533i \(-0.600538\pi\)
−0.310623 + 0.950533i \(0.600538\pi\)
\(558\) 14.0066 0.592945
\(559\) −4.21943 −0.178463
\(560\) −20.5310 −0.867591
\(561\) 25.7522 1.08726
\(562\) 32.9443 1.38967
\(563\) 4.13193 0.174140 0.0870700 0.996202i \(-0.472250\pi\)
0.0870700 + 0.996202i \(0.472250\pi\)
\(564\) 16.5175 0.695513
\(565\) 30.1509 1.26846
\(566\) 29.0072 1.21926
\(567\) 54.4622 2.28720
\(568\) 27.8846 1.17001
\(569\) −40.3252 −1.69052 −0.845260 0.534355i \(-0.820555\pi\)
−0.845260 + 0.534355i \(0.820555\pi\)
\(570\) −86.0854 −3.60572
\(571\) −11.9777 −0.501251 −0.250626 0.968084i \(-0.580636\pi\)
−0.250626 + 0.968084i \(0.580636\pi\)
\(572\) −14.3285 −0.599105
\(573\) −32.1763 −1.34418
\(574\) −48.8758 −2.04004
\(575\) −48.6618 −2.02934
\(576\) −30.6718 −1.27799
\(577\) −12.1989 −0.507849 −0.253924 0.967224i \(-0.581721\pi\)
−0.253924 + 0.967224i \(0.581721\pi\)
\(578\) 25.8517 1.07529
\(579\) −46.0164 −1.91238
\(580\) −48.6746 −2.02110
\(581\) −40.9067 −1.69710
\(582\) 23.9125 0.991205
\(583\) 43.3834 1.79676
\(584\) −12.3028 −0.509092
\(585\) 9.55411 0.395014
\(586\) −16.9040 −0.698299
\(587\) 7.92549 0.327120 0.163560 0.986533i \(-0.447702\pi\)
0.163560 + 0.986533i \(0.447702\pi\)
\(588\) 138.003 5.69116
\(589\) 10.8921 0.448801
\(590\) 25.2246 1.03848
\(591\) −13.3918 −0.550866
\(592\) −10.4851 −0.430936
\(593\) 13.0362 0.535333 0.267667 0.963512i \(-0.413747\pi\)
0.267667 + 0.963512i \(0.413747\pi\)
\(594\) 15.8413 0.649976
\(595\) 48.9705 2.00759
\(596\) −46.5368 −1.90622
\(597\) 55.3344 2.26469
\(598\) −9.54060 −0.390144
\(599\) −22.1148 −0.903587 −0.451793 0.892123i \(-0.649216\pi\)
−0.451793 + 0.892123i \(0.649216\pi\)
\(600\) −59.4178 −2.42572
\(601\) −27.4156 −1.11831 −0.559153 0.829064i \(-0.688874\pi\)
−0.559153 + 0.829064i \(0.688874\pi\)
\(602\) 48.9033 1.99315
\(603\) −11.4037 −0.464393
\(604\) 41.2433 1.67817
\(605\) −47.5178 −1.93187
\(606\) 69.5631 2.82581
\(607\) −0.144931 −0.00588257 −0.00294129 0.999996i \(-0.500936\pi\)
−0.00294129 + 0.999996i \(0.500936\pi\)
\(608\) −27.4402 −1.11285
\(609\) −47.9412 −1.94267
\(610\) 37.6339 1.52375
\(611\) −2.37423 −0.0960510
\(612\) 16.5396 0.668573
\(613\) 8.19498 0.330992 0.165496 0.986210i \(-0.447078\pi\)
0.165496 + 0.986210i \(0.447078\pi\)
\(614\) −57.8339 −2.33398
\(615\) 39.5457 1.59464
\(616\) 55.5554 2.23839
\(617\) −41.5308 −1.67197 −0.835983 0.548756i \(-0.815102\pi\)
−0.835983 + 0.548756i \(0.815102\pi\)
\(618\) 11.7724 0.473556
\(619\) 36.8619 1.48161 0.740803 0.671723i \(-0.234445\pi\)
0.740803 + 0.671723i \(0.234445\pi\)
\(620\) 32.3196 1.29799
\(621\) 6.33329 0.254146
\(622\) 71.3155 2.85949
\(623\) −65.3104 −2.61661
\(624\) 2.26461 0.0906569
\(625\) 48.1600 1.92640
\(626\) −31.9620 −1.27746
\(627\) −45.2830 −1.80843
\(628\) 49.4479 1.97319
\(629\) 25.0091 0.997180
\(630\) −110.732 −4.41168
\(631\) −16.9892 −0.676330 −0.338165 0.941087i \(-0.609806\pi\)
−0.338165 + 0.941087i \(0.609806\pi\)
\(632\) 3.85248 0.153243
\(633\) −52.7820 −2.09790
\(634\) 42.6557 1.69408
\(635\) 55.8086 2.21470
\(636\) 63.3068 2.51028
\(637\) −19.8366 −0.785953
\(638\) −42.6426 −1.68824
\(639\) −29.2360 −1.15656
\(640\) −63.6884 −2.51750
\(641\) 7.62227 0.301062 0.150531 0.988605i \(-0.451902\pi\)
0.150531 + 0.988605i \(0.451902\pi\)
\(642\) −22.8680 −0.902528
\(643\) 15.2419 0.601083 0.300542 0.953769i \(-0.402833\pi\)
0.300542 + 0.953769i \(0.402833\pi\)
\(644\) 66.3932 2.61626
\(645\) −39.5679 −1.55798
\(646\) 21.4211 0.842800
\(647\) 2.21709 0.0871628 0.0435814 0.999050i \(-0.486123\pi\)
0.0435814 + 0.999050i \(0.486123\pi\)
\(648\) 23.6482 0.928988
\(649\) 13.2688 0.520845
\(650\) 25.5301 1.00137
\(651\) 31.8327 1.24762
\(652\) 28.9073 1.13210
\(653\) −28.5694 −1.11801 −0.559003 0.829166i \(-0.688816\pi\)
−0.559003 + 0.829166i \(0.688816\pi\)
\(654\) 52.4515 2.05102
\(655\) −6.82960 −0.266854
\(656\) 4.12559 0.161077
\(657\) 12.8990 0.503239
\(658\) 27.5173 1.07274
\(659\) −30.0421 −1.17028 −0.585138 0.810934i \(-0.698960\pi\)
−0.585138 + 0.810934i \(0.698960\pi\)
\(660\) −134.366 −5.23019
\(661\) −2.02342 −0.0787018 −0.0393509 0.999225i \(-0.512529\pi\)
−0.0393509 + 0.999225i \(0.512529\pi\)
\(662\) −72.4203 −2.81470
\(663\) −5.40155 −0.209779
\(664\) −17.7622 −0.689307
\(665\) −86.1102 −3.33921
\(666\) −56.5508 −2.19130
\(667\) −17.0484 −0.660115
\(668\) 17.7320 0.686070
\(669\) −21.1175 −0.816450
\(670\) −43.8243 −1.69308
\(671\) 19.7964 0.764230
\(672\) −80.1951 −3.09359
\(673\) −19.8977 −0.767002 −0.383501 0.923541i \(-0.625282\pi\)
−0.383501 + 0.923541i \(0.625282\pi\)
\(674\) −0.765321 −0.0294791
\(675\) −16.9475 −0.652310
\(676\) 3.00542 0.115593
\(677\) −7.19902 −0.276681 −0.138340 0.990385i \(-0.544177\pi\)
−0.138340 + 0.990385i \(0.544177\pi\)
\(678\) 38.5449 1.48031
\(679\) 23.9194 0.917942
\(680\) 21.2636 0.815422
\(681\) 41.7127 1.59843
\(682\) 28.3144 1.08422
\(683\) 32.9422 1.26050 0.630249 0.776393i \(-0.282953\pi\)
0.630249 + 0.776393i \(0.282953\pi\)
\(684\) −29.0834 −1.11203
\(685\) 86.0897 3.28932
\(686\) 148.776 5.68029
\(687\) −45.6048 −1.73993
\(688\) −4.12790 −0.157375
\(689\) −9.09971 −0.346671
\(690\) −89.4673 −3.40596
\(691\) 9.51279 0.361884 0.180942 0.983494i \(-0.442085\pi\)
0.180942 + 0.983494i \(0.442085\pi\)
\(692\) 30.5963 1.16310
\(693\) −58.2478 −2.21265
\(694\) −61.0275 −2.31657
\(695\) −71.3765 −2.70747
\(696\) −20.8167 −0.789054
\(697\) −9.84036 −0.372730
\(698\) 28.8888 1.09346
\(699\) −12.6002 −0.476582
\(700\) −177.664 −6.71508
\(701\) 3.19747 0.120767 0.0603833 0.998175i \(-0.480768\pi\)
0.0603833 + 0.998175i \(0.480768\pi\)
\(702\) −3.32272 −0.125408
\(703\) −43.9763 −1.65860
\(704\) −62.0035 −2.33684
\(705\) −22.2644 −0.838526
\(706\) 7.47751 0.281420
\(707\) 69.5832 2.61695
\(708\) 19.3623 0.727680
\(709\) 25.8807 0.971971 0.485985 0.873967i \(-0.338461\pi\)
0.485985 + 0.873967i \(0.338461\pi\)
\(710\) −112.354 −4.21658
\(711\) −4.03919 −0.151481
\(712\) −28.3586 −1.06278
\(713\) 11.3200 0.423938
\(714\) 62.6040 2.34290
\(715\) 19.3138 0.722294
\(716\) −71.7855 −2.68275
\(717\) 47.9322 1.79006
\(718\) −10.4161 −0.388727
\(719\) 35.2863 1.31596 0.657978 0.753037i \(-0.271412\pi\)
0.657978 + 0.753037i \(0.271412\pi\)
\(720\) 9.34686 0.348337
\(721\) 11.7758 0.438554
\(722\) 4.84127 0.180173
\(723\) 40.2075 1.49533
\(724\) −6.49505 −0.241387
\(725\) 45.6205 1.69430
\(726\) −60.7469 −2.25453
\(727\) 8.34614 0.309541 0.154771 0.987950i \(-0.450536\pi\)
0.154771 + 0.987950i \(0.450536\pi\)
\(728\) −11.6528 −0.431881
\(729\) −14.4806 −0.536320
\(730\) 49.5710 1.83470
\(731\) 9.84588 0.364163
\(732\) 28.8876 1.06772
\(733\) 32.2322 1.19052 0.595262 0.803532i \(-0.297048\pi\)
0.595262 + 0.803532i \(0.297048\pi\)
\(734\) 67.8760 2.50535
\(735\) −186.018 −6.86138
\(736\) −28.5182 −1.05119
\(737\) −23.0527 −0.849156
\(738\) 22.2510 0.819072
\(739\) −11.4776 −0.422209 −0.211104 0.977464i \(-0.567706\pi\)
−0.211104 + 0.977464i \(0.567706\pi\)
\(740\) −130.489 −4.79687
\(741\) 9.49814 0.348923
\(742\) 105.466 3.87177
\(743\) 26.6324 0.977047 0.488523 0.872551i \(-0.337536\pi\)
0.488523 + 0.872551i \(0.337536\pi\)
\(744\) 13.8221 0.506744
\(745\) 62.7281 2.29818
\(746\) 14.0021 0.512654
\(747\) 18.6230 0.681382
\(748\) 33.4350 1.22251
\(749\) −22.8746 −0.835819
\(750\) 134.509 4.91156
\(751\) −6.48488 −0.236637 −0.118318 0.992976i \(-0.537750\pi\)
−0.118318 + 0.992976i \(0.537750\pi\)
\(752\) −2.32272 −0.0847010
\(753\) 0.350912 0.0127879
\(754\) 8.94432 0.325733
\(755\) −55.5929 −2.02323
\(756\) 23.1229 0.840971
\(757\) −16.9100 −0.614605 −0.307303 0.951612i \(-0.599426\pi\)
−0.307303 + 0.951612i \(0.599426\pi\)
\(758\) −75.0257 −2.72506
\(759\) −47.0620 −1.70824
\(760\) −37.3901 −1.35628
\(761\) −20.6719 −0.749355 −0.374678 0.927155i \(-0.622247\pi\)
−0.374678 + 0.927155i \(0.622247\pi\)
\(762\) 71.3459 2.58459
\(763\) 52.4667 1.89942
\(764\) −41.7756 −1.51139
\(765\) −22.2941 −0.806046
\(766\) 41.8735 1.51295
\(767\) −2.78313 −0.100493
\(768\) −21.2095 −0.765333
\(769\) −31.3424 −1.13023 −0.565117 0.825011i \(-0.691169\pi\)
−0.565117 + 0.825011i \(0.691169\pi\)
\(770\) −223.847 −8.06687
\(771\) −28.2928 −1.01894
\(772\) −59.7447 −2.15026
\(773\) 40.5333 1.45788 0.728941 0.684576i \(-0.240013\pi\)
0.728941 + 0.684576i \(0.240013\pi\)
\(774\) −22.2635 −0.800246
\(775\) −30.2917 −1.08811
\(776\) 10.3861 0.372839
\(777\) −128.523 −4.61073
\(778\) 15.2223 0.545747
\(779\) 17.3034 0.619958
\(780\) 28.1834 1.00913
\(781\) −59.1010 −2.11480
\(782\) 22.2626 0.796109
\(783\) −5.93746 −0.212188
\(784\) −19.4063 −0.693080
\(785\) −66.6521 −2.37892
\(786\) −8.73098 −0.311424
\(787\) 45.8375 1.63393 0.816965 0.576687i \(-0.195655\pi\)
0.816965 + 0.576687i \(0.195655\pi\)
\(788\) −17.3871 −0.619389
\(789\) 34.5909 1.23147
\(790\) −15.5226 −0.552270
\(791\) 38.5561 1.37090
\(792\) −25.2919 −0.898710
\(793\) −4.15230 −0.147453
\(794\) 8.28592 0.294056
\(795\) −85.3328 −3.02644
\(796\) 71.8425 2.54639
\(797\) 30.5244 1.08123 0.540615 0.841270i \(-0.318192\pi\)
0.540615 + 0.841270i \(0.318192\pi\)
\(798\) −110.084 −3.89691
\(799\) 5.54017 0.195997
\(800\) 76.3130 2.69807
\(801\) 29.7330 1.05056
\(802\) 84.0423 2.96764
\(803\) 26.0755 0.920186
\(804\) −33.6393 −1.18637
\(805\) −89.4931 −3.15422
\(806\) −5.93897 −0.209191
\(807\) −14.6253 −0.514834
\(808\) 30.2139 1.06292
\(809\) −5.23437 −0.184031 −0.0920153 0.995758i \(-0.529331\pi\)
−0.0920153 + 0.995758i \(0.529331\pi\)
\(810\) −95.2846 −3.34796
\(811\) −39.1010 −1.37302 −0.686510 0.727120i \(-0.740858\pi\)
−0.686510 + 0.727120i \(0.740858\pi\)
\(812\) −62.2437 −2.18432
\(813\) 10.5837 0.371187
\(814\) −114.318 −4.00685
\(815\) −38.9649 −1.36488
\(816\) −5.28437 −0.184990
\(817\) −17.3131 −0.605709
\(818\) 37.0022 1.29375
\(819\) 12.2175 0.426915
\(820\) 51.3435 1.79299
\(821\) −2.51187 −0.0876647 −0.0438324 0.999039i \(-0.513957\pi\)
−0.0438324 + 0.999039i \(0.513957\pi\)
\(822\) 110.057 3.83869
\(823\) 8.28117 0.288663 0.144332 0.989529i \(-0.453897\pi\)
0.144332 + 0.989529i \(0.453897\pi\)
\(824\) 5.11321 0.178127
\(825\) 125.935 4.38450
\(826\) 32.2565 1.12235
\(827\) 20.7902 0.722945 0.361473 0.932383i \(-0.382274\pi\)
0.361473 + 0.932383i \(0.382274\pi\)
\(828\) −30.2259 −1.05042
\(829\) 49.4890 1.71882 0.859411 0.511285i \(-0.170830\pi\)
0.859411 + 0.511285i \(0.170830\pi\)
\(830\) 71.5684 2.48418
\(831\) 45.5365 1.57964
\(832\) 13.0053 0.450877
\(833\) 46.2878 1.60378
\(834\) −91.2479 −3.15966
\(835\) −23.9014 −0.827141
\(836\) −58.7925 −2.03338
\(837\) 3.94244 0.136271
\(838\) 50.2622 1.73628
\(839\) −45.6574 −1.57627 −0.788135 0.615502i \(-0.788953\pi\)
−0.788135 + 0.615502i \(0.788953\pi\)
\(840\) −109.274 −3.77032
\(841\) −13.0171 −0.448867
\(842\) −10.9701 −0.378053
\(843\) −34.0862 −1.17399
\(844\) −68.5287 −2.35885
\(845\) −4.05108 −0.139361
\(846\) −12.5274 −0.430702
\(847\) −60.7644 −2.08789
\(848\) −8.90231 −0.305707
\(849\) −30.0126 −1.03003
\(850\) −59.5735 −2.04335
\(851\) −45.7040 −1.56671
\(852\) −86.2424 −2.95462
\(853\) −20.9148 −0.716108 −0.358054 0.933701i \(-0.616560\pi\)
−0.358054 + 0.933701i \(0.616560\pi\)
\(854\) 48.1252 1.64681
\(855\) 39.2022 1.34069
\(856\) −9.93243 −0.339484
\(857\) −45.5327 −1.55537 −0.777684 0.628655i \(-0.783606\pi\)
−0.777684 + 0.628655i \(0.783606\pi\)
\(858\) 24.6908 0.842929
\(859\) −30.0964 −1.02688 −0.513438 0.858127i \(-0.671628\pi\)
−0.513438 + 0.858127i \(0.671628\pi\)
\(860\) −51.3723 −1.75178
\(861\) 50.5699 1.72342
\(862\) 53.6960 1.82889
\(863\) 0.389666 0.0132644 0.00663220 0.999978i \(-0.497889\pi\)
0.00663220 + 0.999978i \(0.497889\pi\)
\(864\) −9.93207 −0.337896
\(865\) −41.2415 −1.40225
\(866\) 78.6587 2.67293
\(867\) −26.7477 −0.908400
\(868\) 41.3294 1.40281
\(869\) −8.16528 −0.276988
\(870\) 83.8757 2.84365
\(871\) 4.83531 0.163838
\(872\) 22.7817 0.771485
\(873\) −10.8895 −0.368552
\(874\) −39.1468 −1.32416
\(875\) 134.547 4.54853
\(876\) 38.0504 1.28560
\(877\) 46.2964 1.56332 0.781659 0.623706i \(-0.214374\pi\)
0.781659 + 0.623706i \(0.214374\pi\)
\(878\) −9.00967 −0.304062
\(879\) 17.4899 0.589921
\(880\) 18.8948 0.636944
\(881\) −19.2251 −0.647710 −0.323855 0.946107i \(-0.604979\pi\)
−0.323855 + 0.946107i \(0.604979\pi\)
\(882\) −104.666 −3.52429
\(883\) 2.93154 0.0986543 0.0493271 0.998783i \(-0.484292\pi\)
0.0493271 + 0.998783i \(0.484292\pi\)
\(884\) −7.01302 −0.235873
\(885\) −26.0989 −0.877306
\(886\) 29.8294 1.00214
\(887\) 46.8097 1.57172 0.785858 0.618407i \(-0.212222\pi\)
0.785858 + 0.618407i \(0.212222\pi\)
\(888\) −55.8062 −1.87273
\(889\) 71.3665 2.39355
\(890\) 114.264 3.83014
\(891\) −50.1220 −1.67915
\(892\) −27.4176 −0.918008
\(893\) −9.74188 −0.326000
\(894\) 80.1918 2.68201
\(895\) 96.7616 3.23438
\(896\) −81.4429 −2.72081
\(897\) 9.87128 0.329592
\(898\) 26.3799 0.880309
\(899\) −10.6125 −0.353947
\(900\) 80.8829 2.69610
\(901\) 21.2338 0.707401
\(902\) 44.9808 1.49770
\(903\) −50.5983 −1.68381
\(904\) 16.7415 0.556815
\(905\) 8.75485 0.291021
\(906\) −71.0701 −2.36115
\(907\) 3.38813 0.112501 0.0562506 0.998417i \(-0.482085\pi\)
0.0562506 + 0.998417i \(0.482085\pi\)
\(908\) 54.1570 1.79726
\(909\) −31.6782 −1.05070
\(910\) 46.9520 1.55644
\(911\) 25.9959 0.861283 0.430642 0.902523i \(-0.358287\pi\)
0.430642 + 0.902523i \(0.358287\pi\)
\(912\) 9.29210 0.307692
\(913\) 37.6468 1.24593
\(914\) −77.0618 −2.54898
\(915\) −38.9384 −1.28726
\(916\) −59.2103 −1.95636
\(917\) −8.73350 −0.288405
\(918\) 7.75344 0.255902
\(919\) −2.70131 −0.0891079 −0.0445539 0.999007i \(-0.514187\pi\)
−0.0445539 + 0.999007i \(0.514187\pi\)
\(920\) −38.8590 −1.28114
\(921\) 59.8384 1.97174
\(922\) 4.07883 0.134329
\(923\) 12.3965 0.408035
\(924\) −171.824 −5.65258
\(925\) 122.301 4.02124
\(926\) 2.23728 0.0735215
\(927\) −5.36102 −0.176079
\(928\) 26.7358 0.877646
\(929\) 57.0827 1.87282 0.936411 0.350905i \(-0.114126\pi\)
0.936411 + 0.350905i \(0.114126\pi\)
\(930\) −55.6929 −1.82624
\(931\) −81.3930 −2.66755
\(932\) −16.3592 −0.535865
\(933\) −73.7874 −2.41569
\(934\) −55.0469 −1.80119
\(935\) −45.0679 −1.47388
\(936\) 5.30500 0.173399
\(937\) 18.5064 0.604579 0.302290 0.953216i \(-0.402249\pi\)
0.302290 + 0.953216i \(0.402249\pi\)
\(938\) −56.0413 −1.82981
\(939\) 33.0698 1.07919
\(940\) −28.9066 −0.942830
\(941\) −8.88120 −0.289519 −0.144759 0.989467i \(-0.546241\pi\)
−0.144759 + 0.989467i \(0.546241\pi\)
\(942\) −85.2082 −2.77623
\(943\) 17.9832 0.585612
\(944\) −2.72276 −0.0886183
\(945\) −31.1679 −1.01389
\(946\) −45.0061 −1.46327
\(947\) −28.3129 −0.920046 −0.460023 0.887907i \(-0.652159\pi\)
−0.460023 + 0.887907i \(0.652159\pi\)
\(948\) −11.9151 −0.386984
\(949\) −5.46936 −0.177543
\(950\) 104.755 3.39869
\(951\) −44.1342 −1.43115
\(952\) 27.1913 0.881274
\(953\) −53.9944 −1.74905 −0.874524 0.484981i \(-0.838826\pi\)
−0.874524 + 0.484981i \(0.838826\pi\)
\(954\) −48.0139 −1.55451
\(955\) 56.3104 1.82216
\(956\) 62.2321 2.01273
\(957\) 44.1206 1.42622
\(958\) 58.5068 1.89027
\(959\) 110.089 3.55496
\(960\) 121.957 3.93616
\(961\) −23.9534 −0.772689
\(962\) 23.9783 0.773092
\(963\) 10.4138 0.335580
\(964\) 52.2028 1.68134
\(965\) 80.5314 2.59240
\(966\) −114.408 −3.68102
\(967\) 41.3037 1.32824 0.664118 0.747628i \(-0.268807\pi\)
0.664118 + 0.747628i \(0.268807\pi\)
\(968\) −26.3847 −0.848035
\(969\) −22.1635 −0.711995
\(970\) −41.8482 −1.34367
\(971\) 4.94888 0.158817 0.0794085 0.996842i \(-0.474697\pi\)
0.0794085 + 0.996842i \(0.474697\pi\)
\(972\) −59.7494 −1.91646
\(973\) −91.2743 −2.92612
\(974\) −55.2851 −1.77145
\(975\) −26.4150 −0.845957
\(976\) −4.06223 −0.130029
\(977\) −24.3468 −0.778925 −0.389462 0.921042i \(-0.627339\pi\)
−0.389462 + 0.921042i \(0.627339\pi\)
\(978\) −49.8128 −1.59284
\(979\) 60.1057 1.92099
\(980\) −241.514 −7.71487
\(981\) −23.8858 −0.762615
\(982\) −9.25926 −0.295475
\(983\) −57.1539 −1.82293 −0.911464 0.411380i \(-0.865047\pi\)
−0.911464 + 0.411380i \(0.865047\pi\)
\(984\) 21.9581 0.699998
\(985\) 23.4365 0.746748
\(986\) −20.8712 −0.664675
\(987\) −28.4711 −0.906244
\(988\) 12.3318 0.392326
\(989\) −17.9933 −0.572152
\(990\) 101.908 3.23884
\(991\) 22.8587 0.726130 0.363065 0.931764i \(-0.381730\pi\)
0.363065 + 0.931764i \(0.381730\pi\)
\(992\) −17.7524 −0.563640
\(993\) 74.9305 2.37785
\(994\) −143.675 −4.55710
\(995\) −96.8384 −3.06998
\(996\) 54.9356 1.74070
\(997\) 40.4888 1.28229 0.641147 0.767418i \(-0.278459\pi\)
0.641147 + 0.767418i \(0.278459\pi\)
\(998\) −30.3622 −0.961098
\(999\) −15.9174 −0.503604
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 \(a_p\))