Properties

Label 8035.2.a.e.1.8
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.59020 q^{2}\) \(-1.81242 q^{3}\) \(+4.70914 q^{4}\) \(+1.00000 q^{5}\) \(+4.69454 q^{6}\) \(+3.39615 q^{7}\) \(-7.01723 q^{8}\) \(+0.284882 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.59020 q^{2}\) \(-1.81242 q^{3}\) \(+4.70914 q^{4}\) \(+1.00000 q^{5}\) \(+4.69454 q^{6}\) \(+3.39615 q^{7}\) \(-7.01723 q^{8}\) \(+0.284882 q^{9}\) \(-2.59020 q^{10}\) \(-1.32471 q^{11}\) \(-8.53497 q^{12}\) \(-3.86304 q^{13}\) \(-8.79671 q^{14}\) \(-1.81242 q^{15}\) \(+8.75774 q^{16}\) \(+3.76805 q^{17}\) \(-0.737903 q^{18}\) \(+6.58689 q^{19}\) \(+4.70914 q^{20}\) \(-6.15527 q^{21}\) \(+3.43126 q^{22}\) \(+7.28957 q^{23}\) \(+12.7182 q^{24}\) \(+1.00000 q^{25}\) \(+10.0061 q^{26}\) \(+4.92095 q^{27}\) \(+15.9930 q^{28}\) \(+8.62813 q^{29}\) \(+4.69454 q^{30}\) \(+6.81479 q^{31}\) \(-8.64987 q^{32}\) \(+2.40093 q^{33}\) \(-9.76000 q^{34}\) \(+3.39615 q^{35}\) \(+1.34155 q^{36}\) \(+5.89626 q^{37}\) \(-17.0614 q^{38}\) \(+7.00147 q^{39}\) \(-7.01723 q^{40}\) \(+2.60937 q^{41}\) \(+15.9434 q^{42}\) \(-4.42923 q^{43}\) \(-6.23824 q^{44}\) \(+0.284882 q^{45}\) \(-18.8815 q^{46}\) \(+9.03366 q^{47}\) \(-15.8727 q^{48}\) \(+4.53384 q^{49}\) \(-2.59020 q^{50}\) \(-6.82930 q^{51}\) \(-18.1916 q^{52}\) \(+0.850156 q^{53}\) \(-12.7462 q^{54}\) \(-1.32471 q^{55}\) \(-23.8316 q^{56}\) \(-11.9382 q^{57}\) \(-22.3486 q^{58}\) \(+11.0464 q^{59}\) \(-8.53497 q^{60}\) \(+11.4790 q^{61}\) \(-17.6517 q^{62}\) \(+0.967503 q^{63}\) \(+4.88941 q^{64}\) \(-3.86304 q^{65}\) \(-6.21890 q^{66}\) \(-1.35486 q^{67}\) \(+17.7443 q^{68}\) \(-13.2118 q^{69}\) \(-8.79671 q^{70}\) \(+13.3330 q^{71}\) \(-1.99908 q^{72}\) \(-14.0983 q^{73}\) \(-15.2725 q^{74}\) \(-1.81242 q^{75}\) \(+31.0186 q^{76}\) \(-4.49891 q^{77}\) \(-18.1352 q^{78}\) \(-3.18348 q^{79}\) \(+8.75774 q^{80}\) \(-9.77349 q^{81}\) \(-6.75879 q^{82}\) \(+2.46109 q^{83}\) \(-28.9860 q^{84}\) \(+3.76805 q^{85}\) \(+11.4726 q^{86}\) \(-15.6378 q^{87}\) \(+9.29578 q^{88}\) \(+7.25621 q^{89}\) \(-0.737903 q^{90}\) \(-13.1195 q^{91}\) \(+34.3277 q^{92}\) \(-12.3513 q^{93}\) \(-23.3990 q^{94}\) \(+6.58689 q^{95}\) \(+15.6772 q^{96}\) \(-4.36597 q^{97}\) \(-11.7436 q^{98}\) \(-0.377386 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(153q \) \(\mathstrut +\mathstrut 18q^{2} \) \(\mathstrut +\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 176q^{4} \) \(\mathstrut +\mathstrut 153q^{5} \) \(\mathstrut +\mathstrut 19q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 206q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 38q^{11} \) \(\mathstrut +\mathstrut 14q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 53q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 214q^{16} \) \(\mathstrut +\mathstrut 50q^{17} \) \(\mathstrut +\mathstrut 47q^{18} \) \(\mathstrut +\mathstrut 65q^{19} \) \(\mathstrut +\mathstrut 176q^{20} \) \(\mathstrut +\mathstrut 109q^{21} \) \(\mathstrut +\mathstrut 13q^{22} \) \(\mathstrut +\mathstrut 52q^{23} \) \(\mathstrut +\mathstrut 66q^{24} \) \(\mathstrut +\mathstrut 153q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 19q^{27} \) \(\mathstrut +\mathstrut 26q^{28} \) \(\mathstrut +\mathstrut 172q^{29} \) \(\mathstrut +\mathstrut 19q^{30} \) \(\mathstrut +\mathstrut 60q^{31} \) \(\mathstrut +\mathstrut 107q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 40q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 241q^{36} \) \(\mathstrut +\mathstrut 65q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut +\mathstrut 56q^{39} \) \(\mathstrut +\mathstrut 57q^{40} \) \(\mathstrut +\mathstrut 152q^{41} \) \(\mathstrut -\mathstrut 19q^{42} \) \(\mathstrut +\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 97q^{44} \) \(\mathstrut +\mathstrut 206q^{45} \) \(\mathstrut +\mathstrut 86q^{46} \) \(\mathstrut +\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut +\mathstrut 260q^{49} \) \(\mathstrut +\mathstrut 18q^{50} \) \(\mathstrut +\mathstrut 102q^{51} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 169q^{53} \) \(\mathstrut +\mathstrut 64q^{54} \) \(\mathstrut +\mathstrut 38q^{55} \) \(\mathstrut +\mathstrut 146q^{56} \) \(\mathstrut +\mathstrut 40q^{57} \) \(\mathstrut -\mathstrut 9q^{58} \) \(\mathstrut +\mathstrut 64q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut +\mathstrut 164q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 19q^{63} \) \(\mathstrut +\mathstrut 259q^{64} \) \(\mathstrut +\mathstrut 28q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 112q^{68} \) \(\mathstrut +\mathstrut 119q^{69} \) \(\mathstrut +\mathstrut 53q^{70} \) \(\mathstrut +\mathstrut 100q^{71} \) \(\mathstrut +\mathstrut 77q^{72} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 98q^{74} \) \(\mathstrut +\mathstrut 7q^{75} \) \(\mathstrut +\mathstrut 126q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 110q^{79} \) \(\mathstrut +\mathstrut 214q^{80} \) \(\mathstrut +\mathstrut 305q^{81} \) \(\mathstrut -\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 36q^{83} \) \(\mathstrut +\mathstrut 172q^{84} \) \(\mathstrut +\mathstrut 50q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 47q^{88} \) \(\mathstrut +\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 47q^{90} \) \(\mathstrut +\mathstrut 82q^{91} \) \(\mathstrut +\mathstrut 130q^{92} \) \(\mathstrut +\mathstrut 31q^{93} \) \(\mathstrut +\mathstrut 77q^{94} \) \(\mathstrut +\mathstrut 65q^{95} \) \(\mathstrut +\mathstrut 57q^{96} \) \(\mathstrut +\mathstrut 11q^{97} \) \(\mathstrut +\mathstrut 29q^{98} \) \(\mathstrut +\mathstrut 99q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59020 −1.83155 −0.915774 0.401693i \(-0.868422\pi\)
−0.915774 + 0.401693i \(0.868422\pi\)
\(3\) −1.81242 −1.04640 −0.523202 0.852209i \(-0.675263\pi\)
−0.523202 + 0.852209i \(0.675263\pi\)
\(4\) 4.70914 2.35457
\(5\) 1.00000 0.447214
\(6\) 4.69454 1.91654
\(7\) 3.39615 1.28362 0.641812 0.766862i \(-0.278183\pi\)
0.641812 + 0.766862i \(0.278183\pi\)
\(8\) −7.01723 −2.48096
\(9\) 0.284882 0.0949608
\(10\) −2.59020 −0.819094
\(11\) −1.32471 −0.399415 −0.199707 0.979856i \(-0.563999\pi\)
−0.199707 + 0.979856i \(0.563999\pi\)
\(12\) −8.53497 −2.46383
\(13\) −3.86304 −1.07142 −0.535708 0.844404i \(-0.679955\pi\)
−0.535708 + 0.844404i \(0.679955\pi\)
\(14\) −8.79671 −2.35102
\(15\) −1.81242 −0.467966
\(16\) 8.75774 2.18944
\(17\) 3.76805 0.913885 0.456943 0.889496i \(-0.348944\pi\)
0.456943 + 0.889496i \(0.348944\pi\)
\(18\) −0.737903 −0.173925
\(19\) 6.58689 1.51114 0.755568 0.655070i \(-0.227361\pi\)
0.755568 + 0.655070i \(0.227361\pi\)
\(20\) 4.70914 1.05300
\(21\) −6.15527 −1.34319
\(22\) 3.43126 0.731547
\(23\) 7.28957 1.51998 0.759991 0.649934i \(-0.225203\pi\)
0.759991 + 0.649934i \(0.225203\pi\)
\(24\) 12.7182 2.59609
\(25\) 1.00000 0.200000
\(26\) 10.0061 1.96235
\(27\) 4.92095 0.947036
\(28\) 15.9930 3.02239
\(29\) 8.62813 1.60220 0.801102 0.598528i \(-0.204247\pi\)
0.801102 + 0.598528i \(0.204247\pi\)
\(30\) 4.69454 0.857103
\(31\) 6.81479 1.22397 0.611986 0.790869i \(-0.290371\pi\)
0.611986 + 0.790869i \(0.290371\pi\)
\(32\) −8.64987 −1.52909
\(33\) 2.40093 0.417949
\(34\) −9.76000 −1.67383
\(35\) 3.39615 0.574054
\(36\) 1.34155 0.223592
\(37\) 5.89626 0.969339 0.484669 0.874697i \(-0.338940\pi\)
0.484669 + 0.874697i \(0.338940\pi\)
\(38\) −17.0614 −2.76772
\(39\) 7.00147 1.12113
\(40\) −7.01723 −1.10952
\(41\) 2.60937 0.407515 0.203757 0.979021i \(-0.434685\pi\)
0.203757 + 0.979021i \(0.434685\pi\)
\(42\) 15.9434 2.46012
\(43\) −4.42923 −0.675451 −0.337726 0.941245i \(-0.609658\pi\)
−0.337726 + 0.941245i \(0.609658\pi\)
\(44\) −6.23824 −0.940450
\(45\) 0.284882 0.0424677
\(46\) −18.8815 −2.78392
\(47\) 9.03366 1.31769 0.658847 0.752277i \(-0.271044\pi\)
0.658847 + 0.752277i \(0.271044\pi\)
\(48\) −15.8727 −2.29103
\(49\) 4.53384 0.647692
\(50\) −2.59020 −0.366310
\(51\) −6.82930 −0.956293
\(52\) −18.1916 −2.52272
\(53\) 0.850156 0.116778 0.0583890 0.998294i \(-0.481404\pi\)
0.0583890 + 0.998294i \(0.481404\pi\)
\(54\) −12.7462 −1.73454
\(55\) −1.32471 −0.178624
\(56\) −23.8316 −3.18463
\(57\) −11.9382 −1.58126
\(58\) −22.3486 −2.93451
\(59\) 11.0464 1.43812 0.719061 0.694946i \(-0.244572\pi\)
0.719061 + 0.694946i \(0.244572\pi\)
\(60\) −8.53497 −1.10186
\(61\) 11.4790 1.46973 0.734867 0.678211i \(-0.237245\pi\)
0.734867 + 0.678211i \(0.237245\pi\)
\(62\) −17.6517 −2.24176
\(63\) 0.967503 0.121894
\(64\) 4.88941 0.611176
\(65\) −3.86304 −0.479151
\(66\) −6.21890 −0.765494
\(67\) −1.35486 −0.165522 −0.0827610 0.996569i \(-0.526374\pi\)
−0.0827610 + 0.996569i \(0.526374\pi\)
\(68\) 17.7443 2.15181
\(69\) −13.2118 −1.59051
\(70\) −8.79671 −1.05141
\(71\) 13.3330 1.58234 0.791168 0.611599i \(-0.209473\pi\)
0.791168 + 0.611599i \(0.209473\pi\)
\(72\) −1.99908 −0.235594
\(73\) −14.0983 −1.65008 −0.825038 0.565078i \(-0.808846\pi\)
−0.825038 + 0.565078i \(0.808846\pi\)
\(74\) −15.2725 −1.77539
\(75\) −1.81242 −0.209281
\(76\) 31.0186 3.55808
\(77\) −4.49891 −0.512698
\(78\) −18.1352 −2.05341
\(79\) −3.18348 −0.358170 −0.179085 0.983834i \(-0.557314\pi\)
−0.179085 + 0.983834i \(0.557314\pi\)
\(80\) 8.75774 0.979146
\(81\) −9.77349 −1.08594
\(82\) −6.75879 −0.746383
\(83\) 2.46109 0.270139 0.135070 0.990836i \(-0.456874\pi\)
0.135070 + 0.990836i \(0.456874\pi\)
\(84\) −28.9860 −3.16264
\(85\) 3.76805 0.408702
\(86\) 11.4726 1.23712
\(87\) −15.6378 −1.67655
\(88\) 9.29578 0.990933
\(89\) 7.25621 0.769157 0.384578 0.923092i \(-0.374347\pi\)
0.384578 + 0.923092i \(0.374347\pi\)
\(90\) −0.737903 −0.0777818
\(91\) −13.1195 −1.37529
\(92\) 34.3277 3.57891
\(93\) −12.3513 −1.28077
\(94\) −23.3990 −2.41342
\(95\) 6.58689 0.675801
\(96\) 15.6772 1.60005
\(97\) −4.36597 −0.443297 −0.221648 0.975127i \(-0.571144\pi\)
−0.221648 + 0.975127i \(0.571144\pi\)
\(98\) −11.7436 −1.18628
\(99\) −0.377386 −0.0379287
\(100\) 4.70914 0.470914
\(101\) 4.48412 0.446186 0.223093 0.974797i \(-0.428385\pi\)
0.223093 + 0.974797i \(0.428385\pi\)
\(102\) 17.6893 1.75150
\(103\) −18.0840 −1.78187 −0.890935 0.454130i \(-0.849950\pi\)
−0.890935 + 0.454130i \(0.849950\pi\)
\(104\) 27.1078 2.65814
\(105\) −6.15527 −0.600693
\(106\) −2.20208 −0.213885
\(107\) 0.142024 0.0137300 0.00686499 0.999976i \(-0.497815\pi\)
0.00686499 + 0.999976i \(0.497815\pi\)
\(108\) 23.1734 2.22987
\(109\) 9.08459 0.870146 0.435073 0.900395i \(-0.356723\pi\)
0.435073 + 0.900395i \(0.356723\pi\)
\(110\) 3.43126 0.327158
\(111\) −10.6865 −1.01432
\(112\) 29.7426 2.81041
\(113\) −3.36861 −0.316892 −0.158446 0.987368i \(-0.550648\pi\)
−0.158446 + 0.987368i \(0.550648\pi\)
\(114\) 30.9224 2.89615
\(115\) 7.28957 0.679756
\(116\) 40.6311 3.77250
\(117\) −1.10051 −0.101742
\(118\) −28.6125 −2.63399
\(119\) 12.7969 1.17309
\(120\) 12.7182 1.16101
\(121\) −9.24515 −0.840468
\(122\) −29.7329 −2.69189
\(123\) −4.72928 −0.426425
\(124\) 32.0918 2.88193
\(125\) 1.00000 0.0894427
\(126\) −2.50603 −0.223255
\(127\) 5.01415 0.444934 0.222467 0.974940i \(-0.428589\pi\)
0.222467 + 0.974940i \(0.428589\pi\)
\(128\) 4.63518 0.409696
\(129\) 8.02765 0.706795
\(130\) 10.0061 0.877589
\(131\) −19.4581 −1.70006 −0.850032 0.526730i \(-0.823418\pi\)
−0.850032 + 0.526730i \(0.823418\pi\)
\(132\) 11.3063 0.984091
\(133\) 22.3701 1.93973
\(134\) 3.50935 0.303162
\(135\) 4.92095 0.423528
\(136\) −26.4412 −2.26732
\(137\) 4.80858 0.410825 0.205412 0.978676i \(-0.434146\pi\)
0.205412 + 0.978676i \(0.434146\pi\)
\(138\) 34.2212 2.91310
\(139\) 17.3714 1.47342 0.736710 0.676209i \(-0.236379\pi\)
0.736710 + 0.676209i \(0.236379\pi\)
\(140\) 15.9930 1.35165
\(141\) −16.3728 −1.37884
\(142\) −34.5352 −2.89813
\(143\) 5.11740 0.427939
\(144\) 2.49493 0.207911
\(145\) 8.62813 0.716527
\(146\) 36.5173 3.02219
\(147\) −8.21724 −0.677747
\(148\) 27.7663 2.28238
\(149\) 17.4498 1.42954 0.714772 0.699358i \(-0.246531\pi\)
0.714772 + 0.699358i \(0.246531\pi\)
\(150\) 4.69454 0.383308
\(151\) 19.5516 1.59109 0.795543 0.605897i \(-0.207186\pi\)
0.795543 + 0.605897i \(0.207186\pi\)
\(152\) −46.2217 −3.74907
\(153\) 1.07345 0.0867833
\(154\) 11.6531 0.939032
\(155\) 6.81479 0.547377
\(156\) 32.9709 2.63979
\(157\) −17.3445 −1.38425 −0.692123 0.721780i \(-0.743324\pi\)
−0.692123 + 0.721780i \(0.743324\pi\)
\(158\) 8.24586 0.656005
\(159\) −1.54084 −0.122197
\(160\) −8.64987 −0.683832
\(161\) 24.7565 1.95109
\(162\) 25.3153 1.98896
\(163\) −4.17029 −0.326642 −0.163321 0.986573i \(-0.552221\pi\)
−0.163321 + 0.986573i \(0.552221\pi\)
\(164\) 12.2879 0.959522
\(165\) 2.40093 0.186912
\(166\) −6.37471 −0.494774
\(167\) 13.3766 1.03512 0.517558 0.855648i \(-0.326841\pi\)
0.517558 + 0.855648i \(0.326841\pi\)
\(168\) 43.1929 3.33240
\(169\) 1.92310 0.147930
\(170\) −9.76000 −0.748558
\(171\) 1.87649 0.143499
\(172\) −20.8579 −1.59040
\(173\) −17.5692 −1.33576 −0.667881 0.744268i \(-0.732799\pi\)
−0.667881 + 0.744268i \(0.732799\pi\)
\(174\) 40.5051 3.07069
\(175\) 3.39615 0.256725
\(176\) −11.6015 −0.874493
\(177\) −20.0208 −1.50486
\(178\) −18.7950 −1.40875
\(179\) −8.67362 −0.648297 −0.324148 0.946006i \(-0.605078\pi\)
−0.324148 + 0.946006i \(0.605078\pi\)
\(180\) 1.34155 0.0999933
\(181\) 2.28975 0.170196 0.0850980 0.996373i \(-0.472880\pi\)
0.0850980 + 0.996373i \(0.472880\pi\)
\(182\) 33.9821 2.51892
\(183\) −20.8048 −1.53794
\(184\) −51.1526 −3.77102
\(185\) 5.89626 0.433501
\(186\) 31.9923 2.34579
\(187\) −4.99156 −0.365019
\(188\) 42.5408 3.10261
\(189\) 16.7123 1.21564
\(190\) −17.0614 −1.23776
\(191\) −11.7395 −0.849439 −0.424719 0.905325i \(-0.639627\pi\)
−0.424719 + 0.905325i \(0.639627\pi\)
\(192\) −8.86169 −0.639537
\(193\) −25.8016 −1.85724 −0.928620 0.371033i \(-0.879004\pi\)
−0.928620 + 0.371033i \(0.879004\pi\)
\(194\) 11.3087 0.811920
\(195\) 7.00147 0.501386
\(196\) 21.3505 1.52504
\(197\) 12.0201 0.856394 0.428197 0.903685i \(-0.359149\pi\)
0.428197 + 0.903685i \(0.359149\pi\)
\(198\) 0.977506 0.0694683
\(199\) −5.30959 −0.376387 −0.188193 0.982132i \(-0.560263\pi\)
−0.188193 + 0.982132i \(0.560263\pi\)
\(200\) −7.01723 −0.496193
\(201\) 2.45557 0.173203
\(202\) −11.6148 −0.817212
\(203\) 29.3024 2.05663
\(204\) −32.1601 −2.25166
\(205\) 2.60937 0.182246
\(206\) 46.8412 3.26358
\(207\) 2.07667 0.144339
\(208\) −33.8315 −2.34579
\(209\) −8.72571 −0.603570
\(210\) 15.9434 1.10020
\(211\) 7.84093 0.539792 0.269896 0.962890i \(-0.413011\pi\)
0.269896 + 0.962890i \(0.413011\pi\)
\(212\) 4.00351 0.274962
\(213\) −24.1651 −1.65576
\(214\) −0.367871 −0.0251471
\(215\) −4.42923 −0.302071
\(216\) −34.5314 −2.34956
\(217\) 23.1440 1.57112
\(218\) −23.5309 −1.59372
\(219\) 25.5520 1.72665
\(220\) −6.23824 −0.420582
\(221\) −14.5561 −0.979151
\(222\) 27.6802 1.85778
\(223\) 5.17734 0.346700 0.173350 0.984860i \(-0.444541\pi\)
0.173350 + 0.984860i \(0.444541\pi\)
\(224\) −29.3763 −1.96278
\(225\) 0.284882 0.0189922
\(226\) 8.72537 0.580403
\(227\) 22.4006 1.48678 0.743391 0.668857i \(-0.233216\pi\)
0.743391 + 0.668857i \(0.233216\pi\)
\(228\) −56.2189 −3.72319
\(229\) −8.94754 −0.591270 −0.295635 0.955301i \(-0.595531\pi\)
−0.295635 + 0.955301i \(0.595531\pi\)
\(230\) −18.8815 −1.24501
\(231\) 8.15393 0.536489
\(232\) −60.5456 −3.97501
\(233\) −27.8092 −1.82184 −0.910921 0.412582i \(-0.864627\pi\)
−0.910921 + 0.412582i \(0.864627\pi\)
\(234\) 2.85055 0.186346
\(235\) 9.03366 0.589291
\(236\) 52.0192 3.38616
\(237\) 5.76982 0.374790
\(238\) −33.1464 −2.14856
\(239\) −6.12700 −0.396323 −0.198161 0.980169i \(-0.563497\pi\)
−0.198161 + 0.980169i \(0.563497\pi\)
\(240\) −15.8727 −1.02458
\(241\) −15.2461 −0.982084 −0.491042 0.871136i \(-0.663384\pi\)
−0.491042 + 0.871136i \(0.663384\pi\)
\(242\) 23.9468 1.53936
\(243\) 2.95087 0.189299
\(244\) 54.0562 3.46059
\(245\) 4.53384 0.289656
\(246\) 12.2498 0.781018
\(247\) −25.4454 −1.61905
\(248\) −47.8209 −3.03663
\(249\) −4.46053 −0.282675
\(250\) −2.59020 −0.163819
\(251\) −15.7528 −0.994307 −0.497153 0.867663i \(-0.665621\pi\)
−0.497153 + 0.867663i \(0.665621\pi\)
\(252\) 4.55611 0.287008
\(253\) −9.65656 −0.607103
\(254\) −12.9876 −0.814918
\(255\) −6.82930 −0.427667
\(256\) −21.7849 −1.36155
\(257\) 10.9656 0.684018 0.342009 0.939697i \(-0.388893\pi\)
0.342009 + 0.939697i \(0.388893\pi\)
\(258\) −20.7932 −1.29453
\(259\) 20.0246 1.24427
\(260\) −18.1916 −1.12820
\(261\) 2.45800 0.152147
\(262\) 50.4005 3.11375
\(263\) −19.7992 −1.22087 −0.610435 0.792066i \(-0.709005\pi\)
−0.610435 + 0.792066i \(0.709005\pi\)
\(264\) −16.8479 −1.03692
\(265\) 0.850156 0.0522247
\(266\) −57.9430 −3.55271
\(267\) −13.1513 −0.804849
\(268\) −6.38021 −0.389733
\(269\) −24.9416 −1.52072 −0.760358 0.649504i \(-0.774977\pi\)
−0.760358 + 0.649504i \(0.774977\pi\)
\(270\) −12.7462 −0.775711
\(271\) −6.58375 −0.399934 −0.199967 0.979803i \(-0.564084\pi\)
−0.199967 + 0.979803i \(0.564084\pi\)
\(272\) 32.9996 2.00089
\(273\) 23.7781 1.43911
\(274\) −12.4552 −0.752445
\(275\) −1.32471 −0.0798829
\(276\) −62.2163 −3.74498
\(277\) −7.17253 −0.430955 −0.215478 0.976509i \(-0.569131\pi\)
−0.215478 + 0.976509i \(0.569131\pi\)
\(278\) −44.9953 −2.69864
\(279\) 1.94141 0.116229
\(280\) −23.8316 −1.42421
\(281\) 2.12600 0.126827 0.0634133 0.997987i \(-0.479801\pi\)
0.0634133 + 0.997987i \(0.479801\pi\)
\(282\) 42.4089 2.52541
\(283\) 16.7610 0.996337 0.498168 0.867080i \(-0.334006\pi\)
0.498168 + 0.867080i \(0.334006\pi\)
\(284\) 62.7870 3.72572
\(285\) −11.9382 −0.707160
\(286\) −13.2551 −0.783791
\(287\) 8.86180 0.523096
\(288\) −2.46419 −0.145204
\(289\) −2.80183 −0.164813
\(290\) −22.3486 −1.31235
\(291\) 7.91298 0.463867
\(292\) −66.3907 −3.88522
\(293\) −15.2160 −0.888926 −0.444463 0.895797i \(-0.646605\pi\)
−0.444463 + 0.895797i \(0.646605\pi\)
\(294\) 21.2843 1.24133
\(295\) 11.0464 0.643148
\(296\) −41.3754 −2.40489
\(297\) −6.51882 −0.378260
\(298\) −45.1985 −2.61828
\(299\) −28.1599 −1.62853
\(300\) −8.53497 −0.492767
\(301\) −15.0423 −0.867026
\(302\) −50.6426 −2.91415
\(303\) −8.12712 −0.466891
\(304\) 57.6863 3.30854
\(305\) 11.4790 0.657285
\(306\) −2.78045 −0.158948
\(307\) 22.7998 1.30125 0.650626 0.759398i \(-0.274507\pi\)
0.650626 + 0.759398i \(0.274507\pi\)
\(308\) −21.1860 −1.20718
\(309\) 32.7759 1.86456
\(310\) −17.6517 −1.00255
\(311\) 31.4060 1.78087 0.890436 0.455108i \(-0.150400\pi\)
0.890436 + 0.455108i \(0.150400\pi\)
\(312\) −49.1309 −2.78149
\(313\) 16.8328 0.951444 0.475722 0.879596i \(-0.342187\pi\)
0.475722 + 0.879596i \(0.342187\pi\)
\(314\) 44.9259 2.53531
\(315\) 0.967503 0.0545126
\(316\) −14.9915 −0.843336
\(317\) 0.279917 0.0157217 0.00786086 0.999969i \(-0.497498\pi\)
0.00786086 + 0.999969i \(0.497498\pi\)
\(318\) 3.99110 0.223810
\(319\) −11.4298 −0.639944
\(320\) 4.88941 0.273326
\(321\) −0.257408 −0.0143671
\(322\) −64.1243 −3.57351
\(323\) 24.8197 1.38101
\(324\) −46.0248 −2.55693
\(325\) −3.86304 −0.214283
\(326\) 10.8019 0.598261
\(327\) −16.4651 −0.910524
\(328\) −18.3105 −1.01103
\(329\) 30.6797 1.69143
\(330\) −6.21890 −0.342339
\(331\) −3.04772 −0.167518 −0.0837588 0.996486i \(-0.526693\pi\)
−0.0837588 + 0.996486i \(0.526693\pi\)
\(332\) 11.5896 0.636063
\(333\) 1.67974 0.0920491
\(334\) −34.6482 −1.89586
\(335\) −1.35486 −0.0740237
\(336\) −53.9063 −2.94083
\(337\) 34.1747 1.86161 0.930807 0.365512i \(-0.119106\pi\)
0.930807 + 0.365512i \(0.119106\pi\)
\(338\) −4.98120 −0.270942
\(339\) 6.10535 0.331597
\(340\) 17.7443 0.962318
\(341\) −9.02760 −0.488872
\(342\) −4.86048 −0.262825
\(343\) −8.37545 −0.452232
\(344\) 31.0809 1.67577
\(345\) −13.2118 −0.711300
\(346\) 45.5078 2.44651
\(347\) 0.248874 0.0133603 0.00668013 0.999978i \(-0.497874\pi\)
0.00668013 + 0.999978i \(0.497874\pi\)
\(348\) −73.6408 −3.94756
\(349\) −35.1882 −1.88358 −0.941791 0.336198i \(-0.890859\pi\)
−0.941791 + 0.336198i \(0.890859\pi\)
\(350\) −8.79671 −0.470204
\(351\) −19.0098 −1.01467
\(352\) 11.4586 0.610743
\(353\) −6.95343 −0.370093 −0.185047 0.982730i \(-0.559244\pi\)
−0.185047 + 0.982730i \(0.559244\pi\)
\(354\) 51.8580 2.75622
\(355\) 13.3330 0.707642
\(356\) 34.1705 1.81104
\(357\) −23.1933 −1.22752
\(358\) 22.4664 1.18739
\(359\) −12.0994 −0.638583 −0.319292 0.947657i \(-0.603445\pi\)
−0.319292 + 0.947657i \(0.603445\pi\)
\(360\) −1.99908 −0.105361
\(361\) 24.3871 1.28353
\(362\) −5.93092 −0.311722
\(363\) 16.7561 0.879469
\(364\) −61.7815 −3.23823
\(365\) −14.0983 −0.737936
\(366\) 53.8886 2.81680
\(367\) −11.5433 −0.602556 −0.301278 0.953536i \(-0.597413\pi\)
−0.301278 + 0.953536i \(0.597413\pi\)
\(368\) 63.8402 3.32790
\(369\) 0.743362 0.0386979
\(370\) −15.2725 −0.793979
\(371\) 2.88726 0.149899
\(372\) −58.1640 −3.01566
\(373\) −5.98838 −0.310066 −0.155033 0.987909i \(-0.549548\pi\)
−0.155033 + 0.987909i \(0.549548\pi\)
\(374\) 12.9292 0.668550
\(375\) −1.81242 −0.0935932
\(376\) −63.3913 −3.26915
\(377\) −33.3308 −1.71663
\(378\) −43.2882 −2.22650
\(379\) 19.8025 1.01719 0.508594 0.861007i \(-0.330166\pi\)
0.508594 + 0.861007i \(0.330166\pi\)
\(380\) 31.0186 1.59122
\(381\) −9.08776 −0.465580
\(382\) 30.4076 1.55579
\(383\) 34.4967 1.76270 0.881349 0.472466i \(-0.156636\pi\)
0.881349 + 0.472466i \(0.156636\pi\)
\(384\) −8.40091 −0.428707
\(385\) −4.49891 −0.229286
\(386\) 66.8313 3.40163
\(387\) −1.26181 −0.0641414
\(388\) −20.5600 −1.04377
\(389\) 27.5347 1.39606 0.698032 0.716066i \(-0.254059\pi\)
0.698032 + 0.716066i \(0.254059\pi\)
\(390\) −18.1352 −0.918313
\(391\) 27.4675 1.38909
\(392\) −31.8150 −1.60690
\(393\) 35.2664 1.77895
\(394\) −31.1344 −1.56853
\(395\) −3.18348 −0.160178
\(396\) −1.77716 −0.0893059
\(397\) −2.20360 −0.110595 −0.0552977 0.998470i \(-0.517611\pi\)
−0.0552977 + 0.998470i \(0.517611\pi\)
\(398\) 13.7529 0.689371
\(399\) −40.5441 −2.02974
\(400\) 8.75774 0.437887
\(401\) 22.9951 1.14832 0.574159 0.818743i \(-0.305329\pi\)
0.574159 + 0.818743i \(0.305329\pi\)
\(402\) −6.36043 −0.317229
\(403\) −26.3258 −1.31138
\(404\) 21.1163 1.05058
\(405\) −9.77349 −0.485649
\(406\) −75.8992 −3.76681
\(407\) −7.81082 −0.387168
\(408\) 47.9227 2.37253
\(409\) 37.3641 1.84753 0.923767 0.382956i \(-0.125094\pi\)
0.923767 + 0.382956i \(0.125094\pi\)
\(410\) −6.75879 −0.333793
\(411\) −8.71518 −0.429888
\(412\) −85.1602 −4.19554
\(413\) 37.5154 1.84601
\(414\) −5.37900 −0.264363
\(415\) 2.46109 0.120810
\(416\) 33.4148 1.63830
\(417\) −31.4843 −1.54179
\(418\) 22.6013 1.10547
\(419\) −18.5700 −0.907205 −0.453603 0.891204i \(-0.649861\pi\)
−0.453603 + 0.891204i \(0.649861\pi\)
\(420\) −28.9860 −1.41437
\(421\) −21.8681 −1.06579 −0.532894 0.846182i \(-0.678895\pi\)
−0.532894 + 0.846182i \(0.678895\pi\)
\(422\) −20.3096 −0.988655
\(423\) 2.57353 0.125129
\(424\) −5.96574 −0.289722
\(425\) 3.76805 0.182777
\(426\) 62.5924 3.03261
\(427\) 38.9844 1.88659
\(428\) 0.668812 0.0323282
\(429\) −9.27491 −0.447797
\(430\) 11.4726 0.553258
\(431\) −13.4451 −0.647626 −0.323813 0.946121i \(-0.604965\pi\)
−0.323813 + 0.946121i \(0.604965\pi\)
\(432\) 43.0964 2.07348
\(433\) −10.6563 −0.512110 −0.256055 0.966662i \(-0.582423\pi\)
−0.256055 + 0.966662i \(0.582423\pi\)
\(434\) −59.9477 −2.87758
\(435\) −15.6378 −0.749777
\(436\) 42.7806 2.04882
\(437\) 48.0156 2.29690
\(438\) −66.1849 −3.16243
\(439\) −22.8873 −1.09235 −0.546174 0.837671i \(-0.683916\pi\)
−0.546174 + 0.837671i \(0.683916\pi\)
\(440\) 9.29578 0.443159
\(441\) 1.29161 0.0615053
\(442\) 37.7033 1.79336
\(443\) −16.9165 −0.803726 −0.401863 0.915700i \(-0.631637\pi\)
−0.401863 + 0.915700i \(0.631637\pi\)
\(444\) −50.3244 −2.38829
\(445\) 7.25621 0.343977
\(446\) −13.4104 −0.634999
\(447\) −31.6265 −1.49588
\(448\) 16.6052 0.784521
\(449\) 4.83364 0.228114 0.114057 0.993474i \(-0.463615\pi\)
0.114057 + 0.993474i \(0.463615\pi\)
\(450\) −0.737903 −0.0347851
\(451\) −3.45665 −0.162767
\(452\) −15.8633 −0.746145
\(453\) −35.4358 −1.66492
\(454\) −58.0222 −2.72311
\(455\) −13.1195 −0.615050
\(456\) 83.7733 3.92305
\(457\) −32.9070 −1.53932 −0.769662 0.638451i \(-0.779576\pi\)
−0.769662 + 0.638451i \(0.779576\pi\)
\(458\) 23.1759 1.08294
\(459\) 18.5424 0.865483
\(460\) 34.3277 1.60053
\(461\) −13.8105 −0.643220 −0.321610 0.946872i \(-0.604224\pi\)
−0.321610 + 0.946872i \(0.604224\pi\)
\(462\) −21.1203 −0.982607
\(463\) −19.6237 −0.911992 −0.455996 0.889982i \(-0.650717\pi\)
−0.455996 + 0.889982i \(0.650717\pi\)
\(464\) 75.5630 3.50792
\(465\) −12.3513 −0.572777
\(466\) 72.0314 3.33679
\(467\) −29.0152 −1.34266 −0.671331 0.741157i \(-0.734277\pi\)
−0.671331 + 0.741157i \(0.734277\pi\)
\(468\) −5.18247 −0.239560
\(469\) −4.60129 −0.212468
\(470\) −23.3990 −1.07932
\(471\) 31.4357 1.44848
\(472\) −77.5153 −3.56793
\(473\) 5.86744 0.269785
\(474\) −14.9450 −0.686446
\(475\) 6.58689 0.302227
\(476\) 60.2622 2.76211
\(477\) 0.242194 0.0110893
\(478\) 15.8702 0.725884
\(479\) −6.77108 −0.309379 −0.154689 0.987963i \(-0.549438\pi\)
−0.154689 + 0.987963i \(0.549438\pi\)
\(480\) 15.6772 0.715564
\(481\) −22.7775 −1.03856
\(482\) 39.4903 1.79874
\(483\) −44.8693 −2.04162
\(484\) −43.5367 −1.97894
\(485\) −4.36597 −0.198248
\(486\) −7.64336 −0.346710
\(487\) −11.6567 −0.528216 −0.264108 0.964493i \(-0.585078\pi\)
−0.264108 + 0.964493i \(0.585078\pi\)
\(488\) −80.5507 −3.64636
\(489\) 7.55833 0.341799
\(490\) −11.7436 −0.530520
\(491\) 10.4262 0.470528 0.235264 0.971932i \(-0.424405\pi\)
0.235264 + 0.971932i \(0.424405\pi\)
\(492\) −22.2709 −1.00405
\(493\) 32.5112 1.46423
\(494\) 65.9088 2.96538
\(495\) −0.377386 −0.0169622
\(496\) 59.6822 2.67981
\(497\) 45.2809 2.03112
\(498\) 11.5537 0.517733
\(499\) −1.03251 −0.0462214 −0.0231107 0.999733i \(-0.507357\pi\)
−0.0231107 + 0.999733i \(0.507357\pi\)
\(500\) 4.70914 0.210599
\(501\) −24.2441 −1.08315
\(502\) 40.8029 1.82112
\(503\) 3.07118 0.136937 0.0684685 0.997653i \(-0.478189\pi\)
0.0684685 + 0.997653i \(0.478189\pi\)
\(504\) −6.78919 −0.302415
\(505\) 4.48412 0.199541
\(506\) 25.0124 1.11194
\(507\) −3.48547 −0.154795
\(508\) 23.6123 1.04763
\(509\) −1.93778 −0.0858907 −0.0429453 0.999077i \(-0.513674\pi\)
−0.0429453 + 0.999077i \(0.513674\pi\)
\(510\) 17.6893 0.783294
\(511\) −47.8798 −2.11808
\(512\) 47.1568 2.08406
\(513\) 32.4137 1.43110
\(514\) −28.4032 −1.25281
\(515\) −18.0840 −0.796877
\(516\) 37.8033 1.66420
\(517\) −11.9670 −0.526307
\(518\) −51.8677 −2.27894
\(519\) 31.8429 1.39775
\(520\) 27.1078 1.18876
\(521\) −40.2414 −1.76301 −0.881503 0.472178i \(-0.843468\pi\)
−0.881503 + 0.472178i \(0.843468\pi\)
\(522\) −6.36672 −0.278664
\(523\) 25.6942 1.12353 0.561765 0.827297i \(-0.310122\pi\)
0.561765 + 0.827297i \(0.310122\pi\)
\(524\) −91.6311 −4.00292
\(525\) −6.15527 −0.268638
\(526\) 51.2839 2.23608
\(527\) 25.6784 1.11857
\(528\) 21.0268 0.915072
\(529\) 30.1379 1.31034
\(530\) −2.20208 −0.0956521
\(531\) 3.14693 0.136565
\(532\) 105.344 4.56724
\(533\) −10.0801 −0.436617
\(534\) 34.0646 1.47412
\(535\) 0.142024 0.00614024
\(536\) 9.50733 0.410654
\(537\) 15.7203 0.678380
\(538\) 64.6038 2.78527
\(539\) −6.00602 −0.258697
\(540\) 23.1734 0.997226
\(541\) 31.4635 1.35272 0.676361 0.736570i \(-0.263556\pi\)
0.676361 + 0.736570i \(0.263556\pi\)
\(542\) 17.0532 0.732499
\(543\) −4.15000 −0.178094
\(544\) −32.5931 −1.39742
\(545\) 9.08459 0.389141
\(546\) −61.5900 −2.63581
\(547\) 26.9061 1.15042 0.575210 0.818006i \(-0.304920\pi\)
0.575210 + 0.818006i \(0.304920\pi\)
\(548\) 22.6443 0.967316
\(549\) 3.27016 0.139567
\(550\) 3.43126 0.146309
\(551\) 56.8326 2.42115
\(552\) 92.7102 3.94601
\(553\) −10.8116 −0.459755
\(554\) 18.5783 0.789316
\(555\) −10.6865 −0.453617
\(556\) 81.8042 3.46927
\(557\) −40.4446 −1.71369 −0.856846 0.515572i \(-0.827580\pi\)
−0.856846 + 0.515572i \(0.827580\pi\)
\(558\) −5.02865 −0.212880
\(559\) 17.1103 0.723689
\(560\) 29.7426 1.25686
\(561\) 9.04683 0.381957
\(562\) −5.50677 −0.232289
\(563\) −12.8532 −0.541697 −0.270849 0.962622i \(-0.587304\pi\)
−0.270849 + 0.962622i \(0.587304\pi\)
\(564\) −77.1020 −3.24658
\(565\) −3.36861 −0.141718
\(566\) −43.4143 −1.82484
\(567\) −33.1922 −1.39394
\(568\) −93.5607 −3.92572
\(569\) 6.90463 0.289457 0.144729 0.989471i \(-0.453769\pi\)
0.144729 + 0.989471i \(0.453769\pi\)
\(570\) 30.9224 1.29520
\(571\) −33.8435 −1.41631 −0.708154 0.706058i \(-0.750472\pi\)
−0.708154 + 0.706058i \(0.750472\pi\)
\(572\) 24.0986 1.00761
\(573\) 21.2769 0.888856
\(574\) −22.9539 −0.958075
\(575\) 7.28957 0.303996
\(576\) 1.39291 0.0580378
\(577\) 0.868174 0.0361426 0.0180713 0.999837i \(-0.494247\pi\)
0.0180713 + 0.999837i \(0.494247\pi\)
\(578\) 7.25729 0.301864
\(579\) 46.7634 1.94342
\(580\) 40.6311 1.68711
\(581\) 8.35822 0.346758
\(582\) −20.4962 −0.849596
\(583\) −1.12621 −0.0466428
\(584\) 98.9306 4.09378
\(585\) −1.10051 −0.0455006
\(586\) 39.4124 1.62811
\(587\) 18.6255 0.768757 0.384379 0.923175i \(-0.374416\pi\)
0.384379 + 0.923175i \(0.374416\pi\)
\(588\) −38.6962 −1.59580
\(589\) 44.8883 1.84959
\(590\) −28.6125 −1.17796
\(591\) −21.7855 −0.896134
\(592\) 51.6379 2.12230
\(593\) 22.3707 0.918656 0.459328 0.888267i \(-0.348090\pi\)
0.459328 + 0.888267i \(0.348090\pi\)
\(594\) 16.8850 0.692802
\(595\) 12.7969 0.524620
\(596\) 82.1736 3.36596
\(597\) 9.62323 0.393852
\(598\) 72.9399 2.98273
\(599\) −24.3762 −0.995985 −0.497993 0.867181i \(-0.665929\pi\)
−0.497993 + 0.867181i \(0.665929\pi\)
\(600\) 12.7182 0.519218
\(601\) 12.2157 0.498288 0.249144 0.968466i \(-0.419851\pi\)
0.249144 + 0.968466i \(0.419851\pi\)
\(602\) 38.9627 1.58800
\(603\) −0.385974 −0.0157181
\(604\) 92.0712 3.74633
\(605\) −9.24515 −0.375869
\(606\) 21.0509 0.855134
\(607\) −37.4271 −1.51912 −0.759560 0.650438i \(-0.774585\pi\)
−0.759560 + 0.650438i \(0.774585\pi\)
\(608\) −56.9757 −2.31067
\(609\) −53.1085 −2.15206
\(610\) −29.7329 −1.20385
\(611\) −34.8974 −1.41180
\(612\) 5.05503 0.204337
\(613\) 28.5154 1.15173 0.575863 0.817547i \(-0.304666\pi\)
0.575863 + 0.817547i \(0.304666\pi\)
\(614\) −59.0560 −2.38331
\(615\) −4.72928 −0.190703
\(616\) 31.5699 1.27199
\(617\) −13.7692 −0.554328 −0.277164 0.960823i \(-0.589395\pi\)
−0.277164 + 0.960823i \(0.589395\pi\)
\(618\) −84.8962 −3.41503
\(619\) 22.6537 0.910531 0.455265 0.890356i \(-0.349544\pi\)
0.455265 + 0.890356i \(0.349544\pi\)
\(620\) 32.0918 1.28884
\(621\) 35.8716 1.43948
\(622\) −81.3479 −3.26175
\(623\) 24.6432 0.987309
\(624\) 61.3171 2.45465
\(625\) 1.00000 0.0400000
\(626\) −43.6002 −1.74262
\(627\) 15.8147 0.631578
\(628\) −81.6780 −3.25931
\(629\) 22.2174 0.885865
\(630\) −2.50603 −0.0998426
\(631\) −36.2838 −1.44444 −0.722218 0.691666i \(-0.756877\pi\)
−0.722218 + 0.691666i \(0.756877\pi\)
\(632\) 22.3392 0.888606
\(633\) −14.2111 −0.564840
\(634\) −0.725042 −0.0287951
\(635\) 5.01415 0.198980
\(636\) −7.25605 −0.287721
\(637\) −17.5144 −0.693947
\(638\) 29.6054 1.17209
\(639\) 3.79834 0.150260
\(640\) 4.63518 0.183221
\(641\) −33.5998 −1.32711 −0.663557 0.748126i \(-0.730954\pi\)
−0.663557 + 0.748126i \(0.730954\pi\)
\(642\) 0.666738 0.0263141
\(643\) −2.31227 −0.0911869 −0.0455935 0.998960i \(-0.514518\pi\)
−0.0455935 + 0.998960i \(0.514518\pi\)
\(644\) 116.582 4.59397
\(645\) 8.02765 0.316088
\(646\) −64.2880 −2.52938
\(647\) −27.6768 −1.08809 −0.544044 0.839057i \(-0.683107\pi\)
−0.544044 + 0.839057i \(0.683107\pi\)
\(648\) 68.5828 2.69419
\(649\) −14.6333 −0.574407
\(650\) 10.0061 0.392470
\(651\) −41.9468 −1.64403
\(652\) −19.6385 −0.769102
\(653\) 42.5956 1.66689 0.833447 0.552600i \(-0.186364\pi\)
0.833447 + 0.552600i \(0.186364\pi\)
\(654\) 42.6480 1.66767
\(655\) −19.4581 −0.760292
\(656\) 22.8522 0.892227
\(657\) −4.01634 −0.156692
\(658\) −79.4665 −3.09793
\(659\) −42.0494 −1.63801 −0.819005 0.573786i \(-0.805474\pi\)
−0.819005 + 0.573786i \(0.805474\pi\)
\(660\) 11.3063 0.440099
\(661\) −20.6057 −0.801469 −0.400735 0.916194i \(-0.631245\pi\)
−0.400735 + 0.916194i \(0.631245\pi\)
\(662\) 7.89420 0.306817
\(663\) 26.3819 1.02459
\(664\) −17.2700 −0.670206
\(665\) 22.3701 0.867474
\(666\) −4.35086 −0.168593
\(667\) 62.8954 2.43532
\(668\) 62.9925 2.43725
\(669\) −9.38354 −0.362789
\(670\) 3.50935 0.135578
\(671\) −15.2063 −0.587033
\(672\) 53.2422 2.05386
\(673\) −35.2427 −1.35851 −0.679253 0.733904i \(-0.737696\pi\)
−0.679253 + 0.733904i \(0.737696\pi\)
\(674\) −88.5193 −3.40964
\(675\) 4.92095 0.189407
\(676\) 9.05613 0.348313
\(677\) 5.10569 0.196227 0.0981137 0.995175i \(-0.468719\pi\)
0.0981137 + 0.995175i \(0.468719\pi\)
\(678\) −15.8141 −0.607336
\(679\) −14.8275 −0.569026
\(680\) −26.4412 −1.01398
\(681\) −40.5995 −1.55577
\(682\) 23.3833 0.895393
\(683\) −9.01076 −0.344787 −0.172394 0.985028i \(-0.555150\pi\)
−0.172394 + 0.985028i \(0.555150\pi\)
\(684\) 8.83665 0.337878
\(685\) 4.80858 0.183726
\(686\) 21.6941 0.828285
\(687\) 16.2167 0.618707
\(688\) −38.7901 −1.47886
\(689\) −3.28419 −0.125118
\(690\) 34.2212 1.30278
\(691\) 26.2076 0.996984 0.498492 0.866894i \(-0.333887\pi\)
0.498492 + 0.866894i \(0.333887\pi\)
\(692\) −82.7359 −3.14515
\(693\) −1.28166 −0.0486862
\(694\) −0.644634 −0.0244700
\(695\) 17.3714 0.658933
\(696\) 109.734 4.15947
\(697\) 9.83222 0.372422
\(698\) 91.1446 3.44987
\(699\) 50.4021 1.90638
\(700\) 15.9930 0.604477
\(701\) 29.3166 1.10727 0.553637 0.832758i \(-0.313240\pi\)
0.553637 + 0.832758i \(0.313240\pi\)
\(702\) 49.2393 1.85842
\(703\) 38.8380 1.46480
\(704\) −6.47704 −0.244113
\(705\) −16.3728 −0.616636
\(706\) 18.0108 0.677844
\(707\) 15.2287 0.572736
\(708\) −94.2809 −3.54329
\(709\) −1.26901 −0.0476586 −0.0238293 0.999716i \(-0.507586\pi\)
−0.0238293 + 0.999716i \(0.507586\pi\)
\(710\) −34.5352 −1.29608
\(711\) −0.906918 −0.0340121
\(712\) −50.9185 −1.90825
\(713\) 49.6769 1.86041
\(714\) 60.0754 2.24827
\(715\) 5.11740 0.191380
\(716\) −40.8453 −1.52646
\(717\) 11.1047 0.414714
\(718\) 31.3399 1.16960
\(719\) −50.5572 −1.88547 −0.942733 0.333549i \(-0.891754\pi\)
−0.942733 + 0.333549i \(0.891754\pi\)
\(720\) 2.49493 0.0929804
\(721\) −61.4160 −2.28725
\(722\) −63.1675 −2.35085
\(723\) 27.6323 1.02766
\(724\) 10.7828 0.400739
\(725\) 8.62813 0.320441
\(726\) −43.4018 −1.61079
\(727\) −36.2039 −1.34273 −0.671364 0.741128i \(-0.734291\pi\)
−0.671364 + 0.741128i \(0.734291\pi\)
\(728\) 92.0623 3.41206
\(729\) 23.9722 0.887860
\(730\) 36.5173 1.35157
\(731\) −16.6895 −0.617285
\(732\) −97.9728 −3.62118
\(733\) 15.8588 0.585759 0.292880 0.956149i \(-0.405386\pi\)
0.292880 + 0.956149i \(0.405386\pi\)
\(734\) 29.8995 1.10361
\(735\) −8.21724 −0.303098
\(736\) −63.0539 −2.32420
\(737\) 1.79479 0.0661119
\(738\) −1.92546 −0.0708771
\(739\) −52.1297 −1.91762 −0.958811 0.284044i \(-0.908324\pi\)
−0.958811 + 0.284044i \(0.908324\pi\)
\(740\) 27.7663 1.02071
\(741\) 46.1179 1.69418
\(742\) −7.47858 −0.274547
\(743\) 41.8970 1.53705 0.768526 0.639819i \(-0.220991\pi\)
0.768526 + 0.639819i \(0.220991\pi\)
\(744\) 86.6718 3.17754
\(745\) 17.4498 0.639311
\(746\) 15.5111 0.567902
\(747\) 0.701120 0.0256526
\(748\) −23.5060 −0.859464
\(749\) 0.482335 0.0176241
\(750\) 4.69454 0.171421
\(751\) 3.76648 0.137441 0.0687204 0.997636i \(-0.478108\pi\)
0.0687204 + 0.997636i \(0.478108\pi\)
\(752\) 79.1145 2.88501
\(753\) 28.5507 1.04045
\(754\) 86.3336 3.14408
\(755\) 19.5516 0.711555
\(756\) 78.7005 2.86231
\(757\) 28.0916 1.02101 0.510503 0.859876i \(-0.329459\pi\)
0.510503 + 0.859876i \(0.329459\pi\)
\(758\) −51.2925 −1.86303
\(759\) 17.5018 0.635275
\(760\) −46.2217 −1.67664
\(761\) 16.9941 0.616036 0.308018 0.951380i \(-0.400334\pi\)
0.308018 + 0.951380i \(0.400334\pi\)
\(762\) 23.5391 0.852733
\(763\) 30.8526 1.11694
\(764\) −55.2829 −2.00006
\(765\) 1.07345 0.0388107
\(766\) −89.3533 −3.22847
\(767\) −42.6728 −1.54083
\(768\) 39.4834 1.42474
\(769\) −40.5957 −1.46392 −0.731959 0.681349i \(-0.761394\pi\)
−0.731959 + 0.681349i \(0.761394\pi\)
\(770\) 11.6531 0.419948
\(771\) −19.8744 −0.715759
\(772\) −121.503 −4.37300
\(773\) 44.7423 1.60927 0.804634 0.593771i \(-0.202361\pi\)
0.804634 + 0.593771i \(0.202361\pi\)
\(774\) 3.26834 0.117478
\(775\) 6.81479 0.244794
\(776\) 30.6370 1.09980
\(777\) −36.2930 −1.30201
\(778\) −71.3204 −2.55696
\(779\) 17.1876 0.615810
\(780\) 32.9709 1.18055
\(781\) −17.6623 −0.632008
\(782\) −71.1462 −2.54418
\(783\) 42.4586 1.51735
\(784\) 39.7062 1.41808
\(785\) −17.3445 −0.619054
\(786\) −91.3471 −3.25824
\(787\) 37.5204 1.33746 0.668729 0.743507i \(-0.266839\pi\)
0.668729 + 0.743507i \(0.266839\pi\)
\(788\) 56.6042 2.01644
\(789\) 35.8845 1.27752
\(790\) 8.24586 0.293374
\(791\) −11.4403 −0.406770
\(792\) 2.64820 0.0940998
\(793\) −44.3438 −1.57470
\(794\) 5.70776 0.202561
\(795\) −1.54084 −0.0546481
\(796\) −25.0036 −0.886230
\(797\) −16.1211 −0.571039 −0.285520 0.958373i \(-0.592166\pi\)
−0.285520 + 0.958373i \(0.592166\pi\)
\(798\) 105.017 3.71757
\(799\) 34.0393 1.20422
\(800\) −8.64987 −0.305819
\(801\) 2.06717 0.0730397
\(802\) −59.5619 −2.10320
\(803\) 18.6761 0.659064
\(804\) 11.5636 0.407818
\(805\) 24.7565 0.872552
\(806\) 68.1892 2.40186
\(807\) 45.2048 1.59128
\(808\) −31.4661 −1.10697
\(809\) 40.0168 1.40692 0.703459 0.710736i \(-0.251638\pi\)
0.703459 + 0.710736i \(0.251638\pi\)
\(810\) 25.3153 0.889489
\(811\) 16.1245 0.566206 0.283103 0.959089i \(-0.408636\pi\)
0.283103 + 0.959089i \(0.408636\pi\)
\(812\) 137.989 4.84248
\(813\) 11.9325 0.418493
\(814\) 20.2316 0.709117
\(815\) −4.17029 −0.146079
\(816\) −59.8093 −2.09374
\(817\) −29.1749 −1.02070
\(818\) −96.7804 −3.38385
\(819\) −3.73751 −0.130599
\(820\) 12.2879 0.429111
\(821\) −32.2379 −1.12511 −0.562555 0.826760i \(-0.690181\pi\)
−0.562555 + 0.826760i \(0.690181\pi\)
\(822\) 22.5741 0.787362
\(823\) −31.3986 −1.09449 −0.547244 0.836973i \(-0.684323\pi\)
−0.547244 + 0.836973i \(0.684323\pi\)
\(824\) 126.900 4.42076
\(825\) 2.40093 0.0835898
\(826\) −97.1723 −3.38106
\(827\) −35.8683 −1.24726 −0.623631 0.781719i \(-0.714343\pi\)
−0.623631 + 0.781719i \(0.714343\pi\)
\(828\) 9.77934 0.339856
\(829\) 29.7801 1.03431 0.517153 0.855893i \(-0.326992\pi\)
0.517153 + 0.855893i \(0.326992\pi\)
\(830\) −6.37471 −0.221269
\(831\) 12.9997 0.450953
\(832\) −18.8880 −0.654824
\(833\) 17.0837 0.591916
\(834\) 81.5506 2.82387
\(835\) 13.3766 0.462918
\(836\) −41.0906 −1.42115
\(837\) 33.5352 1.15915
\(838\) 48.1001 1.66159
\(839\) −0.647770 −0.0223635 −0.0111817 0.999937i \(-0.503559\pi\)
−0.0111817 + 0.999937i \(0.503559\pi\)
\(840\) 43.1929 1.49030
\(841\) 45.4447 1.56706
\(842\) 56.6429 1.95204
\(843\) −3.85322 −0.132712
\(844\) 36.9240 1.27098
\(845\) 1.92310 0.0661565
\(846\) −6.66596 −0.229180
\(847\) −31.3979 −1.07885
\(848\) 7.44545 0.255678
\(849\) −30.3780 −1.04257
\(850\) −9.76000 −0.334765
\(851\) 42.9812 1.47338
\(852\) −113.797 −3.89861
\(853\) −7.16623 −0.245367 −0.122684 0.992446i \(-0.539150\pi\)
−0.122684 + 0.992446i \(0.539150\pi\)
\(854\) −100.977 −3.45538
\(855\) 1.87649 0.0641745
\(856\) −0.996615 −0.0340636
\(857\) −18.5761 −0.634546 −0.317273 0.948334i \(-0.602767\pi\)
−0.317273 + 0.948334i \(0.602767\pi\)
\(858\) 24.0239 0.820162
\(859\) 20.2596 0.691248 0.345624 0.938373i \(-0.387667\pi\)
0.345624 + 0.938373i \(0.387667\pi\)
\(860\) −20.8579 −0.711248
\(861\) −16.0613 −0.547369
\(862\) 34.8254 1.18616
\(863\) −40.3671 −1.37411 −0.687056 0.726605i \(-0.741097\pi\)
−0.687056 + 0.726605i \(0.741097\pi\)
\(864\) −42.5655 −1.44811
\(865\) −17.5692 −0.597371
\(866\) 27.6020 0.937954
\(867\) 5.07810 0.172461
\(868\) 108.989 3.69932
\(869\) 4.21718 0.143058
\(870\) 40.5051 1.37325
\(871\) 5.23386 0.177343
\(872\) −63.7486 −2.15880
\(873\) −1.24379 −0.0420958
\(874\) −124.370 −4.20688
\(875\) 3.39615 0.114811
\(876\) 120.328 4.06551
\(877\) 11.0694 0.373786 0.186893 0.982380i \(-0.440158\pi\)
0.186893 + 0.982380i \(0.440158\pi\)
\(878\) 59.2826 2.00069
\(879\) 27.5778 0.930175
\(880\) −11.6015 −0.391085
\(881\) 39.7284 1.33848 0.669241 0.743045i \(-0.266619\pi\)
0.669241 + 0.743045i \(0.266619\pi\)
\(882\) −3.34553 −0.112650
\(883\) −38.1221 −1.28291 −0.641455 0.767160i \(-0.721669\pi\)
−0.641455 + 0.767160i \(0.721669\pi\)
\(884\) −68.5469 −2.30548
\(885\) −20.0208 −0.672993
\(886\) 43.8171 1.47206
\(887\) 21.3100 0.715521 0.357760 0.933813i \(-0.383540\pi\)
0.357760 + 0.933813i \(0.383540\pi\)
\(888\) 74.9897 2.51649
\(889\) 17.0288 0.571128
\(890\) −18.7950 −0.630012
\(891\) 12.9470 0.433742
\(892\) 24.3808 0.816331
\(893\) 59.5037 1.99122
\(894\) 81.9189 2.73978
\(895\) −8.67362 −0.289927
\(896\) 15.7418 0.525895
\(897\) 51.0378 1.70410
\(898\) −12.5201 −0.417801
\(899\) 58.7989 1.96105
\(900\) 1.34155 0.0447184
\(901\) 3.20343 0.106722
\(902\) 8.95342 0.298116
\(903\) 27.2631 0.907259
\(904\) 23.6383 0.786198
\(905\) 2.28975 0.0761140
\(906\) 91.7858 3.04938
\(907\) −42.8511 −1.42285 −0.711423 0.702764i \(-0.751949\pi\)
−0.711423 + 0.702764i \(0.751949\pi\)
\(908\) 105.488 3.50074
\(909\) 1.27745 0.0423702
\(910\) 33.9821 1.12650
\(911\) 20.5782 0.681785 0.340892 0.940102i \(-0.389271\pi\)
0.340892 + 0.940102i \(0.389271\pi\)
\(912\) −104.552 −3.46206
\(913\) −3.26022 −0.107898
\(914\) 85.2358 2.81935
\(915\) −20.8048 −0.687785
\(916\) −42.1353 −1.39219
\(917\) −66.0827 −2.18224
\(918\) −48.0284 −1.58517
\(919\) −0.606079 −0.0199927 −0.00999635 0.999950i \(-0.503182\pi\)
−0.00999635 + 0.999950i \(0.503182\pi\)
\(920\) −51.1526 −1.68645
\(921\) −41.3229 −1.36163
\(922\) 35.7720 1.17809
\(923\) −51.5059 −1.69534
\(924\) 38.3980 1.26320
\(925\) 5.89626 0.193868
\(926\) 50.8294 1.67036
\(927\) −5.15181 −0.169208
\(928\) −74.6322 −2.44992
\(929\) 17.3701 0.569895 0.284947 0.958543i \(-0.408024\pi\)
0.284947 + 0.958543i \(0.408024\pi\)
\(930\) 31.9923 1.04907
\(931\) 29.8639 0.978750
\(932\) −130.958 −4.28966
\(933\) −56.9210 −1.86351
\(934\) 75.1552 2.45915
\(935\) −4.99156 −0.163242
\(936\) 7.72254 0.252419
\(937\) 9.22360 0.301322 0.150661 0.988586i \(-0.451860\pi\)
0.150661 + 0.988586i \(0.451860\pi\)
\(938\) 11.9183 0.389146
\(939\) −30.5081 −0.995594
\(940\) 42.5408 1.38753
\(941\) −23.8738 −0.778265 −0.389133 0.921182i \(-0.627225\pi\)
−0.389133 + 0.921182i \(0.627225\pi\)
\(942\) −81.4248 −2.65296
\(943\) 19.0212 0.619415
\(944\) 96.7418 3.14868
\(945\) 16.7123 0.543650
\(946\) −15.1978 −0.494125
\(947\) 20.8721 0.678251 0.339126 0.940741i \(-0.389869\pi\)
0.339126 + 0.940741i \(0.389869\pi\)
\(948\) 27.1709 0.882470
\(949\) 54.4621 1.76792
\(950\) −17.0614 −0.553544
\(951\) −0.507329 −0.0164513
\(952\) −89.7984 −2.91038
\(953\) −19.1648 −0.620810 −0.310405 0.950604i \(-0.600465\pi\)
−0.310405 + 0.950604i \(0.600465\pi\)
\(954\) −0.627332 −0.0203106
\(955\) −11.7395 −0.379881
\(956\) −28.8529 −0.933170
\(957\) 20.7156 0.669639
\(958\) 17.5385 0.566642
\(959\) 16.3307 0.527344
\(960\) −8.86169 −0.286010
\(961\) 15.4413 0.498107
\(962\) 58.9983 1.90218
\(963\) 0.0404601 0.00130381
\(964\) −71.7958 −2.31239
\(965\) −25.8016 −0.830583
\(966\) 116.220 3.73933
\(967\) −45.6857 −1.46915 −0.734577 0.678526i \(-0.762619\pi\)
−0.734577 + 0.678526i \(0.762619\pi\)
\(968\) 64.8753 2.08517
\(969\) −44.9838 −1.44509
\(970\) 11.3087 0.363101
\(971\) 0.256015 0.00821593 0.00410796 0.999992i \(-0.498692\pi\)
0.00410796 + 0.999992i \(0.498692\pi\)
\(972\) 13.8961 0.445717
\(973\) 58.9957 1.89132
\(974\) 30.1933 0.967454
\(975\) 7.00147 0.224227
\(976\) 100.530 3.21789
\(977\) −48.2134 −1.54248 −0.771242 0.636542i \(-0.780364\pi\)
−0.771242 + 0.636542i \(0.780364\pi\)
\(978\) −19.5776 −0.626022
\(979\) −9.61236 −0.307212
\(980\) 21.3505 0.682017
\(981\) 2.58804 0.0826297
\(982\) −27.0060 −0.861795
\(983\) 43.8001 1.39701 0.698503 0.715607i \(-0.253850\pi\)
0.698503 + 0.715607i \(0.253850\pi\)
\(984\) 33.1864 1.05794
\(985\) 12.0201 0.382991
\(986\) −84.2106 −2.68181
\(987\) −55.6046 −1.76991
\(988\) −119.826 −3.81218
\(989\) −32.2872 −1.02667
\(990\) 0.977506 0.0310672
\(991\) 22.7807 0.723652 0.361826 0.932246i \(-0.382154\pi\)
0.361826 + 0.932246i \(0.382154\pi\)
\(992\) −58.9470 −1.87157
\(993\) 5.52376 0.175291
\(994\) −117.287 −3.72010
\(995\) −5.30959 −0.168325
\(996\) −21.0053 −0.665578
\(997\) −23.5871 −0.747012 −0.373506 0.927628i \(-0.621844\pi\)
−0.373506 + 0.927628i \(0.621844\pi\)
\(998\) 2.67441 0.0846568
\(999\) 29.0152 0.917999
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 \(a_p\))