Properties

Label 8023.2.a.c.1.11
Level 8023
Weight 2
Character 8023.1
Self dual Yes
Analytic conductor 64.064
Analytic rank 1
Dimension 158
CM No

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Newspace parameters

Level: \( N \) = \( 8023 = 71 \cdot 113 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(158\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 8023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.60210 q^{2}\) \(-3.36394 q^{3}\) \(+4.77094 q^{4}\) \(+3.49358 q^{5}\) \(+8.75331 q^{6}\) \(+4.61670 q^{7}\) \(-7.21028 q^{8}\) \(+8.31606 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.60210 q^{2}\) \(-3.36394 q^{3}\) \(+4.77094 q^{4}\) \(+3.49358 q^{5}\) \(+8.75331 q^{6}\) \(+4.61670 q^{7}\) \(-7.21028 q^{8}\) \(+8.31606 q^{9}\) \(-9.09066 q^{10}\) \(+5.76146 q^{11}\) \(-16.0491 q^{12}\) \(-3.60496 q^{13}\) \(-12.0131 q^{14}\) \(-11.7522 q^{15}\) \(+9.22002 q^{16}\) \(-6.25498 q^{17}\) \(-21.6393 q^{18}\) \(+1.10055 q^{19}\) \(+16.6677 q^{20}\) \(-15.5303 q^{21}\) \(-14.9919 q^{22}\) \(-5.25956 q^{23}\) \(+24.2549 q^{24}\) \(+7.20511 q^{25}\) \(+9.38048 q^{26}\) \(-17.8829 q^{27}\) \(+22.0260 q^{28}\) \(-0.286773 q^{29}\) \(+30.5804 q^{30}\) \(-5.82152 q^{31}\) \(-9.57088 q^{32}\) \(-19.3812 q^{33}\) \(+16.2761 q^{34}\) \(+16.1288 q^{35}\) \(+39.6755 q^{36}\) \(+6.50400 q^{37}\) \(-2.86376 q^{38}\) \(+12.1269 q^{39}\) \(-25.1897 q^{40}\) \(+1.67633 q^{41}\) \(+40.4114 q^{42}\) \(-6.74649 q^{43}\) \(+27.4876 q^{44}\) \(+29.0528 q^{45}\) \(+13.6859 q^{46}\) \(-6.65750 q^{47}\) \(-31.0155 q^{48}\) \(+14.3139 q^{49}\) \(-18.7484 q^{50}\) \(+21.0414 q^{51}\) \(-17.1991 q^{52}\) \(-8.93512 q^{53}\) \(+46.5331 q^{54}\) \(+20.1281 q^{55}\) \(-33.2877 q^{56}\) \(-3.70219 q^{57}\) \(+0.746213 q^{58}\) \(+0.421069 q^{59}\) \(-56.0690 q^{60}\) \(-5.32593 q^{61}\) \(+15.1482 q^{62}\) \(+38.3928 q^{63}\) \(+6.46438 q^{64}\) \(-12.5942 q^{65}\) \(+50.4318 q^{66}\) \(-4.40120 q^{67}\) \(-29.8422 q^{68}\) \(+17.6928 q^{69}\) \(-41.9689 q^{70}\) \(-1.00000 q^{71}\) \(-59.9612 q^{72}\) \(-5.64956 q^{73}\) \(-16.9241 q^{74}\) \(-24.2375 q^{75}\) \(+5.25068 q^{76}\) \(+26.5989 q^{77}\) \(-31.5553 q^{78}\) \(-10.1255 q^{79}\) \(+32.2109 q^{80}\) \(+35.2087 q^{81}\) \(-4.36198 q^{82}\) \(+9.41179 q^{83}\) \(-74.0941 q^{84}\) \(-21.8523 q^{85}\) \(+17.5551 q^{86}\) \(+0.964686 q^{87}\) \(-41.5418 q^{88}\) \(-5.01685 q^{89}\) \(-75.5985 q^{90}\) \(-16.6430 q^{91}\) \(-25.0930 q^{92}\) \(+19.5832 q^{93}\) \(+17.3235 q^{94}\) \(+3.84488 q^{95}\) \(+32.1958 q^{96}\) \(-5.93740 q^{97}\) \(-37.2463 q^{98}\) \(+47.9127 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(158q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 158q^{4} \) \(\mathstrut -\mathstrut 31q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 135q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut 46q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 27q^{14} \) \(\mathstrut -\mathstrut 41q^{15} \) \(\mathstrut +\mathstrut 150q^{16} \) \(\mathstrut -\mathstrut 137q^{17} \) \(\mathstrut -\mathstrut 67q^{18} \) \(\mathstrut -\mathstrut 42q^{19} \) \(\mathstrut -\mathstrut 66q^{20} \) \(\mathstrut -\mathstrut 46q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 48q^{24} \) \(\mathstrut +\mathstrut 129q^{25} \) \(\mathstrut -\mathstrut 67q^{26} \) \(\mathstrut -\mathstrut 89q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 79q^{29} \) \(\mathstrut -\mathstrut 11q^{30} \) \(\mathstrut +\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 147q^{32} \) \(\mathstrut -\mathstrut 112q^{33} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 53q^{35} \) \(\mathstrut +\mathstrut 141q^{36} \) \(\mathstrut -\mathstrut 60q^{37} \) \(\mathstrut -\mathstrut 53q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 128q^{41} \) \(\mathstrut +\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 63q^{43} \) \(\mathstrut -\mathstrut 88q^{45} \) \(\mathstrut -\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 92q^{47} \) \(\mathstrut -\mathstrut 131q^{48} \) \(\mathstrut +\mathstrut 122q^{49} \) \(\mathstrut -\mathstrut 116q^{50} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 89q^{52} \) \(\mathstrut -\mathstrut 94q^{53} \) \(\mathstrut -\mathstrut 71q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 104q^{56} \) \(\mathstrut -\mathstrut 93q^{57} \) \(\mathstrut -\mathstrut 65q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut -\mathstrut 12q^{60} \) \(\mathstrut +\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 97q^{62} \) \(\mathstrut -\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 163q^{64} \) \(\mathstrut -\mathstrut 163q^{65} \) \(\mathstrut -\mathstrut 65q^{66} \) \(\mathstrut -\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 217q^{68} \) \(\mathstrut -\mathstrut 46q^{69} \) \(\mathstrut -\mathstrut 79q^{70} \) \(\mathstrut -\mathstrut 158q^{71} \) \(\mathstrut -\mathstrut 99q^{72} \) \(\mathstrut -\mathstrut 165q^{73} \) \(\mathstrut -\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 93q^{76} \) \(\mathstrut -\mathstrut 140q^{77} \) \(\mathstrut +\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut 134q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut +\mathstrut 10q^{82} \) \(\mathstrut -\mathstrut 158q^{83} \) \(\mathstrut -\mathstrut 160q^{84} \) \(\mathstrut +\mathstrut 23q^{85} \) \(\mathstrut -\mathstrut 122q^{86} \) \(\mathstrut -\mathstrut 71q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 251q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut -\mathstrut 57q^{91} \) \(\mathstrut -\mathstrut 58q^{92} \) \(\mathstrut -\mathstrut 52q^{93} \) \(\mathstrut -\mathstrut 64q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 98q^{96} \) \(\mathstrut -\mathstrut 48q^{97} \) \(\mathstrut -\mathstrut 84q^{98} \) \(\mathstrut +\mathstrut 85q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60210 −1.83997 −0.919983 0.391959i \(-0.871797\pi\)
−0.919983 + 0.391959i \(0.871797\pi\)
\(3\) −3.36394 −1.94217 −0.971084 0.238736i \(-0.923267\pi\)
−0.971084 + 0.238736i \(0.923267\pi\)
\(4\) 4.77094 2.38547
\(5\) 3.49358 1.56238 0.781188 0.624295i \(-0.214614\pi\)
0.781188 + 0.624295i \(0.214614\pi\)
\(6\) 8.75331 3.57352
\(7\) 4.61670 1.74495 0.872474 0.488660i \(-0.162514\pi\)
0.872474 + 0.488660i \(0.162514\pi\)
\(8\) −7.21028 −2.54922
\(9\) 8.31606 2.77202
\(10\) −9.09066 −2.87472
\(11\) 5.76146 1.73715 0.868573 0.495561i \(-0.165038\pi\)
0.868573 + 0.495561i \(0.165038\pi\)
\(12\) −16.0491 −4.63299
\(13\) −3.60496 −0.999836 −0.499918 0.866073i \(-0.666637\pi\)
−0.499918 + 0.866073i \(0.666637\pi\)
\(14\) −12.0131 −3.21065
\(15\) −11.7522 −3.03440
\(16\) 9.22002 2.30500
\(17\) −6.25498 −1.51706 −0.758528 0.651640i \(-0.774081\pi\)
−0.758528 + 0.651640i \(0.774081\pi\)
\(18\) −21.6393 −5.10042
\(19\) 1.10055 0.252485 0.126242 0.991999i \(-0.459708\pi\)
0.126242 + 0.991999i \(0.459708\pi\)
\(20\) 16.6677 3.72701
\(21\) −15.5303 −3.38899
\(22\) −14.9919 −3.19629
\(23\) −5.25956 −1.09669 −0.548347 0.836251i \(-0.684743\pi\)
−0.548347 + 0.836251i \(0.684743\pi\)
\(24\) 24.2549 4.95102
\(25\) 7.20511 1.44102
\(26\) 9.38048 1.83966
\(27\) −17.8829 −3.44156
\(28\) 22.0260 4.16253
\(29\) −0.286773 −0.0532524 −0.0266262 0.999645i \(-0.508476\pi\)
−0.0266262 + 0.999645i \(0.508476\pi\)
\(30\) 30.5804 5.58319
\(31\) −5.82152 −1.04558 −0.522788 0.852463i \(-0.675108\pi\)
−0.522788 + 0.852463i \(0.675108\pi\)
\(32\) −9.57088 −1.69191
\(33\) −19.3812 −3.37383
\(34\) 16.2761 2.79133
\(35\) 16.1288 2.72627
\(36\) 39.6755 6.61258
\(37\) 6.50400 1.06925 0.534625 0.845089i \(-0.320453\pi\)
0.534625 + 0.845089i \(0.320453\pi\)
\(38\) −2.86376 −0.464563
\(39\) 12.1269 1.94185
\(40\) −25.1897 −3.98284
\(41\) 1.67633 0.261799 0.130899 0.991396i \(-0.458214\pi\)
0.130899 + 0.991396i \(0.458214\pi\)
\(42\) 40.4114 6.23562
\(43\) −6.74649 −1.02883 −0.514415 0.857542i \(-0.671991\pi\)
−0.514415 + 0.857542i \(0.671991\pi\)
\(44\) 27.4876 4.14391
\(45\) 29.0528 4.33094
\(46\) 13.6859 2.01788
\(47\) −6.65750 −0.971097 −0.485548 0.874210i \(-0.661380\pi\)
−0.485548 + 0.874210i \(0.661380\pi\)
\(48\) −31.0155 −4.47671
\(49\) 14.3139 2.04485
\(50\) −18.7484 −2.65143
\(51\) 21.0414 2.94638
\(52\) −17.1991 −2.38508
\(53\) −8.93512 −1.22733 −0.613667 0.789565i \(-0.710306\pi\)
−0.613667 + 0.789565i \(0.710306\pi\)
\(54\) 46.5331 6.33236
\(55\) 20.1281 2.71408
\(56\) −33.2877 −4.44826
\(57\) −3.70219 −0.490368
\(58\) 0.746213 0.0979826
\(59\) 0.421069 0.0548186 0.0274093 0.999624i \(-0.491274\pi\)
0.0274093 + 0.999624i \(0.491274\pi\)
\(60\) −56.0690 −7.23848
\(61\) −5.32593 −0.681916 −0.340958 0.940079i \(-0.610751\pi\)
−0.340958 + 0.940079i \(0.610751\pi\)
\(62\) 15.1482 1.92382
\(63\) 38.3928 4.83703
\(64\) 6.46438 0.808047
\(65\) −12.5942 −1.56212
\(66\) 50.4318 6.20773
\(67\) −4.40120 −0.537692 −0.268846 0.963183i \(-0.586642\pi\)
−0.268846 + 0.963183i \(0.586642\pi\)
\(68\) −29.8422 −3.61890
\(69\) 17.6928 2.12996
\(70\) −41.9689 −5.01624
\(71\) −1.00000 −0.118678
\(72\) −59.9612 −7.06649
\(73\) −5.64956 −0.661231 −0.330615 0.943766i \(-0.607256\pi\)
−0.330615 + 0.943766i \(0.607256\pi\)
\(74\) −16.9241 −1.96738
\(75\) −24.2375 −2.79871
\(76\) 5.25068 0.602295
\(77\) 26.5989 3.03123
\(78\) −31.5553 −3.57294
\(79\) −10.1255 −1.13920 −0.569602 0.821921i \(-0.692903\pi\)
−0.569602 + 0.821921i \(0.692903\pi\)
\(80\) 32.2109 3.60129
\(81\) 35.2087 3.91208
\(82\) −4.36198 −0.481700
\(83\) 9.41179 1.03308 0.516539 0.856264i \(-0.327220\pi\)
0.516539 + 0.856264i \(0.327220\pi\)
\(84\) −74.0941 −8.08433
\(85\) −21.8523 −2.37021
\(86\) 17.5551 1.89301
\(87\) 0.964686 0.103425
\(88\) −41.5418 −4.42837
\(89\) −5.01685 −0.531785 −0.265892 0.964003i \(-0.585667\pi\)
−0.265892 + 0.964003i \(0.585667\pi\)
\(90\) −75.5985 −7.96878
\(91\) −16.6430 −1.74466
\(92\) −25.0930 −2.61613
\(93\) 19.5832 2.03069
\(94\) 17.3235 1.78678
\(95\) 3.84488 0.394476
\(96\) 32.1958 3.28597
\(97\) −5.93740 −0.602851 −0.301426 0.953490i \(-0.597463\pi\)
−0.301426 + 0.953490i \(0.597463\pi\)
\(98\) −37.2463 −3.76245
\(99\) 47.9127 4.81540
\(100\) 34.3752 3.43752
\(101\) −13.0117 −1.29471 −0.647354 0.762189i \(-0.724124\pi\)
−0.647354 + 0.762189i \(0.724124\pi\)
\(102\) −54.7518 −5.42124
\(103\) 15.1364 1.49144 0.745719 0.666260i \(-0.232106\pi\)
0.745719 + 0.666260i \(0.232106\pi\)
\(104\) 25.9928 2.54880
\(105\) −54.2563 −5.29487
\(106\) 23.2501 2.25825
\(107\) −8.20679 −0.793381 −0.396690 0.917953i \(-0.629841\pi\)
−0.396690 + 0.917953i \(0.629841\pi\)
\(108\) −85.3182 −8.20975
\(109\) −12.6905 −1.21553 −0.607767 0.794116i \(-0.707934\pi\)
−0.607767 + 0.794116i \(0.707934\pi\)
\(110\) −52.3755 −4.99381
\(111\) −21.8790 −2.07667
\(112\) 42.5661 4.02212
\(113\) −1.00000 −0.0940721
\(114\) 9.63349 0.902259
\(115\) −18.3747 −1.71345
\(116\) −1.36818 −0.127032
\(117\) −29.9791 −2.77157
\(118\) −1.09567 −0.100864
\(119\) −28.8774 −2.64719
\(120\) 84.7365 7.73535
\(121\) 22.1944 2.01768
\(122\) 13.8586 1.25470
\(123\) −5.63906 −0.508457
\(124\) −27.7742 −2.49419
\(125\) 7.70371 0.689041
\(126\) −99.9020 −8.89997
\(127\) 21.9765 1.95010 0.975049 0.221988i \(-0.0712546\pi\)
0.975049 + 0.221988i \(0.0712546\pi\)
\(128\) 2.32077 0.205129
\(129\) 22.6947 1.99816
\(130\) 32.7715 2.87425
\(131\) −12.3591 −1.07982 −0.539909 0.841723i \(-0.681541\pi\)
−0.539909 + 0.841723i \(0.681541\pi\)
\(132\) −92.4665 −8.04818
\(133\) 5.08093 0.440573
\(134\) 11.4524 0.989335
\(135\) −62.4753 −5.37702
\(136\) 45.1002 3.86731
\(137\) −7.92953 −0.677465 −0.338733 0.940883i \(-0.609998\pi\)
−0.338733 + 0.940883i \(0.609998\pi\)
\(138\) −46.0385 −3.91906
\(139\) −9.59529 −0.813862 −0.406931 0.913459i \(-0.633401\pi\)
−0.406931 + 0.913459i \(0.633401\pi\)
\(140\) 76.9497 6.50343
\(141\) 22.3954 1.88603
\(142\) 2.60210 0.218364
\(143\) −20.7698 −1.73686
\(144\) 76.6742 6.38952
\(145\) −1.00187 −0.0832004
\(146\) 14.7007 1.21664
\(147\) −48.1511 −3.97144
\(148\) 31.0302 2.55067
\(149\) 6.19872 0.507819 0.253909 0.967228i \(-0.418284\pi\)
0.253909 + 0.967228i \(0.418284\pi\)
\(150\) 63.0685 5.14952
\(151\) −0.0475608 −0.00387044 −0.00193522 0.999998i \(-0.500616\pi\)
−0.00193522 + 0.999998i \(0.500616\pi\)
\(152\) −7.93531 −0.643639
\(153\) −52.0168 −4.20531
\(154\) −69.2132 −5.57736
\(155\) −20.3380 −1.63358
\(156\) 57.8565 4.63223
\(157\) −0.151653 −0.0121032 −0.00605161 0.999982i \(-0.501926\pi\)
−0.00605161 + 0.999982i \(0.501926\pi\)
\(158\) 26.3475 2.09610
\(159\) 30.0572 2.38369
\(160\) −33.4366 −2.64340
\(161\) −24.2818 −1.91367
\(162\) −91.6167 −7.19808
\(163\) 20.1194 1.57587 0.787936 0.615757i \(-0.211150\pi\)
0.787936 + 0.615757i \(0.211150\pi\)
\(164\) 7.99767 0.624513
\(165\) −67.7097 −5.27119
\(166\) −24.4904 −1.90083
\(167\) −14.3182 −1.10797 −0.553986 0.832526i \(-0.686894\pi\)
−0.553986 + 0.832526i \(0.686894\pi\)
\(168\) 111.978 8.63927
\(169\) −0.00425693 −0.000327457 0
\(170\) 56.8619 4.36111
\(171\) 9.15228 0.699892
\(172\) −32.1871 −2.45424
\(173\) 1.29430 0.0984042 0.0492021 0.998789i \(-0.484332\pi\)
0.0492021 + 0.998789i \(0.484332\pi\)
\(174\) −2.51021 −0.190299
\(175\) 33.2638 2.51451
\(176\) 53.1208 4.00413
\(177\) −1.41645 −0.106467
\(178\) 13.0544 0.978466
\(179\) 20.3183 1.51866 0.759329 0.650707i \(-0.225527\pi\)
0.759329 + 0.650707i \(0.225527\pi\)
\(180\) 138.609 10.3313
\(181\) −4.71899 −0.350760 −0.175380 0.984501i \(-0.556115\pi\)
−0.175380 + 0.984501i \(0.556115\pi\)
\(182\) 43.3069 3.21012
\(183\) 17.9161 1.32440
\(184\) 37.9229 2.79571
\(185\) 22.7222 1.67057
\(186\) −50.9576 −3.73639
\(187\) −36.0378 −2.63535
\(188\) −31.7626 −2.31652
\(189\) −82.5599 −6.00535
\(190\) −10.0048 −0.725822
\(191\) −9.41762 −0.681435 −0.340718 0.940166i \(-0.610670\pi\)
−0.340718 + 0.940166i \(0.610670\pi\)
\(192\) −21.7457 −1.56936
\(193\) −3.23023 −0.232517 −0.116259 0.993219i \(-0.537090\pi\)
−0.116259 + 0.993219i \(0.537090\pi\)
\(194\) 15.4497 1.10923
\(195\) 42.3661 3.03390
\(196\) 68.2909 4.87792
\(197\) −21.9713 −1.56539 −0.782697 0.622403i \(-0.786156\pi\)
−0.782697 + 0.622403i \(0.786156\pi\)
\(198\) −124.674 −8.86017
\(199\) −11.7698 −0.834341 −0.417171 0.908828i \(-0.636978\pi\)
−0.417171 + 0.908828i \(0.636978\pi\)
\(200\) −51.9508 −3.67348
\(201\) 14.8054 1.04429
\(202\) 33.8577 2.38222
\(203\) −1.32395 −0.0929228
\(204\) 100.387 7.02851
\(205\) 5.85639 0.409028
\(206\) −39.3866 −2.74419
\(207\) −43.7388 −3.04006
\(208\) −33.2378 −2.30463
\(209\) 6.34080 0.438602
\(210\) 141.181 9.74238
\(211\) −23.7673 −1.63621 −0.818104 0.575070i \(-0.804975\pi\)
−0.818104 + 0.575070i \(0.804975\pi\)
\(212\) −42.6290 −2.92777
\(213\) 3.36394 0.230493
\(214\) 21.3549 1.45979
\(215\) −23.5694 −1.60742
\(216\) 128.941 8.77330
\(217\) −26.8762 −1.82448
\(218\) 33.0221 2.23654
\(219\) 19.0048 1.28422
\(220\) 96.0302 6.47435
\(221\) 22.5490 1.51681
\(222\) 56.9315 3.82099
\(223\) 11.9856 0.802613 0.401307 0.915944i \(-0.368556\pi\)
0.401307 + 0.915944i \(0.368556\pi\)
\(224\) −44.1859 −2.95229
\(225\) 59.9181 3.99454
\(226\) 2.60210 0.173089
\(227\) 1.07170 0.0711311 0.0355655 0.999367i \(-0.488677\pi\)
0.0355655 + 0.999367i \(0.488677\pi\)
\(228\) −17.6630 −1.16976
\(229\) 6.90899 0.456559 0.228280 0.973596i \(-0.426690\pi\)
0.228280 + 0.973596i \(0.426690\pi\)
\(230\) 47.8128 3.15268
\(231\) −89.4771 −5.88716
\(232\) 2.06772 0.135752
\(233\) 8.51296 0.557702 0.278851 0.960334i \(-0.410046\pi\)
0.278851 + 0.960334i \(0.410046\pi\)
\(234\) 78.0087 5.09959
\(235\) −23.2585 −1.51722
\(236\) 2.00890 0.130768
\(237\) 34.0614 2.21253
\(238\) 75.1420 4.87073
\(239\) −25.4717 −1.64762 −0.823812 0.566863i \(-0.808157\pi\)
−0.823812 + 0.566863i \(0.808157\pi\)
\(240\) −108.355 −6.99430
\(241\) 6.62060 0.426470 0.213235 0.977001i \(-0.431600\pi\)
0.213235 + 0.977001i \(0.431600\pi\)
\(242\) −57.7522 −3.71245
\(243\) −64.7911 −4.15635
\(244\) −25.4097 −1.62669
\(245\) 50.0069 3.19482
\(246\) 14.6734 0.935543
\(247\) −3.96746 −0.252443
\(248\) 41.9748 2.66541
\(249\) −31.6606 −2.00641
\(250\) −20.0459 −1.26781
\(251\) −25.8699 −1.63290 −0.816448 0.577419i \(-0.804060\pi\)
−0.816448 + 0.577419i \(0.804060\pi\)
\(252\) 183.170 11.5386
\(253\) −30.3027 −1.90512
\(254\) −57.1851 −3.58811
\(255\) 73.5097 4.60336
\(256\) −18.9676 −1.18548
\(257\) −26.5578 −1.65663 −0.828315 0.560263i \(-0.810700\pi\)
−0.828315 + 0.560263i \(0.810700\pi\)
\(258\) −59.0541 −3.67655
\(259\) 30.0270 1.86579
\(260\) −60.0863 −3.72640
\(261\) −2.38482 −0.147617
\(262\) 32.1596 1.98683
\(263\) −0.925928 −0.0570952 −0.0285476 0.999592i \(-0.509088\pi\)
−0.0285476 + 0.999592i \(0.509088\pi\)
\(264\) 139.744 8.60064
\(265\) −31.2156 −1.91756
\(266\) −13.2211 −0.810638
\(267\) 16.8764 1.03282
\(268\) −20.9979 −1.28265
\(269\) −1.46557 −0.0893571 −0.0446785 0.999001i \(-0.514226\pi\)
−0.0446785 + 0.999001i \(0.514226\pi\)
\(270\) 162.567 9.89353
\(271\) 12.4067 0.753654 0.376827 0.926284i \(-0.377015\pi\)
0.376827 + 0.926284i \(0.377015\pi\)
\(272\) −57.6711 −3.49682
\(273\) 55.9861 3.38843
\(274\) 20.6334 1.24651
\(275\) 41.5119 2.50326
\(276\) 84.4114 5.08097
\(277\) 0.381825 0.0229417 0.0114708 0.999934i \(-0.496349\pi\)
0.0114708 + 0.999934i \(0.496349\pi\)
\(278\) 24.9679 1.49748
\(279\) −48.4122 −2.89836
\(280\) −116.293 −6.94986
\(281\) 12.7609 0.761250 0.380625 0.924730i \(-0.375709\pi\)
0.380625 + 0.924730i \(0.375709\pi\)
\(282\) −58.2752 −3.47024
\(283\) 9.54306 0.567276 0.283638 0.958931i \(-0.408459\pi\)
0.283638 + 0.958931i \(0.408459\pi\)
\(284\) −4.77094 −0.283103
\(285\) −12.9339 −0.766139
\(286\) 54.0453 3.19576
\(287\) 7.73911 0.456825
\(288\) −79.5920 −4.69000
\(289\) 22.1248 1.30146
\(290\) 2.60696 0.153086
\(291\) 19.9730 1.17084
\(292\) −26.9537 −1.57735
\(293\) −23.7162 −1.38551 −0.692757 0.721171i \(-0.743604\pi\)
−0.692757 + 0.721171i \(0.743604\pi\)
\(294\) 125.294 7.30731
\(295\) 1.47104 0.0856472
\(296\) −46.8957 −2.72576
\(297\) −103.032 −5.97850
\(298\) −16.1297 −0.934369
\(299\) 18.9605 1.09651
\(300\) −115.636 −6.67624
\(301\) −31.1465 −1.79525
\(302\) 0.123758 0.00712148
\(303\) 43.7704 2.51454
\(304\) 10.1471 0.581978
\(305\) −18.6066 −1.06541
\(306\) 135.353 7.73763
\(307\) 30.9024 1.76370 0.881848 0.471534i \(-0.156300\pi\)
0.881848 + 0.471534i \(0.156300\pi\)
\(308\) 126.902 7.23092
\(309\) −50.9180 −2.89663
\(310\) 52.9215 3.00574
\(311\) 15.1817 0.860874 0.430437 0.902621i \(-0.358359\pi\)
0.430437 + 0.902621i \(0.358359\pi\)
\(312\) −87.4381 −4.95021
\(313\) 6.32076 0.357271 0.178635 0.983915i \(-0.442832\pi\)
0.178635 + 0.983915i \(0.442832\pi\)
\(314\) 0.394616 0.0222695
\(315\) 134.128 7.55727
\(316\) −48.3080 −2.71754
\(317\) 28.3071 1.58988 0.794941 0.606687i \(-0.207502\pi\)
0.794941 + 0.606687i \(0.207502\pi\)
\(318\) −78.2119 −4.38590
\(319\) −1.65223 −0.0925072
\(320\) 22.5838 1.26247
\(321\) 27.6071 1.54088
\(322\) 63.1838 3.52109
\(323\) −6.88395 −0.383033
\(324\) 167.979 9.33215
\(325\) −25.9741 −1.44079
\(326\) −52.3527 −2.89955
\(327\) 42.6901 2.36077
\(328\) −12.0868 −0.667382
\(329\) −30.7357 −1.69451
\(330\) 176.188 9.69881
\(331\) −5.78196 −0.317805 −0.158903 0.987294i \(-0.550796\pi\)
−0.158903 + 0.987294i \(0.550796\pi\)
\(332\) 44.9031 2.46438
\(333\) 54.0877 2.96399
\(334\) 37.2573 2.03863
\(335\) −15.3760 −0.840078
\(336\) −143.189 −7.81163
\(337\) −16.5683 −0.902532 −0.451266 0.892390i \(-0.649027\pi\)
−0.451266 + 0.892390i \(0.649027\pi\)
\(338\) 0.0110770 0.000602509 0
\(339\) 3.36394 0.182704
\(340\) −104.256 −5.65408
\(341\) −33.5405 −1.81632
\(342\) −23.8152 −1.28778
\(343\) 33.7662 1.82320
\(344\) 48.6441 2.62271
\(345\) 61.8112 3.32781
\(346\) −3.36792 −0.181060
\(347\) 15.5392 0.834186 0.417093 0.908864i \(-0.363049\pi\)
0.417093 + 0.908864i \(0.363049\pi\)
\(348\) 4.60246 0.246718
\(349\) −19.3686 −1.03678 −0.518388 0.855146i \(-0.673468\pi\)
−0.518388 + 0.855146i \(0.673468\pi\)
\(350\) −86.5559 −4.62661
\(351\) 64.4671 3.44100
\(352\) −55.1422 −2.93909
\(353\) −5.50452 −0.292976 −0.146488 0.989212i \(-0.546797\pi\)
−0.146488 + 0.989212i \(0.546797\pi\)
\(354\) 3.68575 0.195895
\(355\) −3.49358 −0.185420
\(356\) −23.9351 −1.26856
\(357\) 97.1417 5.14128
\(358\) −52.8702 −2.79428
\(359\) −17.1453 −0.904894 −0.452447 0.891791i \(-0.649449\pi\)
−0.452447 + 0.891791i \(0.649449\pi\)
\(360\) −209.479 −11.0405
\(361\) −17.7888 −0.936252
\(362\) 12.2793 0.645386
\(363\) −74.6606 −3.91867
\(364\) −79.4029 −4.16185
\(365\) −19.7372 −1.03309
\(366\) −46.6195 −2.43684
\(367\) −11.7232 −0.611947 −0.305973 0.952040i \(-0.598982\pi\)
−0.305973 + 0.952040i \(0.598982\pi\)
\(368\) −48.4932 −2.52788
\(369\) 13.9405 0.725711
\(370\) −59.1256 −3.07380
\(371\) −41.2508 −2.14163
\(372\) 93.4305 4.84415
\(373\) 7.34320 0.380217 0.190108 0.981763i \(-0.439116\pi\)
0.190108 + 0.981763i \(0.439116\pi\)
\(374\) 93.7742 4.84895
\(375\) −25.9148 −1.33823
\(376\) 48.0025 2.47554
\(377\) 1.03381 0.0532437
\(378\) 214.830 11.0496
\(379\) −22.1987 −1.14027 −0.570135 0.821551i \(-0.693109\pi\)
−0.570135 + 0.821551i \(0.693109\pi\)
\(380\) 18.3437 0.941011
\(381\) −73.9275 −3.78742
\(382\) 24.5056 1.25382
\(383\) 0.507200 0.0259167 0.0129583 0.999916i \(-0.495875\pi\)
0.0129583 + 0.999916i \(0.495875\pi\)
\(384\) −7.80693 −0.398396
\(385\) 92.9255 4.73592
\(386\) 8.40540 0.427824
\(387\) −56.1042 −2.85194
\(388\) −28.3270 −1.43808
\(389\) 4.95049 0.251000 0.125500 0.992094i \(-0.459947\pi\)
0.125500 + 0.992094i \(0.459947\pi\)
\(390\) −110.241 −5.58228
\(391\) 32.8984 1.66375
\(392\) −103.207 −5.21276
\(393\) 41.5752 2.09719
\(394\) 57.1717 2.88027
\(395\) −35.3741 −1.77987
\(396\) 228.589 11.4870
\(397\) −12.8861 −0.646734 −0.323367 0.946274i \(-0.604815\pi\)
−0.323367 + 0.946274i \(0.604815\pi\)
\(398\) 30.6263 1.53516
\(399\) −17.0919 −0.855666
\(400\) 66.4312 3.32156
\(401\) 31.1149 1.55380 0.776901 0.629623i \(-0.216791\pi\)
0.776901 + 0.629623i \(0.216791\pi\)
\(402\) −38.5251 −1.92146
\(403\) 20.9864 1.04541
\(404\) −62.0779 −3.08849
\(405\) 123.004 6.11214
\(406\) 3.44504 0.170975
\(407\) 37.4725 1.85744
\(408\) −151.714 −7.51097
\(409\) −12.3617 −0.611245 −0.305623 0.952153i \(-0.598865\pi\)
−0.305623 + 0.952153i \(0.598865\pi\)
\(410\) −15.2389 −0.752597
\(411\) 26.6744 1.31575
\(412\) 72.2151 3.55778
\(413\) 1.94395 0.0956556
\(414\) 113.813 5.59360
\(415\) 32.8808 1.61406
\(416\) 34.5026 1.69163
\(417\) 32.2779 1.58066
\(418\) −16.4994 −0.807013
\(419\) 14.6550 0.715945 0.357973 0.933732i \(-0.383468\pi\)
0.357973 + 0.933732i \(0.383468\pi\)
\(420\) −258.854 −12.6308
\(421\) −14.1174 −0.688038 −0.344019 0.938963i \(-0.611789\pi\)
−0.344019 + 0.938963i \(0.611789\pi\)
\(422\) 61.8450 3.01057
\(423\) −55.3642 −2.69190
\(424\) 64.4248 3.12874
\(425\) −45.0678 −2.18611
\(426\) −8.75331 −0.424099
\(427\) −24.5882 −1.18991
\(428\) −39.1541 −1.89259
\(429\) 69.8684 3.37328
\(430\) 61.3300 2.95760
\(431\) −11.7049 −0.563804 −0.281902 0.959443i \(-0.590965\pi\)
−0.281902 + 0.959443i \(0.590965\pi\)
\(432\) −164.881 −7.93282
\(433\) 25.3699 1.21920 0.609599 0.792710i \(-0.291330\pi\)
0.609599 + 0.792710i \(0.291330\pi\)
\(434\) 69.9348 3.35698
\(435\) 3.37021 0.161589
\(436\) −60.5458 −2.89962
\(437\) −5.78843 −0.276898
\(438\) −49.4523 −2.36292
\(439\) −0.759129 −0.0362312 −0.0181156 0.999836i \(-0.505767\pi\)
−0.0181156 + 0.999836i \(0.505767\pi\)
\(440\) −145.130 −6.91878
\(441\) 119.036 5.66836
\(442\) −58.6748 −2.79087
\(443\) 9.26568 0.440226 0.220113 0.975474i \(-0.429357\pi\)
0.220113 + 0.975474i \(0.429357\pi\)
\(444\) −104.384 −4.95383
\(445\) −17.5268 −0.830848
\(446\) −31.1877 −1.47678
\(447\) −20.8521 −0.986270
\(448\) 29.8441 1.41000
\(449\) −33.0167 −1.55815 −0.779077 0.626928i \(-0.784312\pi\)
−0.779077 + 0.626928i \(0.784312\pi\)
\(450\) −155.913 −7.34981
\(451\) 9.65810 0.454782
\(452\) −4.77094 −0.224406
\(453\) 0.159991 0.00751705
\(454\) −2.78867 −0.130879
\(455\) −58.1438 −2.72582
\(456\) 26.6939 1.25005
\(457\) 2.28127 0.106713 0.0533566 0.998576i \(-0.483008\pi\)
0.0533566 + 0.998576i \(0.483008\pi\)
\(458\) −17.9779 −0.840053
\(459\) 111.857 5.22105
\(460\) −87.6646 −4.08738
\(461\) −12.7426 −0.593484 −0.296742 0.954958i \(-0.595900\pi\)
−0.296742 + 0.954958i \(0.595900\pi\)
\(462\) 232.829 10.8322
\(463\) 28.0052 1.30151 0.650755 0.759288i \(-0.274452\pi\)
0.650755 + 0.759288i \(0.274452\pi\)
\(464\) −2.64405 −0.122747
\(465\) 68.4156 3.17270
\(466\) −22.1516 −1.02615
\(467\) 32.5484 1.50616 0.753080 0.657929i \(-0.228567\pi\)
0.753080 + 0.657929i \(0.228567\pi\)
\(468\) −143.028 −6.61149
\(469\) −20.3190 −0.938246
\(470\) 60.5211 2.79163
\(471\) 0.510150 0.0235065
\(472\) −3.03603 −0.139745
\(473\) −38.8696 −1.78723
\(474\) −88.6314 −4.07097
\(475\) 7.92961 0.363835
\(476\) −137.772 −6.31479
\(477\) −74.3050 −3.40219
\(478\) 66.2799 3.03157
\(479\) −23.3134 −1.06522 −0.532609 0.846361i \(-0.678788\pi\)
−0.532609 + 0.846361i \(0.678788\pi\)
\(480\) 112.479 5.13392
\(481\) −23.4467 −1.06908
\(482\) −17.2275 −0.784690
\(483\) 81.6824 3.71668
\(484\) 105.888 4.81311
\(485\) −20.7428 −0.941881
\(486\) 168.593 7.64754
\(487\) −29.1496 −1.32089 −0.660447 0.750873i \(-0.729633\pi\)
−0.660447 + 0.750873i \(0.729633\pi\)
\(488\) 38.4015 1.73835
\(489\) −67.6803 −3.06061
\(490\) −130.123 −5.87836
\(491\) −18.3627 −0.828696 −0.414348 0.910119i \(-0.635990\pi\)
−0.414348 + 0.910119i \(0.635990\pi\)
\(492\) −26.9036 −1.21291
\(493\) 1.79376 0.0807870
\(494\) 10.3237 0.464487
\(495\) 167.387 7.52347
\(496\) −53.6746 −2.41006
\(497\) −4.61670 −0.207087
\(498\) 82.3843 3.69173
\(499\) 10.7663 0.481968 0.240984 0.970529i \(-0.422530\pi\)
0.240984 + 0.970529i \(0.422530\pi\)
\(500\) 36.7540 1.64369
\(501\) 48.1654 2.15187
\(502\) 67.3162 3.00447
\(503\) −4.90844 −0.218857 −0.109428 0.993995i \(-0.534902\pi\)
−0.109428 + 0.993995i \(0.534902\pi\)
\(504\) −276.823 −12.3307
\(505\) −45.4573 −2.02282
\(506\) 78.8508 3.50535
\(507\) 0.0143201 0.000635976 0
\(508\) 104.849 4.65191
\(509\) −19.5874 −0.868197 −0.434099 0.900865i \(-0.642933\pi\)
−0.434099 + 0.900865i \(0.642933\pi\)
\(510\) −191.280 −8.47001
\(511\) −26.0823 −1.15381
\(512\) 44.7142 1.97611
\(513\) −19.6811 −0.868941
\(514\) 69.1061 3.04814
\(515\) 52.8804 2.33019
\(516\) 108.275 4.76656
\(517\) −38.3569 −1.68694
\(518\) −78.1334 −3.43299
\(519\) −4.35396 −0.191118
\(520\) 90.8079 3.98219
\(521\) 6.59752 0.289043 0.144521 0.989502i \(-0.453836\pi\)
0.144521 + 0.989502i \(0.453836\pi\)
\(522\) 6.20556 0.271610
\(523\) 25.4889 1.11455 0.557277 0.830327i \(-0.311846\pi\)
0.557277 + 0.830327i \(0.311846\pi\)
\(524\) −58.9645 −2.57588
\(525\) −111.897 −4.88360
\(526\) 2.40936 0.105053
\(527\) 36.4135 1.58620
\(528\) −178.695 −7.77669
\(529\) 4.66293 0.202736
\(530\) 81.2261 3.52824
\(531\) 3.50164 0.151958
\(532\) 24.2408 1.05097
\(533\) −6.04310 −0.261756
\(534\) −43.9140 −1.90035
\(535\) −28.6711 −1.23956
\(536\) 31.7339 1.37070
\(537\) −68.3493 −2.94949
\(538\) 3.81355 0.164414
\(539\) 82.4691 3.55220
\(540\) −298.066 −12.8267
\(541\) 20.6224 0.886625 0.443313 0.896367i \(-0.353803\pi\)
0.443313 + 0.896367i \(0.353803\pi\)
\(542\) −32.2836 −1.38670
\(543\) 15.8744 0.681235
\(544\) 59.8657 2.56672
\(545\) −44.3354 −1.89912
\(546\) −145.682 −6.23459
\(547\) 39.2785 1.67943 0.839714 0.543028i \(-0.182722\pi\)
0.839714 + 0.543028i \(0.182722\pi\)
\(548\) −37.8313 −1.61607
\(549\) −44.2908 −1.89028
\(550\) −108.018 −4.60592
\(551\) −0.315609 −0.0134454
\(552\) −127.570 −5.42975
\(553\) −46.7463 −1.98785
\(554\) −0.993550 −0.0422119
\(555\) −76.4362 −3.24453
\(556\) −45.7786 −1.94144
\(557\) −45.1309 −1.91226 −0.956129 0.292947i \(-0.905364\pi\)
−0.956129 + 0.292947i \(0.905364\pi\)
\(558\) 125.973 5.33288
\(559\) 24.3208 1.02866
\(560\) 148.708 6.28406
\(561\) 121.229 5.11829
\(562\) −33.2051 −1.40067
\(563\) −26.3040 −1.10858 −0.554291 0.832323i \(-0.687010\pi\)
−0.554291 + 0.832323i \(0.687010\pi\)
\(564\) 106.847 4.49908
\(565\) −3.49358 −0.146976
\(566\) −24.8320 −1.04377
\(567\) 162.548 6.82637
\(568\) 7.21028 0.302537
\(569\) 28.2473 1.18419 0.592094 0.805869i \(-0.298302\pi\)
0.592094 + 0.805869i \(0.298302\pi\)
\(570\) 33.6554 1.40967
\(571\) −8.28304 −0.346634 −0.173317 0.984866i \(-0.555449\pi\)
−0.173317 + 0.984866i \(0.555449\pi\)
\(572\) −99.0917 −4.14323
\(573\) 31.6803 1.32346
\(574\) −20.1380 −0.840542
\(575\) −37.8957 −1.58036
\(576\) 53.7581 2.23992
\(577\) −26.4974 −1.10310 −0.551551 0.834141i \(-0.685964\pi\)
−0.551551 + 0.834141i \(0.685964\pi\)
\(578\) −57.5711 −2.39464
\(579\) 10.8663 0.451588
\(580\) −4.77984 −0.198472
\(581\) 43.4514 1.80267
\(582\) −51.9719 −2.15430
\(583\) −51.4794 −2.13206
\(584\) 40.7349 1.68562
\(585\) −104.734 −4.33023
\(586\) 61.7119 2.54930
\(587\) −5.11979 −0.211316 −0.105658 0.994403i \(-0.533695\pi\)
−0.105658 + 0.994403i \(0.533695\pi\)
\(588\) −229.726 −9.47375
\(589\) −6.40690 −0.263992
\(590\) −3.82780 −0.157588
\(591\) 73.9102 3.04026
\(592\) 59.9670 2.46463
\(593\) −31.1582 −1.27951 −0.639756 0.768578i \(-0.720965\pi\)
−0.639756 + 0.768578i \(0.720965\pi\)
\(594\) 268.099 11.0002
\(595\) −100.886 −4.13590
\(596\) 29.5737 1.21139
\(597\) 39.5930 1.62043
\(598\) −49.3372 −2.01755
\(599\) −8.85367 −0.361751 −0.180875 0.983506i \(-0.557893\pi\)
−0.180875 + 0.983506i \(0.557893\pi\)
\(600\) 174.759 7.13452
\(601\) 10.7159 0.437112 0.218556 0.975824i \(-0.429865\pi\)
0.218556 + 0.975824i \(0.429865\pi\)
\(602\) 81.0464 3.30321
\(603\) −36.6007 −1.49049
\(604\) −0.226910 −0.00923283
\(605\) 77.5380 3.15237
\(606\) −113.895 −4.62667
\(607\) 36.9484 1.49969 0.749844 0.661615i \(-0.230129\pi\)
0.749844 + 0.661615i \(0.230129\pi\)
\(608\) −10.5333 −0.427181
\(609\) 4.45367 0.180472
\(610\) 48.4162 1.96032
\(611\) 24.0000 0.970938
\(612\) −248.169 −10.0317
\(613\) −6.31769 −0.255169 −0.127584 0.991828i \(-0.540722\pi\)
−0.127584 + 0.991828i \(0.540722\pi\)
\(614\) −80.4114 −3.24514
\(615\) −19.7005 −0.794402
\(616\) −191.786 −7.72727
\(617\) 4.53669 0.182640 0.0913202 0.995822i \(-0.470891\pi\)
0.0913202 + 0.995822i \(0.470891\pi\)
\(618\) 132.494 5.32969
\(619\) −31.7078 −1.27445 −0.637223 0.770679i \(-0.719917\pi\)
−0.637223 + 0.770679i \(0.719917\pi\)
\(620\) −97.0313 −3.89687
\(621\) 94.0560 3.77434
\(622\) −39.5043 −1.58398
\(623\) −23.1613 −0.927937
\(624\) 111.810 4.47598
\(625\) −9.11199 −0.364479
\(626\) −16.4473 −0.657366
\(627\) −21.3300 −0.851840
\(628\) −0.723527 −0.0288719
\(629\) −40.6824 −1.62211
\(630\) −349.016 −13.9051
\(631\) 13.9395 0.554922 0.277461 0.960737i \(-0.410507\pi\)
0.277461 + 0.960737i \(0.410507\pi\)
\(632\) 73.0075 2.90408
\(633\) 79.9517 3.17779
\(634\) −73.6579 −2.92533
\(635\) 76.7767 3.04679
\(636\) 143.401 5.68622
\(637\) −51.6012 −2.04451
\(638\) 4.29928 0.170210
\(639\) −8.31606 −0.328978
\(640\) 8.10781 0.320489
\(641\) −13.8794 −0.548205 −0.274103 0.961700i \(-0.588381\pi\)
−0.274103 + 0.961700i \(0.588381\pi\)
\(642\) −71.8366 −2.83516
\(643\) 6.51654 0.256987 0.128494 0.991710i \(-0.458986\pi\)
0.128494 + 0.991710i \(0.458986\pi\)
\(644\) −115.847 −4.56502
\(645\) 79.2859 3.12188
\(646\) 17.9128 0.704768
\(647\) 18.8360 0.740519 0.370259 0.928928i \(-0.379269\pi\)
0.370259 + 0.928928i \(0.379269\pi\)
\(648\) −253.865 −9.97274
\(649\) 2.42597 0.0952278
\(650\) 67.5874 2.65099
\(651\) 90.4099 3.54344
\(652\) 95.9885 3.75920
\(653\) −42.7094 −1.67135 −0.835674 0.549226i \(-0.814923\pi\)
−0.835674 + 0.549226i \(0.814923\pi\)
\(654\) −111.084 −4.34374
\(655\) −43.1775 −1.68708
\(656\) 15.4558 0.603447
\(657\) −46.9821 −1.83295
\(658\) 79.9775 3.11785
\(659\) 13.5203 0.526675 0.263338 0.964704i \(-0.415177\pi\)
0.263338 + 0.964704i \(0.415177\pi\)
\(660\) −323.039 −12.5743
\(661\) 22.3097 0.867746 0.433873 0.900974i \(-0.357147\pi\)
0.433873 + 0.900974i \(0.357147\pi\)
\(662\) 15.0453 0.584751
\(663\) −75.8533 −2.94590
\(664\) −67.8616 −2.63354
\(665\) 17.7506 0.688340
\(666\) −140.742 −5.45363
\(667\) 1.50830 0.0584016
\(668\) −68.3111 −2.64304
\(669\) −40.3187 −1.55881
\(670\) 40.0098 1.54571
\(671\) −30.6851 −1.18459
\(672\) 148.638 5.73385
\(673\) 5.72025 0.220499 0.110250 0.993904i \(-0.464835\pi\)
0.110250 + 0.993904i \(0.464835\pi\)
\(674\) 43.1124 1.66063
\(675\) −128.848 −4.95936
\(676\) −0.0203096 −0.000781138 0
\(677\) 1.02100 0.0392404 0.0196202 0.999808i \(-0.493754\pi\)
0.0196202 + 0.999808i \(0.493754\pi\)
\(678\) −8.75331 −0.336169
\(679\) −27.4112 −1.05194
\(680\) 157.561 6.04220
\(681\) −3.60512 −0.138149
\(682\) 87.2758 3.34196
\(683\) 43.7709 1.67485 0.837423 0.546555i \(-0.184061\pi\)
0.837423 + 0.546555i \(0.184061\pi\)
\(684\) 43.6650 1.66957
\(685\) −27.7024 −1.05846
\(686\) −87.8632 −3.35463
\(687\) −23.2414 −0.886715
\(688\) −62.2027 −2.37146
\(689\) 32.2108 1.22713
\(690\) −160.839 −6.12305
\(691\) 44.5879 1.69621 0.848103 0.529832i \(-0.177745\pi\)
0.848103 + 0.529832i \(0.177745\pi\)
\(692\) 6.17506 0.234740
\(693\) 221.198 8.40263
\(694\) −40.4345 −1.53487
\(695\) −33.5219 −1.27156
\(696\) −6.95566 −0.263654
\(697\) −10.4854 −0.397163
\(698\) 50.3990 1.90763
\(699\) −28.6370 −1.08315
\(700\) 158.700 5.99829
\(701\) −3.02534 −0.114266 −0.0571328 0.998367i \(-0.518196\pi\)
−0.0571328 + 0.998367i \(0.518196\pi\)
\(702\) −167.750 −6.33132
\(703\) 7.15801 0.269969
\(704\) 37.2442 1.40370
\(705\) 78.2402 2.94670
\(706\) 14.3233 0.539066
\(707\) −60.0709 −2.25920
\(708\) −6.75780 −0.253974
\(709\) −17.4752 −0.656294 −0.328147 0.944627i \(-0.606424\pi\)
−0.328147 + 0.944627i \(0.606424\pi\)
\(710\) 9.09066 0.341166
\(711\) −84.2040 −3.15790
\(712\) 36.1729 1.35564
\(713\) 30.6186 1.14668
\(714\) −252.773 −9.45978
\(715\) −72.5611 −2.71363
\(716\) 96.9372 3.62271
\(717\) 85.6850 3.19997
\(718\) 44.6138 1.66497
\(719\) 44.2919 1.65181 0.825905 0.563809i \(-0.190665\pi\)
0.825905 + 0.563809i \(0.190665\pi\)
\(720\) 267.868 9.98284
\(721\) 69.8804 2.60248
\(722\) 46.2883 1.72267
\(723\) −22.2713 −0.828277
\(724\) −22.5140 −0.836728
\(725\) −2.06623 −0.0767379
\(726\) 194.275 7.21021
\(727\) 2.33574 0.0866278 0.0433139 0.999062i \(-0.486208\pi\)
0.0433139 + 0.999062i \(0.486208\pi\)
\(728\) 120.001 4.44753
\(729\) 112.327 4.16026
\(730\) 51.3582 1.90085
\(731\) 42.1992 1.56079
\(732\) 85.4767 3.15931
\(733\) 28.4414 1.05051 0.525254 0.850946i \(-0.323970\pi\)
0.525254 + 0.850946i \(0.323970\pi\)
\(734\) 30.5050 1.12596
\(735\) −168.220 −6.20488
\(736\) 50.3386 1.85550
\(737\) −25.3574 −0.934050
\(738\) −36.2745 −1.33528
\(739\) 44.6834 1.64371 0.821853 0.569700i \(-0.192941\pi\)
0.821853 + 0.569700i \(0.192941\pi\)
\(740\) 108.407 3.98510
\(741\) 13.3463 0.490287
\(742\) 107.339 3.94053
\(743\) 9.16128 0.336095 0.168047 0.985779i \(-0.446254\pi\)
0.168047 + 0.985779i \(0.446254\pi\)
\(744\) −141.201 −5.17667
\(745\) 21.6557 0.793404
\(746\) −19.1078 −0.699585
\(747\) 78.2690 2.86371
\(748\) −171.935 −6.28655
\(749\) −37.8883 −1.38441
\(750\) 67.4330 2.46230
\(751\) 41.1496 1.50157 0.750785 0.660547i \(-0.229676\pi\)
0.750785 + 0.660547i \(0.229676\pi\)
\(752\) −61.3823 −2.23838
\(753\) 87.0248 3.17136
\(754\) −2.69007 −0.0979666
\(755\) −0.166157 −0.00604709
\(756\) −393.889 −14.3256
\(757\) 24.7802 0.900651 0.450325 0.892864i \(-0.351308\pi\)
0.450325 + 0.892864i \(0.351308\pi\)
\(758\) 57.7633 2.09806
\(759\) 101.936 3.70006
\(760\) −27.7226 −1.00561
\(761\) −44.9674 −1.63007 −0.815034 0.579414i \(-0.803282\pi\)
−0.815034 + 0.579414i \(0.803282\pi\)
\(762\) 192.367 6.96872
\(763\) −58.5884 −2.12104
\(764\) −44.9309 −1.62554
\(765\) −181.725 −6.57028
\(766\) −1.31979 −0.0476858
\(767\) −1.51794 −0.0548096
\(768\) 63.8059 2.30240
\(769\) −3.47686 −0.125379 −0.0626893 0.998033i \(-0.519968\pi\)
−0.0626893 + 0.998033i \(0.519968\pi\)
\(770\) −241.802 −8.71394
\(771\) 89.3387 3.21745
\(772\) −15.4113 −0.554663
\(773\) −22.6372 −0.814204 −0.407102 0.913383i \(-0.633461\pi\)
−0.407102 + 0.913383i \(0.633461\pi\)
\(774\) 145.989 5.24746
\(775\) −41.9447 −1.50670
\(776\) 42.8103 1.53680
\(777\) −101.009 −3.62368
\(778\) −12.8817 −0.461831
\(779\) 1.84489 0.0661001
\(780\) 202.127 7.23729
\(781\) −5.76146 −0.206161
\(782\) −85.6052 −3.06123
\(783\) 5.12833 0.183272
\(784\) 131.975 4.71338
\(785\) −0.529811 −0.0189098
\(786\) −108.183 −3.85876
\(787\) 3.54946 0.126525 0.0632624 0.997997i \(-0.479850\pi\)
0.0632624 + 0.997997i \(0.479850\pi\)
\(788\) −104.824 −3.73420
\(789\) 3.11476 0.110888
\(790\) 92.0472 3.27489
\(791\) −4.61670 −0.164151
\(792\) −345.464 −12.2755
\(793\) 19.1998 0.681804
\(794\) 33.5309 1.18997
\(795\) 105.007 3.72422
\(796\) −56.1532 −1.99030
\(797\) −22.8919 −0.810871 −0.405436 0.914124i \(-0.632880\pi\)
−0.405436 + 0.914124i \(0.632880\pi\)
\(798\) 44.4750 1.57440
\(799\) 41.6426 1.47321
\(800\) −68.9592 −2.43807
\(801\) −41.7204 −1.47412
\(802\) −80.9641 −2.85894
\(803\) −32.5497 −1.14865
\(804\) 70.6355 2.49112
\(805\) −84.8304 −2.98988
\(806\) −54.6087 −1.92351
\(807\) 4.93007 0.173547
\(808\) 93.8177 3.30050
\(809\) 46.9371 1.65022 0.825110 0.564972i \(-0.191113\pi\)
0.825110 + 0.564972i \(0.191113\pi\)
\(810\) −320.070 −11.2461
\(811\) 46.4110 1.62971 0.814855 0.579664i \(-0.196816\pi\)
0.814855 + 0.579664i \(0.196816\pi\)
\(812\) −6.31647 −0.221665
\(813\) −41.7354 −1.46372
\(814\) −97.5074 −3.41763
\(815\) 70.2887 2.46211
\(816\) 194.002 6.79142
\(817\) −7.42487 −0.259763
\(818\) 32.1663 1.12467
\(819\) −138.404 −4.83624
\(820\) 27.9405 0.975725
\(821\) −25.4774 −0.889168 −0.444584 0.895737i \(-0.646649\pi\)
−0.444584 + 0.895737i \(0.646649\pi\)
\(822\) −69.4096 −2.42094
\(823\) 22.4718 0.783318 0.391659 0.920111i \(-0.371901\pi\)
0.391659 + 0.920111i \(0.371901\pi\)
\(824\) −109.138 −3.80200
\(825\) −139.643 −4.86176
\(826\) −5.05836 −0.176003
\(827\) −27.1017 −0.942417 −0.471208 0.882022i \(-0.656182\pi\)
−0.471208 + 0.882022i \(0.656182\pi\)
\(828\) −208.675 −7.25197
\(829\) 26.2755 0.912584 0.456292 0.889830i \(-0.349177\pi\)
0.456292 + 0.889830i \(0.349177\pi\)
\(830\) −85.5593 −2.96981
\(831\) −1.28444 −0.0445566
\(832\) −23.3038 −0.807915
\(833\) −89.5334 −3.10215
\(834\) −83.9905 −2.90835
\(835\) −50.0216 −1.73107
\(836\) 30.2516 1.04627
\(837\) 104.106 3.59842
\(838\) −38.1339 −1.31731
\(839\) −21.9814 −0.758883 −0.379441 0.925216i \(-0.623884\pi\)
−0.379441 + 0.925216i \(0.623884\pi\)
\(840\) 391.203 13.4978
\(841\) −28.9178 −0.997164
\(842\) 36.7349 1.26597
\(843\) −42.9267 −1.47848
\(844\) −113.392 −3.90313
\(845\) −0.0148719 −0.000511610 0
\(846\) 144.063 4.95300
\(847\) 102.465 3.52074
\(848\) −82.3820 −2.82901
\(849\) −32.1022 −1.10175
\(850\) 117.271 4.02237
\(851\) −34.2082 −1.17264
\(852\) 16.0491 0.549835
\(853\) −10.3915 −0.355797 −0.177898 0.984049i \(-0.556930\pi\)
−0.177898 + 0.984049i \(0.556930\pi\)
\(854\) 63.9811 2.18939
\(855\) 31.9742 1.09350
\(856\) 59.1733 2.02250
\(857\) −24.2506 −0.828384 −0.414192 0.910190i \(-0.635936\pi\)
−0.414192 + 0.910190i \(0.635936\pi\)
\(858\) −181.805 −6.20671
\(859\) −48.5643 −1.65699 −0.828497 0.559994i \(-0.810803\pi\)
−0.828497 + 0.559994i \(0.810803\pi\)
\(860\) −112.448 −3.83445
\(861\) −26.0339 −0.887232
\(862\) 30.4573 1.03738
\(863\) −31.2733 −1.06455 −0.532277 0.846570i \(-0.678664\pi\)
−0.532277 + 0.846570i \(0.678664\pi\)
\(864\) 171.155 5.82281
\(865\) 4.52176 0.153744
\(866\) −66.0150 −2.24328
\(867\) −74.4265 −2.52766
\(868\) −128.225 −4.35224
\(869\) −58.3375 −1.97896
\(870\) −8.76963 −0.297318
\(871\) 15.8662 0.537604
\(872\) 91.5024 3.09866
\(873\) −49.3758 −1.67112
\(874\) 15.0621 0.509483
\(875\) 35.5657 1.20234
\(876\) 90.6706 3.06348
\(877\) 58.8247 1.98637 0.993184 0.116556i \(-0.0371856\pi\)
0.993184 + 0.116556i \(0.0371856\pi\)
\(878\) 1.97533 0.0666642
\(879\) 79.7797 2.69090
\(880\) 185.582 6.25596
\(881\) −39.1516 −1.31905 −0.659525 0.751682i \(-0.729243\pi\)
−0.659525 + 0.751682i \(0.729243\pi\)
\(882\) −309.743 −10.4296
\(883\) 4.39632 0.147948 0.0739740 0.997260i \(-0.476432\pi\)
0.0739740 + 0.997260i \(0.476432\pi\)
\(884\) 107.580 3.61830
\(885\) −4.94848 −0.166341
\(886\) −24.1103 −0.810000
\(887\) 17.5656 0.589796 0.294898 0.955529i \(-0.404714\pi\)
0.294898 + 0.955529i \(0.404714\pi\)
\(888\) 157.754 5.29388
\(889\) 101.459 3.40282
\(890\) 45.6065 1.52873
\(891\) 202.853 6.79585
\(892\) 57.1825 1.91461
\(893\) −7.32695 −0.245187
\(894\) 54.2593 1.81470
\(895\) 70.9835 2.37272
\(896\) 10.7143 0.357940
\(897\) −63.7819 −2.12961
\(898\) 85.9129 2.86695
\(899\) 1.66946 0.0556795
\(900\) 285.866 9.52886
\(901\) 55.8890 1.86193
\(902\) −25.1314 −0.836784
\(903\) 104.775 3.48669
\(904\) 7.21028 0.239810
\(905\) −16.4862 −0.548019
\(906\) −0.416314 −0.0138311
\(907\) 8.08787 0.268553 0.134277 0.990944i \(-0.457129\pi\)
0.134277 + 0.990944i \(0.457129\pi\)
\(908\) 5.11301 0.169681
\(909\) −108.206 −3.58896
\(910\) 151.296 5.01542
\(911\) −46.1273 −1.52826 −0.764132 0.645060i \(-0.776832\pi\)
−0.764132 + 0.645060i \(0.776832\pi\)
\(912\) −34.1343 −1.13030
\(913\) 54.2256 1.79461
\(914\) −5.93610 −0.196349
\(915\) 62.5913 2.06920
\(916\) 32.9624 1.08911
\(917\) −57.0582 −1.88423
\(918\) −291.064 −9.60654
\(919\) −20.0091 −0.660040 −0.330020 0.943974i \(-0.607056\pi\)
−0.330020 + 0.943974i \(0.607056\pi\)
\(920\) 132.487 4.36796
\(921\) −103.954 −3.42540
\(922\) 33.1577 1.09199
\(923\) 3.60496 0.118659
\(924\) −426.890 −14.0437
\(925\) 46.8620 1.54081
\(926\) −72.8723 −2.39473
\(927\) 125.876 4.13430
\(928\) 2.74467 0.0900982
\(929\) 35.6807 1.17065 0.585323 0.810800i \(-0.300968\pi\)
0.585323 + 0.810800i \(0.300968\pi\)
\(930\) −178.024 −5.83765
\(931\) 15.7533 0.516292
\(932\) 40.6148 1.33038
\(933\) −51.0702 −1.67196
\(934\) −84.6943 −2.77128
\(935\) −125.901 −4.11741
\(936\) 216.158 7.06533
\(937\) −49.3387 −1.61182 −0.805912 0.592036i \(-0.798324\pi\)
−0.805912 + 0.592036i \(0.798324\pi\)
\(938\) 52.8722 1.72634
\(939\) −21.2626 −0.693880
\(940\) −110.965 −3.61928
\(941\) 2.79330 0.0910590 0.0455295 0.998963i \(-0.485502\pi\)
0.0455295 + 0.998963i \(0.485502\pi\)
\(942\) −1.32746 −0.0432511
\(943\) −8.81675 −0.287113
\(944\) 3.88227 0.126357
\(945\) −288.430 −9.38262
\(946\) 101.143 3.28843
\(947\) −19.3674 −0.629357 −0.314678 0.949198i \(-0.601897\pi\)
−0.314678 + 0.949198i \(0.601897\pi\)
\(948\) 162.505 5.27792
\(949\) 20.3664 0.661123
\(950\) −20.6337 −0.669445
\(951\) −95.2231 −3.08782
\(952\) 208.214 6.74826
\(953\) −3.64981 −0.118229 −0.0591145 0.998251i \(-0.518828\pi\)
−0.0591145 + 0.998251i \(0.518828\pi\)
\(954\) 193.349 6.25992
\(955\) −32.9012 −1.06466
\(956\) −121.524 −3.93036
\(957\) 5.55800 0.179665
\(958\) 60.6640 1.95997
\(959\) −36.6082 −1.18214
\(960\) −75.9705 −2.45194
\(961\) 2.89015 0.0932305
\(962\) 61.0107 1.96706
\(963\) −68.2482 −2.19927
\(964\) 31.5865 1.01733
\(965\) −11.2851 −0.363279
\(966\) −212.546 −6.83856
\(967\) −42.0133 −1.35106 −0.675528 0.737334i \(-0.736084\pi\)
−0.675528 + 0.737334i \(0.736084\pi\)
\(968\) −160.028 −5.14350
\(969\) 23.1572 0.743915
\(970\) 53.9748 1.73303
\(971\) 0.606672 0.0194690 0.00973451 0.999953i \(-0.496901\pi\)
0.00973451 + 0.999953i \(0.496901\pi\)
\(972\) −309.115 −9.91486
\(973\) −44.2986 −1.42015
\(974\) 75.8503 2.43040
\(975\) 87.3753 2.79825
\(976\) −49.1052 −1.57182
\(977\) −39.5593 −1.26561 −0.632807 0.774310i \(-0.718097\pi\)
−0.632807 + 0.774310i \(0.718097\pi\)
\(978\) 176.111 5.63142
\(979\) −28.9044 −0.923788
\(980\) 238.580 7.62116
\(981\) −105.535 −3.36948
\(982\) 47.7816 1.52477
\(983\) 32.9685 1.05153 0.525766 0.850629i \(-0.323779\pi\)
0.525766 + 0.850629i \(0.323779\pi\)
\(984\) 40.6592 1.29617
\(985\) −76.7586 −2.44573
\(986\) −4.66755 −0.148645
\(987\) 103.393 3.29103
\(988\) −18.9285 −0.602196
\(989\) 35.4835 1.12831
\(990\) −435.558 −13.8429
\(991\) 4.88552 0.155194 0.0775969 0.996985i \(-0.475275\pi\)
0.0775969 + 0.996985i \(0.475275\pi\)
\(992\) 55.7171 1.76902
\(993\) 19.4501 0.617232
\(994\) 12.0131 0.381034
\(995\) −41.1189 −1.30356
\(996\) −151.051 −4.78624
\(997\) −5.65953 −0.179239 −0.0896195 0.995976i \(-0.528565\pi\)
−0.0896195 + 0.995976i \(0.528565\pi\)
\(998\) −28.0151 −0.886804
\(999\) −116.310 −3.67989
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 \(a_p\))