Properties

Label 8003.2.a.c.1.12
Level 8003
Weight 2
Character 8003.1
Self dual Yes
Analytic conductor 63.904
Analytic rank 0
Dimension 172
CM No

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Newspace parameters

Level: \( N \) = \( 8003 = 53 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(0\)
Dimension: \(172\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 8003.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.53688 q^{2}\) \(-2.79023 q^{3}\) \(+4.43578 q^{4}\) \(+3.33172 q^{5}\) \(+7.07848 q^{6}\) \(-4.26650 q^{7}\) \(-6.17928 q^{8}\) \(+4.78538 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.53688 q^{2}\) \(-2.79023 q^{3}\) \(+4.43578 q^{4}\) \(+3.33172 q^{5}\) \(+7.07848 q^{6}\) \(-4.26650 q^{7}\) \(-6.17928 q^{8}\) \(+4.78538 q^{9}\) \(-8.45219 q^{10}\) \(-4.42179 q^{11}\) \(-12.3768 q^{12}\) \(+6.67188 q^{13}\) \(+10.8236 q^{14}\) \(-9.29627 q^{15}\) \(+6.80456 q^{16}\) \(-2.89072 q^{17}\) \(-12.1399 q^{18}\) \(-7.22734 q^{19}\) \(+14.7788 q^{20}\) \(+11.9045 q^{21}\) \(+11.2176 q^{22}\) \(-3.14906 q^{23}\) \(+17.2416 q^{24}\) \(+6.10037 q^{25}\) \(-16.9258 q^{26}\) \(-4.98161 q^{27}\) \(-18.9252 q^{28}\) \(-9.62452 q^{29}\) \(+23.5835 q^{30}\) \(+8.77694 q^{31}\) \(-4.90381 q^{32}\) \(+12.3378 q^{33}\) \(+7.33341 q^{34}\) \(-14.2148 q^{35}\) \(+21.2269 q^{36}\) \(-0.615614 q^{37}\) \(+18.3349 q^{38}\) \(-18.6161 q^{39}\) \(-20.5876 q^{40}\) \(-5.40120 q^{41}\) \(-30.2004 q^{42}\) \(-5.31325 q^{43}\) \(-19.6141 q^{44}\) \(+15.9435 q^{45}\) \(+7.98881 q^{46}\) \(+5.48086 q^{47}\) \(-18.9863 q^{48}\) \(+11.2030 q^{49}\) \(-15.4759 q^{50}\) \(+8.06576 q^{51}\) \(+29.5949 q^{52}\) \(-1.00000 q^{53}\) \(+12.6378 q^{54}\) \(-14.7322 q^{55}\) \(+26.3639 q^{56}\) \(+20.1659 q^{57}\) \(+24.4163 q^{58}\) \(-8.73398 q^{59}\) \(-41.2362 q^{60}\) \(-9.66490 q^{61}\) \(-22.2661 q^{62}\) \(-20.4168 q^{63}\) \(-1.16872 q^{64}\) \(+22.2288 q^{65}\) \(-31.2996 q^{66}\) \(-5.02390 q^{67}\) \(-12.8226 q^{68}\) \(+8.78661 q^{69}\) \(+36.0613 q^{70}\) \(-15.3294 q^{71}\) \(-29.5702 q^{72}\) \(-2.68984 q^{73}\) \(+1.56174 q^{74}\) \(-17.0214 q^{75}\) \(-32.0589 q^{76}\) \(+18.8656 q^{77}\) \(+47.2268 q^{78}\) \(-0.747072 q^{79}\) \(+22.6709 q^{80}\) \(-0.456299 q^{81}\) \(+13.7022 q^{82}\) \(+2.15515 q^{83}\) \(+52.8057 q^{84}\) \(-9.63107 q^{85}\) \(+13.4791 q^{86}\) \(+26.8546 q^{87}\) \(+27.3235 q^{88}\) \(-12.3172 q^{89}\) \(-40.4469 q^{90}\) \(-28.4656 q^{91}\) \(-13.9685 q^{92}\) \(-24.4897 q^{93}\) \(-13.9043 q^{94}\) \(-24.0795 q^{95}\) \(+13.6828 q^{96}\) \(+12.0937 q^{97}\) \(-28.4208 q^{98}\) \(-21.1599 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(172q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 188q^{4} \) \(\mathstrut +\mathstrut 27q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 31q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 179q^{9} \) \(\mathstrut +\mathstrut 20q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 66q^{12} \) \(\mathstrut +\mathstrut 121q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 212q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 40q^{18} \) \(\mathstrut +\mathstrut 41q^{19} \) \(\mathstrut +\mathstrut 64q^{20} \) \(\mathstrut +\mathstrut 56q^{21} \) \(\mathstrut +\mathstrut 50q^{22} \) \(\mathstrut +\mathstrut 28q^{23} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 231q^{25} \) \(\mathstrut +\mathstrut 38q^{26} \) \(\mathstrut +\mathstrut 100q^{27} \) \(\mathstrut +\mathstrut 80q^{28} \) \(\mathstrut +\mathstrut 26q^{29} \) \(\mathstrut +\mathstrut 55q^{30} \) \(\mathstrut +\mathstrut 66q^{31} \) \(\mathstrut +\mathstrut 65q^{32} \) \(\mathstrut +\mathstrut 99q^{33} \) \(\mathstrut +\mathstrut 81q^{34} \) \(\mathstrut +\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 212q^{36} \) \(\mathstrut +\mathstrut 153q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut +\mathstrut 59q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 50q^{42} \) \(\mathstrut +\mathstrut 39q^{43} \) \(\mathstrut -\mathstrut 51q^{44} \) \(\mathstrut +\mathstrut 123q^{45} \) \(\mathstrut +\mathstrut 59q^{46} \) \(\mathstrut +\mathstrut 29q^{47} \) \(\mathstrut +\mathstrut 128q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut +\mathstrut 19q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 215q^{52} \) \(\mathstrut -\mathstrut 172q^{53} \) \(\mathstrut +\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut 40q^{55} \) \(\mathstrut +\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 54q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut -\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 92q^{63} \) \(\mathstrut +\mathstrut 253q^{64} \) \(\mathstrut +\mathstrut 77q^{65} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut +\mathstrut 126q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut +\mathstrut 47q^{69} \) \(\mathstrut +\mathstrut 72q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 65q^{72} \) \(\mathstrut +\mathstrut 185q^{73} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 75q^{75} \) \(\mathstrut +\mathstrut 38q^{76} \) \(\mathstrut +\mathstrut 120q^{77} \) \(\mathstrut +\mathstrut 75q^{78} \) \(\mathstrut +\mathstrut 79q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 232q^{81} \) \(\mathstrut +\mathstrut 110q^{82} \) \(\mathstrut +\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 158q^{84} \) \(\mathstrut +\mathstrut 115q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 61q^{87} \) \(\mathstrut +\mathstrut 15q^{88} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 6q^{90} \) \(\mathstrut +\mathstrut 33q^{91} \) \(\mathstrut +\mathstrut 139q^{92} \) \(\mathstrut +\mathstrut 103q^{93} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 45q^{95} \) \(\mathstrut +\mathstrut 34q^{96} \) \(\mathstrut +\mathstrut 159q^{97} \) \(\mathstrut -\mathstrut 36q^{98} \) \(\mathstrut +\mathstrut 27q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53688 −1.79385 −0.896924 0.442185i \(-0.854203\pi\)
−0.896924 + 0.442185i \(0.854203\pi\)
\(3\) −2.79023 −1.61094 −0.805470 0.592637i \(-0.798087\pi\)
−0.805470 + 0.592637i \(0.798087\pi\)
\(4\) 4.43578 2.21789
\(5\) 3.33172 1.48999 0.744996 0.667069i \(-0.232452\pi\)
0.744996 + 0.667069i \(0.232452\pi\)
\(6\) 7.07848 2.88978
\(7\) −4.26650 −1.61259 −0.806293 0.591517i \(-0.798529\pi\)
−0.806293 + 0.591517i \(0.798529\pi\)
\(8\) −6.17928 −2.18471
\(9\) 4.78538 1.59513
\(10\) −8.45219 −2.67282
\(11\) −4.42179 −1.33322 −0.666610 0.745407i \(-0.732255\pi\)
−0.666610 + 0.745407i \(0.732255\pi\)
\(12\) −12.3768 −3.57288
\(13\) 6.67188 1.85045 0.925223 0.379424i \(-0.123878\pi\)
0.925223 + 0.379424i \(0.123878\pi\)
\(14\) 10.8236 2.89273
\(15\) −9.29627 −2.40029
\(16\) 6.80456 1.70114
\(17\) −2.89072 −0.701102 −0.350551 0.936544i \(-0.614006\pi\)
−0.350551 + 0.936544i \(0.614006\pi\)
\(18\) −12.1399 −2.86141
\(19\) −7.22734 −1.65807 −0.829033 0.559200i \(-0.811108\pi\)
−0.829033 + 0.559200i \(0.811108\pi\)
\(20\) 14.7788 3.30463
\(21\) 11.9045 2.59778
\(22\) 11.2176 2.39159
\(23\) −3.14906 −0.656625 −0.328313 0.944569i \(-0.606480\pi\)
−0.328313 + 0.944569i \(0.606480\pi\)
\(24\) 17.2416 3.51943
\(25\) 6.10037 1.22007
\(26\) −16.9258 −3.31942
\(27\) −4.98161 −0.958711
\(28\) −18.9252 −3.57653
\(29\) −9.62452 −1.78723 −0.893614 0.448837i \(-0.851838\pi\)
−0.893614 + 0.448837i \(0.851838\pi\)
\(30\) 23.5835 4.30575
\(31\) 8.77694 1.57639 0.788193 0.615428i \(-0.211017\pi\)
0.788193 + 0.615428i \(0.211017\pi\)
\(32\) −4.90381 −0.866880
\(33\) 12.3378 2.14774
\(34\) 7.33341 1.25767
\(35\) −14.2148 −2.40274
\(36\) 21.2269 3.53781
\(37\) −0.615614 −0.101206 −0.0506031 0.998719i \(-0.516114\pi\)
−0.0506031 + 0.998719i \(0.516114\pi\)
\(38\) 18.3349 2.97432
\(39\) −18.6161 −2.98096
\(40\) −20.5876 −3.25519
\(41\) −5.40120 −0.843526 −0.421763 0.906706i \(-0.638588\pi\)
−0.421763 + 0.906706i \(0.638588\pi\)
\(42\) −30.2004 −4.66002
\(43\) −5.31325 −0.810263 −0.405131 0.914258i \(-0.632774\pi\)
−0.405131 + 0.914258i \(0.632774\pi\)
\(44\) −19.6141 −2.95693
\(45\) 15.9435 2.37672
\(46\) 7.98881 1.17789
\(47\) 5.48086 0.799465 0.399733 0.916632i \(-0.369103\pi\)
0.399733 + 0.916632i \(0.369103\pi\)
\(48\) −18.9863 −2.74043
\(49\) 11.2030 1.60043
\(50\) −15.4759 −2.18863
\(51\) 8.06576 1.12943
\(52\) 29.5949 4.10408
\(53\) −1.00000 −0.137361
\(54\) 12.6378 1.71978
\(55\) −14.7322 −1.98649
\(56\) 26.3639 3.52302
\(57\) 20.1659 2.67104
\(58\) 24.4163 3.20601
\(59\) −8.73398 −1.13707 −0.568533 0.822660i \(-0.692489\pi\)
−0.568533 + 0.822660i \(0.692489\pi\)
\(60\) −41.2362 −5.32357
\(61\) −9.66490 −1.23746 −0.618732 0.785602i \(-0.712353\pi\)
−0.618732 + 0.785602i \(0.712353\pi\)
\(62\) −22.2661 −2.82780
\(63\) −20.4168 −2.57228
\(64\) −1.16872 −0.146090
\(65\) 22.2288 2.75715
\(66\) −31.2996 −3.85271
\(67\) −5.02390 −0.613767 −0.306883 0.951747i \(-0.599286\pi\)
−0.306883 + 0.951747i \(0.599286\pi\)
\(68\) −12.8226 −1.55497
\(69\) 8.78661 1.05778
\(70\) 36.0613 4.31015
\(71\) −15.3294 −1.81926 −0.909630 0.415419i \(-0.863635\pi\)
−0.909630 + 0.415419i \(0.863635\pi\)
\(72\) −29.5702 −3.48488
\(73\) −2.68984 −0.314822 −0.157411 0.987533i \(-0.550315\pi\)
−0.157411 + 0.987533i \(0.550315\pi\)
\(74\) 1.56174 0.181549
\(75\) −17.0214 −1.96547
\(76\) −32.0589 −3.67740
\(77\) 18.8656 2.14993
\(78\) 47.2268 5.34738
\(79\) −0.747072 −0.0840521 −0.0420261 0.999117i \(-0.513381\pi\)
−0.0420261 + 0.999117i \(0.513381\pi\)
\(80\) 22.6709 2.53468
\(81\) −0.456299 −0.0506999
\(82\) 13.7022 1.51316
\(83\) 2.15515 0.236559 0.118279 0.992980i \(-0.462262\pi\)
0.118279 + 0.992980i \(0.462262\pi\)
\(84\) 52.8057 5.76158
\(85\) −9.63107 −1.04464
\(86\) 13.4791 1.45349
\(87\) 26.8546 2.87912
\(88\) 27.3235 2.91269
\(89\) −12.3172 −1.30562 −0.652812 0.757520i \(-0.726411\pi\)
−0.652812 + 0.757520i \(0.726411\pi\)
\(90\) −40.4469 −4.26348
\(91\) −28.4656 −2.98400
\(92\) −13.9685 −1.45632
\(93\) −24.4897 −2.53946
\(94\) −13.9043 −1.43412
\(95\) −24.0795 −2.47050
\(96\) 13.6828 1.39649
\(97\) 12.0937 1.22793 0.613964 0.789334i \(-0.289574\pi\)
0.613964 + 0.789334i \(0.289574\pi\)
\(98\) −28.4208 −2.87093
\(99\) −21.1599 −2.12665
\(100\) 27.0599 2.70599
\(101\) 11.1599 1.11046 0.555228 0.831698i \(-0.312631\pi\)
0.555228 + 0.831698i \(0.312631\pi\)
\(102\) −20.4619 −2.02603
\(103\) 4.73867 0.466915 0.233458 0.972367i \(-0.424996\pi\)
0.233458 + 0.972367i \(0.424996\pi\)
\(104\) −41.2274 −4.04268
\(105\) 39.6625 3.87067
\(106\) 2.53688 0.246404
\(107\) 17.3994 1.68206 0.841031 0.540987i \(-0.181949\pi\)
0.841031 + 0.540987i \(0.181949\pi\)
\(108\) −22.0973 −2.12631
\(109\) −7.22806 −0.692323 −0.346161 0.938175i \(-0.612515\pi\)
−0.346161 + 0.938175i \(0.612515\pi\)
\(110\) 37.3738 3.56345
\(111\) 1.71770 0.163037
\(112\) −29.0317 −2.74323
\(113\) −16.3070 −1.53403 −0.767017 0.641627i \(-0.778260\pi\)
−0.767017 + 0.641627i \(0.778260\pi\)
\(114\) −51.1586 −4.79144
\(115\) −10.4918 −0.978366
\(116\) −42.6922 −3.96387
\(117\) 31.9274 2.95169
\(118\) 22.1571 2.03972
\(119\) 12.3332 1.13059
\(120\) 57.4442 5.24392
\(121\) 8.55224 0.777476
\(122\) 24.5187 2.21982
\(123\) 15.0706 1.35887
\(124\) 38.9326 3.49625
\(125\) 3.66613 0.327909
\(126\) 51.7951 4.61427
\(127\) −7.93101 −0.703763 −0.351881 0.936045i \(-0.614458\pi\)
−0.351881 + 0.936045i \(0.614458\pi\)
\(128\) 12.7725 1.12894
\(129\) 14.8252 1.30528
\(130\) −56.3920 −4.94590
\(131\) −1.73019 −0.151168 −0.0755838 0.997139i \(-0.524082\pi\)
−0.0755838 + 0.997139i \(0.524082\pi\)
\(132\) 54.7278 4.76344
\(133\) 30.8355 2.67377
\(134\) 12.7450 1.10100
\(135\) −16.5973 −1.42847
\(136\) 17.8626 1.53170
\(137\) 1.56124 0.133386 0.0666928 0.997774i \(-0.478755\pi\)
0.0666928 + 0.997774i \(0.478755\pi\)
\(138\) −22.2906 −1.89750
\(139\) −0.245290 −0.0208053 −0.0104026 0.999946i \(-0.503311\pi\)
−0.0104026 + 0.999946i \(0.503311\pi\)
\(140\) −63.0536 −5.32900
\(141\) −15.2929 −1.28789
\(142\) 38.8888 3.26348
\(143\) −29.5016 −2.46705
\(144\) 32.5624 2.71353
\(145\) −32.0662 −2.66295
\(146\) 6.82381 0.564743
\(147\) −31.2590 −2.57820
\(148\) −2.73073 −0.224464
\(149\) 14.9407 1.22399 0.611995 0.790862i \(-0.290367\pi\)
0.611995 + 0.790862i \(0.290367\pi\)
\(150\) 43.1814 3.52575
\(151\) 1.00000 0.0813788
\(152\) 44.6598 3.62239
\(153\) −13.8332 −1.11835
\(154\) −47.8597 −3.85665
\(155\) 29.2423 2.34880
\(156\) −82.5767 −6.61143
\(157\) 1.42369 0.113623 0.0568115 0.998385i \(-0.481907\pi\)
0.0568115 + 0.998385i \(0.481907\pi\)
\(158\) 1.89523 0.150777
\(159\) 2.79023 0.221280
\(160\) −16.3381 −1.29164
\(161\) 13.4355 1.05886
\(162\) 1.15758 0.0909479
\(163\) 16.7984 1.31575 0.657876 0.753126i \(-0.271455\pi\)
0.657876 + 0.753126i \(0.271455\pi\)
\(164\) −23.9585 −1.87085
\(165\) 41.1061 3.20011
\(166\) −5.46737 −0.424350
\(167\) 2.09222 0.161901 0.0809503 0.996718i \(-0.474205\pi\)
0.0809503 + 0.996718i \(0.474205\pi\)
\(168\) −73.5613 −5.67538
\(169\) 31.5139 2.42415
\(170\) 24.4329 1.87392
\(171\) −34.5856 −2.64482
\(172\) −23.5684 −1.79707
\(173\) −8.43659 −0.641422 −0.320711 0.947177i \(-0.603922\pi\)
−0.320711 + 0.947177i \(0.603922\pi\)
\(174\) −68.1270 −5.16469
\(175\) −26.0272 −1.96747
\(176\) −30.0883 −2.26799
\(177\) 24.3698 1.83175
\(178\) 31.2474 2.34209
\(179\) −1.23546 −0.0923423 −0.0461711 0.998934i \(-0.514702\pi\)
−0.0461711 + 0.998934i \(0.514702\pi\)
\(180\) 70.7220 5.27131
\(181\) 11.5450 0.858132 0.429066 0.903273i \(-0.358843\pi\)
0.429066 + 0.903273i \(0.358843\pi\)
\(182\) 72.2138 5.35284
\(183\) 26.9673 1.99348
\(184\) 19.4589 1.43453
\(185\) −2.05105 −0.150797
\(186\) 62.1275 4.55541
\(187\) 12.7822 0.934723
\(188\) 24.3119 1.77313
\(189\) 21.2540 1.54600
\(190\) 61.0869 4.43171
\(191\) 16.2448 1.17544 0.587718 0.809066i \(-0.300027\pi\)
0.587718 + 0.809066i \(0.300027\pi\)
\(192\) 3.26100 0.235342
\(193\) −18.7181 −1.34736 −0.673678 0.739025i \(-0.735287\pi\)
−0.673678 + 0.739025i \(0.735287\pi\)
\(194\) −30.6803 −2.20271
\(195\) −62.0235 −4.44160
\(196\) 49.6941 3.54958
\(197\) 7.49512 0.534005 0.267002 0.963696i \(-0.413967\pi\)
0.267002 + 0.963696i \(0.413967\pi\)
\(198\) 53.6803 3.81489
\(199\) 8.87690 0.629266 0.314633 0.949213i \(-0.398118\pi\)
0.314633 + 0.949213i \(0.398118\pi\)
\(200\) −37.6959 −2.66550
\(201\) 14.0178 0.988741
\(202\) −28.3115 −1.99199
\(203\) 41.0630 2.88206
\(204\) 35.7779 2.50496
\(205\) −17.9953 −1.25685
\(206\) −12.0215 −0.837575
\(207\) −15.0695 −1.04740
\(208\) 45.3992 3.14787
\(209\) 31.9578 2.21057
\(210\) −100.619 −6.94338
\(211\) −10.3385 −0.711729 −0.355864 0.934538i \(-0.615813\pi\)
−0.355864 + 0.934538i \(0.615813\pi\)
\(212\) −4.43578 −0.304650
\(213\) 42.7724 2.93072
\(214\) −44.1402 −3.01736
\(215\) −17.7023 −1.20728
\(216\) 30.7828 2.09450
\(217\) −37.4468 −2.54206
\(218\) 18.3367 1.24192
\(219\) 7.50527 0.507159
\(220\) −65.3486 −4.40581
\(221\) −19.2865 −1.29735
\(222\) −4.35761 −0.292464
\(223\) 7.98377 0.534633 0.267317 0.963609i \(-0.413863\pi\)
0.267317 + 0.963609i \(0.413863\pi\)
\(224\) 20.9221 1.39792
\(225\) 29.1926 1.94617
\(226\) 41.3690 2.75182
\(227\) −13.1155 −0.870509 −0.435255 0.900307i \(-0.643342\pi\)
−0.435255 + 0.900307i \(0.643342\pi\)
\(228\) 89.4516 5.92408
\(229\) −15.2888 −1.01031 −0.505156 0.863028i \(-0.668565\pi\)
−0.505156 + 0.863028i \(0.668565\pi\)
\(230\) 26.6165 1.75504
\(231\) −52.6393 −3.46341
\(232\) 59.4726 3.90457
\(233\) −19.3898 −1.27027 −0.635134 0.772402i \(-0.719055\pi\)
−0.635134 + 0.772402i \(0.719055\pi\)
\(234\) −80.9962 −5.29489
\(235\) 18.2607 1.19120
\(236\) −38.7420 −2.52189
\(237\) 2.08450 0.135403
\(238\) −31.2880 −2.02810
\(239\) 3.16945 0.205015 0.102507 0.994732i \(-0.467313\pi\)
0.102507 + 0.994732i \(0.467313\pi\)
\(240\) −63.2570 −4.08322
\(241\) −20.0435 −1.29111 −0.645557 0.763712i \(-0.723375\pi\)
−0.645557 + 0.763712i \(0.723375\pi\)
\(242\) −21.6960 −1.39467
\(243\) 16.2180 1.04039
\(244\) −42.8713 −2.74456
\(245\) 37.3253 2.38463
\(246\) −38.2323 −2.43760
\(247\) −48.2199 −3.06816
\(248\) −54.2352 −3.44394
\(249\) −6.01337 −0.381082
\(250\) −9.30055 −0.588218
\(251\) −10.8561 −0.685232 −0.342616 0.939476i \(-0.611313\pi\)
−0.342616 + 0.939476i \(0.611313\pi\)
\(252\) −90.5644 −5.70502
\(253\) 13.9245 0.875426
\(254\) 20.1200 1.26244
\(255\) 26.8729 1.68285
\(256\) −30.0650 −1.87906
\(257\) −1.26039 −0.0786211 −0.0393105 0.999227i \(-0.512516\pi\)
−0.0393105 + 0.999227i \(0.512516\pi\)
\(258\) −37.6097 −2.34148
\(259\) 2.62652 0.163204
\(260\) 98.6021 6.11505
\(261\) −46.0569 −2.85085
\(262\) 4.38929 0.271171
\(263\) −9.72372 −0.599590 −0.299795 0.954004i \(-0.596918\pi\)
−0.299795 + 0.954004i \(0.596918\pi\)
\(264\) −76.2388 −4.69217
\(265\) −3.33172 −0.204666
\(266\) −78.2259 −4.79634
\(267\) 34.3679 2.10328
\(268\) −22.2849 −1.36127
\(269\) −1.87130 −0.114095 −0.0570476 0.998371i \(-0.518169\pi\)
−0.0570476 + 0.998371i \(0.518169\pi\)
\(270\) 42.1055 2.56246
\(271\) 0.909353 0.0552392 0.0276196 0.999619i \(-0.491207\pi\)
0.0276196 + 0.999619i \(0.491207\pi\)
\(272\) −19.6701 −1.19267
\(273\) 79.4254 4.80704
\(274\) −3.96068 −0.239274
\(275\) −26.9746 −1.62663
\(276\) 38.9754 2.34604
\(277\) −18.9285 −1.13730 −0.568652 0.822578i \(-0.692535\pi\)
−0.568652 + 0.822578i \(0.692535\pi\)
\(278\) 0.622273 0.0373214
\(279\) 42.0010 2.51453
\(280\) 87.8372 5.24928
\(281\) −25.1585 −1.50083 −0.750415 0.660967i \(-0.770146\pi\)
−0.750415 + 0.660967i \(0.770146\pi\)
\(282\) 38.7962 2.31028
\(283\) 11.5483 0.686473 0.343237 0.939249i \(-0.388477\pi\)
0.343237 + 0.939249i \(0.388477\pi\)
\(284\) −67.9976 −4.03492
\(285\) 67.1873 3.97983
\(286\) 74.8422 4.42551
\(287\) 23.0442 1.36026
\(288\) −23.4666 −1.38278
\(289\) −8.64375 −0.508456
\(290\) 81.3482 4.77693
\(291\) −33.7442 −1.97812
\(292\) −11.9315 −0.698240
\(293\) 1.59756 0.0933307 0.0466653 0.998911i \(-0.485141\pi\)
0.0466653 + 0.998911i \(0.485141\pi\)
\(294\) 79.3004 4.62489
\(295\) −29.0992 −1.69422
\(296\) 3.80405 0.221106
\(297\) 22.0276 1.27817
\(298\) −37.9028 −2.19565
\(299\) −21.0102 −1.21505
\(300\) −75.5033 −4.35918
\(301\) 22.6690 1.30662
\(302\) −2.53688 −0.145981
\(303\) −31.1388 −1.78888
\(304\) −49.1789 −2.82060
\(305\) −32.2008 −1.84381
\(306\) 35.0931 2.00614
\(307\) 2.22523 0.127000 0.0635002 0.997982i \(-0.479774\pi\)
0.0635002 + 0.997982i \(0.479774\pi\)
\(308\) 83.6835 4.76831
\(309\) −13.2220 −0.752172
\(310\) −74.1844 −4.21339
\(311\) −30.8442 −1.74902 −0.874508 0.485010i \(-0.838816\pi\)
−0.874508 + 0.485010i \(0.838816\pi\)
\(312\) 115.034 6.51251
\(313\) −26.0160 −1.47051 −0.735256 0.677789i \(-0.762938\pi\)
−0.735256 + 0.677789i \(0.762938\pi\)
\(314\) −3.61174 −0.203822
\(315\) −68.0231 −3.83267
\(316\) −3.31384 −0.186418
\(317\) −13.6480 −0.766548 −0.383274 0.923635i \(-0.625204\pi\)
−0.383274 + 0.923635i \(0.625204\pi\)
\(318\) −7.07848 −0.396942
\(319\) 42.5576 2.38277
\(320\) −3.89385 −0.217673
\(321\) −48.5482 −2.70970
\(322\) −34.0842 −1.89944
\(323\) 20.8922 1.16247
\(324\) −2.02404 −0.112447
\(325\) 40.7009 2.25768
\(326\) −42.6156 −2.36026
\(327\) 20.1679 1.11529
\(328\) 33.3755 1.84285
\(329\) −23.3841 −1.28921
\(330\) −104.281 −5.74051
\(331\) 4.00337 0.220045 0.110023 0.993929i \(-0.464908\pi\)
0.110023 + 0.993929i \(0.464908\pi\)
\(332\) 9.55978 0.524661
\(333\) −2.94594 −0.161437
\(334\) −5.30771 −0.290425
\(335\) −16.7382 −0.914507
\(336\) 81.0049 4.41918
\(337\) 15.2092 0.828496 0.414248 0.910164i \(-0.364045\pi\)
0.414248 + 0.910164i \(0.364045\pi\)
\(338\) −79.9472 −4.34855
\(339\) 45.5003 2.47124
\(340\) −42.7213 −2.31689
\(341\) −38.8098 −2.10167
\(342\) 87.7395 4.74441
\(343\) −17.9322 −0.968247
\(344\) 32.8321 1.77019
\(345\) 29.2745 1.57609
\(346\) 21.4026 1.15061
\(347\) 24.8818 1.33572 0.667862 0.744285i \(-0.267210\pi\)
0.667862 + 0.744285i \(0.267210\pi\)
\(348\) 119.121 6.38556
\(349\) −10.4576 −0.559784 −0.279892 0.960032i \(-0.590299\pi\)
−0.279892 + 0.960032i \(0.590299\pi\)
\(350\) 66.0281 3.52935
\(351\) −33.2367 −1.77404
\(352\) 21.6836 1.15574
\(353\) 10.6149 0.564977 0.282488 0.959271i \(-0.408840\pi\)
0.282488 + 0.959271i \(0.408840\pi\)
\(354\) −61.8233 −3.28587
\(355\) −51.0732 −2.71068
\(356\) −54.6365 −2.89573
\(357\) −34.4126 −1.82131
\(358\) 3.13421 0.165648
\(359\) 18.3411 0.968006 0.484003 0.875066i \(-0.339182\pi\)
0.484003 + 0.875066i \(0.339182\pi\)
\(360\) −98.5196 −5.19244
\(361\) 33.2345 1.74918
\(362\) −29.2883 −1.53936
\(363\) −23.8627 −1.25247
\(364\) −126.267 −6.61818
\(365\) −8.96180 −0.469082
\(366\) −68.4129 −3.57600
\(367\) −31.9156 −1.66598 −0.832991 0.553286i \(-0.813373\pi\)
−0.832991 + 0.553286i \(0.813373\pi\)
\(368\) −21.4280 −1.11701
\(369\) −25.8468 −1.34553
\(370\) 5.20329 0.270506
\(371\) 4.26650 0.221506
\(372\) −108.631 −5.63224
\(373\) 1.91673 0.0992448 0.0496224 0.998768i \(-0.484198\pi\)
0.0496224 + 0.998768i \(0.484198\pi\)
\(374\) −32.4268 −1.67675
\(375\) −10.2293 −0.528241
\(376\) −33.8678 −1.74660
\(377\) −64.2136 −3.30717
\(378\) −53.9190 −2.77329
\(379\) −31.9891 −1.64317 −0.821585 0.570086i \(-0.806910\pi\)
−0.821585 + 0.570086i \(0.806910\pi\)
\(380\) −106.811 −5.47930
\(381\) 22.1293 1.13372
\(382\) −41.2113 −2.10855
\(383\) 27.4791 1.40412 0.702058 0.712120i \(-0.252265\pi\)
0.702058 + 0.712120i \(0.252265\pi\)
\(384\) −35.6383 −1.81866
\(385\) 62.8548 3.20338
\(386\) 47.4856 2.41695
\(387\) −25.4259 −1.29247
\(388\) 53.6449 2.72341
\(389\) 32.4682 1.64620 0.823102 0.567893i \(-0.192241\pi\)
0.823102 + 0.567893i \(0.192241\pi\)
\(390\) 157.346 7.96755
\(391\) 9.10305 0.460361
\(392\) −69.2266 −3.49647
\(393\) 4.82763 0.243522
\(394\) −19.0142 −0.957923
\(395\) −2.48904 −0.125237
\(396\) −93.8607 −4.71668
\(397\) 24.3180 1.22049 0.610244 0.792214i \(-0.291071\pi\)
0.610244 + 0.792214i \(0.291071\pi\)
\(398\) −22.5196 −1.12881
\(399\) −86.0380 −4.30729
\(400\) 41.5103 2.07552
\(401\) 17.7472 0.886253 0.443127 0.896459i \(-0.353869\pi\)
0.443127 + 0.896459i \(0.353869\pi\)
\(402\) −35.5616 −1.77365
\(403\) 58.5587 2.91702
\(404\) 49.5030 2.46287
\(405\) −1.52026 −0.0755424
\(406\) −104.172 −5.16997
\(407\) 2.72212 0.134930
\(408\) −49.8406 −2.46748
\(409\) −4.29402 −0.212325 −0.106163 0.994349i \(-0.533856\pi\)
−0.106163 + 0.994349i \(0.533856\pi\)
\(410\) 45.6520 2.25459
\(411\) −4.35621 −0.214876
\(412\) 21.0197 1.03557
\(413\) 37.2635 1.83362
\(414\) 38.2294 1.87887
\(415\) 7.18037 0.352471
\(416\) −32.7176 −1.60411
\(417\) 0.684416 0.0335160
\(418\) −81.0732 −3.96542
\(419\) −12.3248 −0.602108 −0.301054 0.953607i \(-0.597338\pi\)
−0.301054 + 0.953607i \(0.597338\pi\)
\(420\) 175.934 8.58470
\(421\) 23.5935 1.14988 0.574939 0.818196i \(-0.305026\pi\)
0.574939 + 0.818196i \(0.305026\pi\)
\(422\) 26.2274 1.27673
\(423\) 26.2280 1.27525
\(424\) 6.17928 0.300092
\(425\) −17.6345 −0.855397
\(426\) −108.509 −5.25726
\(427\) 41.2353 1.99552
\(428\) 77.1797 3.73062
\(429\) 82.3163 3.97427
\(430\) 44.9086 2.16568
\(431\) −8.18146 −0.394087 −0.197044 0.980395i \(-0.563134\pi\)
−0.197044 + 0.980395i \(0.563134\pi\)
\(432\) −33.8977 −1.63090
\(433\) 11.8709 0.570477 0.285239 0.958457i \(-0.407927\pi\)
0.285239 + 0.958457i \(0.407927\pi\)
\(434\) 94.9982 4.56006
\(435\) 89.4721 4.28986
\(436\) −32.0621 −1.53549
\(437\) 22.7594 1.08873
\(438\) −19.0400 −0.909766
\(439\) 38.5659 1.84065 0.920325 0.391154i \(-0.127924\pi\)
0.920325 + 0.391154i \(0.127924\pi\)
\(440\) 91.0343 4.33989
\(441\) 53.6107 2.55289
\(442\) 48.9276 2.32725
\(443\) 2.39972 0.114014 0.0570071 0.998374i \(-0.481844\pi\)
0.0570071 + 0.998374i \(0.481844\pi\)
\(444\) 7.61935 0.361598
\(445\) −41.0376 −1.94537
\(446\) −20.2539 −0.959050
\(447\) −41.6880 −1.97177
\(448\) 4.98635 0.235583
\(449\) −6.43202 −0.303546 −0.151773 0.988415i \(-0.548498\pi\)
−0.151773 + 0.988415i \(0.548498\pi\)
\(450\) −74.0582 −3.49114
\(451\) 23.8830 1.12461
\(452\) −72.3342 −3.40232
\(453\) −2.79023 −0.131096
\(454\) 33.2726 1.56156
\(455\) −94.8393 −4.44614
\(456\) −124.611 −5.83544
\(457\) −13.4364 −0.628531 −0.314265 0.949335i \(-0.601758\pi\)
−0.314265 + 0.949335i \(0.601758\pi\)
\(458\) 38.7859 1.81235
\(459\) 14.4004 0.672154
\(460\) −46.5393 −2.16991
\(461\) −35.2743 −1.64289 −0.821444 0.570289i \(-0.806831\pi\)
−0.821444 + 0.570289i \(0.806831\pi\)
\(462\) 133.540 6.21283
\(463\) 2.76050 0.128291 0.0641457 0.997941i \(-0.479568\pi\)
0.0641457 + 0.997941i \(0.479568\pi\)
\(464\) −65.4906 −3.04032
\(465\) −81.5928 −3.78378
\(466\) 49.1897 2.27867
\(467\) −35.8710 −1.65991 −0.829956 0.557829i \(-0.811635\pi\)
−0.829956 + 0.557829i \(0.811635\pi\)
\(468\) 141.623 6.54652
\(469\) 21.4345 0.989752
\(470\) −46.3253 −2.13682
\(471\) −3.97243 −0.183040
\(472\) 53.9697 2.48416
\(473\) 23.4941 1.08026
\(474\) −5.28814 −0.242892
\(475\) −44.0895 −2.02296
\(476\) 54.7075 2.50752
\(477\) −4.78538 −0.219107
\(478\) −8.04053 −0.367765
\(479\) −7.79711 −0.356259 −0.178129 0.984007i \(-0.557005\pi\)
−0.178129 + 0.984007i \(0.557005\pi\)
\(480\) 45.5871 2.08076
\(481\) −4.10730 −0.187277
\(482\) 50.8480 2.31606
\(483\) −37.4881 −1.70577
\(484\) 37.9358 1.72435
\(485\) 40.2928 1.82960
\(486\) −41.1432 −1.86629
\(487\) 22.3134 1.01112 0.505558 0.862793i \(-0.331287\pi\)
0.505558 + 0.862793i \(0.331287\pi\)
\(488\) 59.7221 2.70349
\(489\) −46.8714 −2.11960
\(490\) −94.6900 −4.27766
\(491\) 0.762988 0.0344332 0.0172166 0.999852i \(-0.494520\pi\)
0.0172166 + 0.999852i \(0.494520\pi\)
\(492\) 66.8497 3.01382
\(493\) 27.8218 1.25303
\(494\) 122.328 5.50381
\(495\) −70.4990 −3.16870
\(496\) 59.7232 2.68165
\(497\) 65.4027 2.93371
\(498\) 15.2552 0.683603
\(499\) −4.25179 −0.190336 −0.0951682 0.995461i \(-0.530339\pi\)
−0.0951682 + 0.995461i \(0.530339\pi\)
\(500\) 16.2621 0.727265
\(501\) −5.83776 −0.260812
\(502\) 27.5407 1.22920
\(503\) −31.9438 −1.42430 −0.712152 0.702026i \(-0.752279\pi\)
−0.712152 + 0.702026i \(0.752279\pi\)
\(504\) 126.161 5.61967
\(505\) 37.1818 1.65457
\(506\) −35.3248 −1.57038
\(507\) −87.9311 −3.90516
\(508\) −35.1802 −1.56087
\(509\) 27.2916 1.20968 0.604839 0.796348i \(-0.293237\pi\)
0.604839 + 0.796348i \(0.293237\pi\)
\(510\) −68.1734 −3.01877
\(511\) 11.4762 0.507677
\(512\) 50.7263 2.24181
\(513\) 36.0038 1.58961
\(514\) 3.19747 0.141034
\(515\) 15.7879 0.695700
\(516\) 65.7612 2.89497
\(517\) −24.2352 −1.06586
\(518\) −6.66317 −0.292763
\(519\) 23.5400 1.03329
\(520\) −137.358 −6.02356
\(521\) −29.1086 −1.27527 −0.637636 0.770338i \(-0.720088\pi\)
−0.637636 + 0.770338i \(0.720088\pi\)
\(522\) 116.841 5.11399
\(523\) −18.0367 −0.788688 −0.394344 0.918963i \(-0.629028\pi\)
−0.394344 + 0.918963i \(0.629028\pi\)
\(524\) −7.67474 −0.335273
\(525\) 72.6219 3.16948
\(526\) 24.6679 1.07557
\(527\) −25.3717 −1.10521
\(528\) 83.9534 3.65360
\(529\) −13.0834 −0.568844
\(530\) 8.45219 0.367140
\(531\) −41.7954 −1.81376
\(532\) 136.779 5.93013
\(533\) −36.0361 −1.56090
\(534\) −87.1874 −3.77297
\(535\) 57.9699 2.50626
\(536\) 31.0441 1.34090
\(537\) 3.44720 0.148758
\(538\) 4.74727 0.204669
\(539\) −49.5374 −2.13373
\(540\) −73.6221 −3.16819
\(541\) −15.7832 −0.678572 −0.339286 0.940683i \(-0.610185\pi\)
−0.339286 + 0.940683i \(0.610185\pi\)
\(542\) −2.30692 −0.0990908
\(543\) −32.2132 −1.38240
\(544\) 14.1755 0.607771
\(545\) −24.0819 −1.03155
\(546\) −201.493 −8.62310
\(547\) 13.5489 0.579309 0.289655 0.957131i \(-0.406460\pi\)
0.289655 + 0.957131i \(0.406460\pi\)
\(548\) 6.92531 0.295835
\(549\) −46.2502 −1.97391
\(550\) 68.4313 2.91792
\(551\) 69.5597 2.96334
\(552\) −54.2949 −2.31094
\(553\) 3.18738 0.135541
\(554\) 48.0194 2.04015
\(555\) 5.72291 0.242924
\(556\) −1.08805 −0.0461437
\(557\) −36.3645 −1.54081 −0.770407 0.637552i \(-0.779947\pi\)
−0.770407 + 0.637552i \(0.779947\pi\)
\(558\) −106.552 −4.51069
\(559\) −35.4493 −1.49935
\(560\) −96.7254 −4.08739
\(561\) −35.6651 −1.50578
\(562\) 63.8242 2.69226
\(563\) 35.1359 1.48080 0.740400 0.672166i \(-0.234636\pi\)
0.740400 + 0.672166i \(0.234636\pi\)
\(564\) −67.8357 −2.85640
\(565\) −54.3304 −2.28570
\(566\) −29.2966 −1.23143
\(567\) 1.94680 0.0817579
\(568\) 94.7244 3.97455
\(569\) 13.5574 0.568355 0.284178 0.958772i \(-0.408279\pi\)
0.284178 + 0.958772i \(0.408279\pi\)
\(570\) −170.446 −7.13921
\(571\) 21.6231 0.904900 0.452450 0.891790i \(-0.350550\pi\)
0.452450 + 0.891790i \(0.350550\pi\)
\(572\) −130.863 −5.47164
\(573\) −45.3268 −1.89356
\(574\) −58.4605 −2.44009
\(575\) −19.2105 −0.801131
\(576\) −5.59277 −0.233032
\(577\) −10.9765 −0.456959 −0.228479 0.973549i \(-0.573375\pi\)
−0.228479 + 0.973549i \(0.573375\pi\)
\(578\) 21.9282 0.912092
\(579\) 52.2277 2.17051
\(580\) −142.239 −5.90613
\(581\) −9.19496 −0.381471
\(582\) 85.6050 3.54844
\(583\) 4.42179 0.183132
\(584\) 16.6213 0.687793
\(585\) 106.373 4.39800
\(586\) −4.05283 −0.167421
\(587\) 1.19047 0.0491361 0.0245681 0.999698i \(-0.492179\pi\)
0.0245681 + 0.999698i \(0.492179\pi\)
\(588\) −138.658 −5.71815
\(589\) −63.4340 −2.61375
\(590\) 73.8212 3.03917
\(591\) −20.9131 −0.860250
\(592\) −4.18898 −0.172166
\(593\) −28.8636 −1.18529 −0.592643 0.805465i \(-0.701915\pi\)
−0.592643 + 0.805465i \(0.701915\pi\)
\(594\) −55.8815 −2.29285
\(595\) 41.0910 1.68456
\(596\) 66.2736 2.71467
\(597\) −24.7686 −1.01371
\(598\) 53.3003 2.17961
\(599\) 45.0409 1.84032 0.920161 0.391540i \(-0.128058\pi\)
0.920161 + 0.391540i \(0.128058\pi\)
\(600\) 105.180 4.29396
\(601\) −4.05588 −0.165443 −0.0827215 0.996573i \(-0.526361\pi\)
−0.0827215 + 0.996573i \(0.526361\pi\)
\(602\) −57.5085 −2.34387
\(603\) −24.0413 −0.979035
\(604\) 4.43578 0.180489
\(605\) 28.4937 1.15843
\(606\) 78.9954 3.20897
\(607\) −20.2712 −0.822783 −0.411392 0.911459i \(-0.634957\pi\)
−0.411392 + 0.911459i \(0.634957\pi\)
\(608\) 35.4415 1.43734
\(609\) −114.575 −4.64282
\(610\) 81.6896 3.30751
\(611\) 36.5676 1.47937
\(612\) −61.3609 −2.48037
\(613\) 23.9420 0.967009 0.483504 0.875342i \(-0.339364\pi\)
0.483504 + 0.875342i \(0.339364\pi\)
\(614\) −5.64514 −0.227819
\(615\) 50.2110 2.02470
\(616\) −116.576 −4.69697
\(617\) −2.09864 −0.0844881 −0.0422441 0.999107i \(-0.513451\pi\)
−0.0422441 + 0.999107i \(0.513451\pi\)
\(618\) 33.5426 1.34928
\(619\) −30.8519 −1.24004 −0.620022 0.784584i \(-0.712876\pi\)
−0.620022 + 0.784584i \(0.712876\pi\)
\(620\) 129.712 5.20938
\(621\) 15.6874 0.629514
\(622\) 78.2483 3.13747
\(623\) 52.5515 2.10543
\(624\) −126.674 −5.07102
\(625\) −18.2873 −0.731493
\(626\) 65.9996 2.63788
\(627\) −89.1696 −3.56109
\(628\) 6.31518 0.252003
\(629\) 1.77957 0.0709559
\(630\) 172.567 6.87522
\(631\) 21.0748 0.838976 0.419488 0.907761i \(-0.362210\pi\)
0.419488 + 0.907761i \(0.362210\pi\)
\(632\) 4.61637 0.183629
\(633\) 28.8467 1.14655
\(634\) 34.6234 1.37507
\(635\) −26.4239 −1.04860
\(636\) 12.3768 0.490773
\(637\) 74.7452 2.96151
\(638\) −107.964 −4.27432
\(639\) −73.3568 −2.90195
\(640\) 42.5545 1.68212
\(641\) 10.2635 0.405386 0.202693 0.979242i \(-0.435031\pi\)
0.202693 + 0.979242i \(0.435031\pi\)
\(642\) 123.161 4.86079
\(643\) −15.6338 −0.616538 −0.308269 0.951299i \(-0.599750\pi\)
−0.308269 + 0.951299i \(0.599750\pi\)
\(644\) 59.5968 2.34844
\(645\) 49.3934 1.94486
\(646\) −53.0011 −2.08530
\(647\) 23.3802 0.919170 0.459585 0.888134i \(-0.347998\pi\)
0.459585 + 0.888134i \(0.347998\pi\)
\(648\) 2.81960 0.110764
\(649\) 38.6198 1.51596
\(650\) −103.253 −4.04993
\(651\) 104.485 4.09510
\(652\) 74.5139 2.91819
\(653\) −3.16171 −0.123727 −0.0618637 0.998085i \(-0.519704\pi\)
−0.0618637 + 0.998085i \(0.519704\pi\)
\(654\) −51.1637 −2.00066
\(655\) −5.76452 −0.225238
\(656\) −36.7528 −1.43495
\(657\) −12.8719 −0.502181
\(658\) 59.3227 2.31264
\(659\) −42.7875 −1.66676 −0.833382 0.552698i \(-0.813598\pi\)
−0.833382 + 0.552698i \(0.813598\pi\)
\(660\) 182.338 7.09748
\(661\) 34.9870 1.36084 0.680418 0.732824i \(-0.261798\pi\)
0.680418 + 0.732824i \(0.261798\pi\)
\(662\) −10.1561 −0.394727
\(663\) 53.8138 2.08995
\(664\) −13.3173 −0.516811
\(665\) 102.735 3.98390
\(666\) 7.47352 0.289593
\(667\) 30.3082 1.17354
\(668\) 9.28060 0.359077
\(669\) −22.2766 −0.861261
\(670\) 42.4629 1.64049
\(671\) 42.7362 1.64981
\(672\) −58.3775 −2.25196
\(673\) −4.83381 −0.186330 −0.0931648 0.995651i \(-0.529698\pi\)
−0.0931648 + 0.995651i \(0.529698\pi\)
\(674\) −38.5839 −1.48620
\(675\) −30.3897 −1.16970
\(676\) 139.789 5.37649
\(677\) −26.0103 −0.999657 −0.499828 0.866124i \(-0.666604\pi\)
−0.499828 + 0.866124i \(0.666604\pi\)
\(678\) −115.429 −4.43302
\(679\) −51.5977 −1.98014
\(680\) 59.5131 2.28222
\(681\) 36.5954 1.40234
\(682\) 98.4560 3.77007
\(683\) −3.43112 −0.131288 −0.0656440 0.997843i \(-0.520910\pi\)
−0.0656440 + 0.997843i \(0.520910\pi\)
\(684\) −153.414 −5.86592
\(685\) 5.20162 0.198744
\(686\) 45.4919 1.73689
\(687\) 42.6593 1.62755
\(688\) −36.1543 −1.37837
\(689\) −6.67188 −0.254178
\(690\) −74.2661 −2.82726
\(691\) 3.54444 0.134837 0.0674185 0.997725i \(-0.478524\pi\)
0.0674185 + 0.997725i \(0.478524\pi\)
\(692\) −37.4228 −1.42260
\(693\) 90.2789 3.42941
\(694\) −63.1222 −2.39609
\(695\) −0.817239 −0.0309996
\(696\) −165.942 −6.29002
\(697\) 15.6133 0.591397
\(698\) 26.5298 1.00417
\(699\) 54.1020 2.04633
\(700\) −115.451 −4.36364
\(701\) 14.3919 0.543576 0.271788 0.962357i \(-0.412385\pi\)
0.271788 + 0.962357i \(0.412385\pi\)
\(702\) 84.3176 3.18236
\(703\) 4.44925 0.167807
\(704\) 5.16784 0.194770
\(705\) −50.9515 −1.91895
\(706\) −26.9289 −1.01348
\(707\) −47.6139 −1.79070
\(708\) 108.099 4.06261
\(709\) −11.6729 −0.438385 −0.219193 0.975682i \(-0.570342\pi\)
−0.219193 + 0.975682i \(0.570342\pi\)
\(710\) 129.567 4.86255
\(711\) −3.57502 −0.134074
\(712\) 76.1117 2.85241
\(713\) −27.6391 −1.03509
\(714\) 87.3007 3.26715
\(715\) −98.2913 −3.67588
\(716\) −5.48020 −0.204805
\(717\) −8.84349 −0.330266
\(718\) −46.5292 −1.73645
\(719\) −15.3409 −0.572118 −0.286059 0.958212i \(-0.592345\pi\)
−0.286059 + 0.958212i \(0.592345\pi\)
\(720\) 108.489 4.04314
\(721\) −20.2175 −0.752941
\(722\) −84.3120 −3.13777
\(723\) 55.9259 2.07991
\(724\) 51.2110 1.90324
\(725\) −58.7131 −2.18055
\(726\) 60.5369 2.24673
\(727\) 12.0691 0.447618 0.223809 0.974633i \(-0.428151\pi\)
0.223809 + 0.974633i \(0.428151\pi\)
\(728\) 175.897 6.51916
\(729\) −43.8831 −1.62530
\(730\) 22.7350 0.841462
\(731\) 15.3591 0.568077
\(732\) 119.621 4.42131
\(733\) 49.0519 1.81177 0.905886 0.423522i \(-0.139206\pi\)
0.905886 + 0.423522i \(0.139206\pi\)
\(734\) 80.9662 2.98852
\(735\) −104.146 −3.84149
\(736\) 15.4424 0.569215
\(737\) 22.2146 0.818286
\(738\) 65.5702 2.41367
\(739\) 11.7857 0.433543 0.216772 0.976222i \(-0.430447\pi\)
0.216772 + 0.976222i \(0.430447\pi\)
\(740\) −9.09802 −0.334450
\(741\) 134.545 4.94262
\(742\) −10.8236 −0.397347
\(743\) 26.9068 0.987116 0.493558 0.869713i \(-0.335696\pi\)
0.493558 + 0.869713i \(0.335696\pi\)
\(744\) 151.329 5.54798
\(745\) 49.7783 1.82373
\(746\) −4.86253 −0.178030
\(747\) 10.3132 0.377341
\(748\) 56.6988 2.07311
\(749\) −74.2344 −2.71247
\(750\) 25.9507 0.947584
\(751\) 25.0729 0.914924 0.457462 0.889229i \(-0.348759\pi\)
0.457462 + 0.889229i \(0.348759\pi\)
\(752\) 37.2948 1.36000
\(753\) 30.2911 1.10387
\(754\) 162.902 5.93255
\(755\) 3.33172 0.121254
\(756\) 94.2782 3.42886
\(757\) 39.9659 1.45258 0.726292 0.687386i \(-0.241242\pi\)
0.726292 + 0.687386i \(0.241242\pi\)
\(758\) 81.1527 2.94760
\(759\) −38.8525 −1.41026
\(760\) 148.794 5.39732
\(761\) 12.4607 0.451699 0.225850 0.974162i \(-0.427484\pi\)
0.225850 + 0.974162i \(0.427484\pi\)
\(762\) −56.1395 −2.03372
\(763\) 30.8385 1.11643
\(764\) 72.0585 2.60698
\(765\) −46.0883 −1.66633
\(766\) −69.7112 −2.51877
\(767\) −58.2720 −2.10408
\(768\) 83.8882 3.02705
\(769\) 28.3942 1.02392 0.511960 0.859009i \(-0.328920\pi\)
0.511960 + 0.859009i \(0.328920\pi\)
\(770\) −159.455 −5.74637
\(771\) 3.51678 0.126654
\(772\) −83.0292 −2.98829
\(773\) 9.31668 0.335098 0.167549 0.985864i \(-0.446415\pi\)
0.167549 + 0.985864i \(0.446415\pi\)
\(774\) 64.5025 2.31850
\(775\) 53.5426 1.92331
\(776\) −74.7303 −2.68266
\(777\) −7.32858 −0.262911
\(778\) −82.3681 −2.95304
\(779\) 39.0363 1.39862
\(780\) −275.123 −9.85097
\(781\) 67.7832 2.42547
\(782\) −23.0934 −0.825818
\(783\) 47.9456 1.71344
\(784\) 76.2316 2.72256
\(785\) 4.74335 0.169297
\(786\) −12.2471 −0.436841
\(787\) 45.2900 1.61442 0.807208 0.590268i \(-0.200978\pi\)
0.807208 + 0.590268i \(0.200978\pi\)
\(788\) 33.2467 1.18436
\(789\) 27.1314 0.965904
\(790\) 6.31439 0.224656
\(791\) 69.5738 2.47376
\(792\) 130.753 4.64611
\(793\) −64.4830 −2.28986
\(794\) −61.6920 −2.18937
\(795\) 9.29627 0.329705
\(796\) 39.3759 1.39564
\(797\) −24.1518 −0.855499 −0.427749 0.903897i \(-0.640693\pi\)
−0.427749 + 0.903897i \(0.640693\pi\)
\(798\) 218.268 7.72661
\(799\) −15.8436 −0.560507
\(800\) −29.9151 −1.05766
\(801\) −58.9426 −2.08264
\(802\) −45.0226 −1.58980
\(803\) 11.8939 0.419727
\(804\) 62.1800 2.19292
\(805\) 44.7633 1.57770
\(806\) −148.557 −5.23268
\(807\) 5.22135 0.183800
\(808\) −68.9604 −2.42602
\(809\) −5.47453 −0.192474 −0.0962372 0.995358i \(-0.530681\pi\)
−0.0962372 + 0.995358i \(0.530681\pi\)
\(810\) 3.85673 0.135512
\(811\) −34.1169 −1.19801 −0.599004 0.800746i \(-0.704436\pi\)
−0.599004 + 0.800746i \(0.704436\pi\)
\(812\) 182.146 6.39208
\(813\) −2.53730 −0.0889871
\(814\) −6.90569 −0.242044
\(815\) 55.9676 1.96046
\(816\) 54.8840 1.92132
\(817\) 38.4007 1.34347
\(818\) 10.8934 0.380879
\(819\) −136.218 −4.75986
\(820\) −79.8231 −2.78754
\(821\) 1.64495 0.0574091 0.0287046 0.999588i \(-0.490862\pi\)
0.0287046 + 0.999588i \(0.490862\pi\)
\(822\) 11.0512 0.385455
\(823\) 6.81136 0.237429 0.118715 0.992928i \(-0.462123\pi\)
0.118715 + 0.992928i \(0.462123\pi\)
\(824\) −29.2816 −1.02007
\(825\) 75.2652 2.62040
\(826\) −94.5332 −3.28923
\(827\) −49.1504 −1.70913 −0.854563 0.519348i \(-0.826175\pi\)
−0.854563 + 0.519348i \(0.826175\pi\)
\(828\) −66.8447 −2.32301
\(829\) −45.9876 −1.59721 −0.798607 0.601853i \(-0.794429\pi\)
−0.798607 + 0.601853i \(0.794429\pi\)
\(830\) −18.2158 −0.632278
\(831\) 52.8149 1.83213
\(832\) −7.79756 −0.270332
\(833\) −32.3848 −1.12207
\(834\) −1.73628 −0.0601226
\(835\) 6.97068 0.241230
\(836\) 141.758 4.90279
\(837\) −43.7233 −1.51130
\(838\) 31.2667 1.08009
\(839\) −35.5172 −1.22619 −0.613095 0.790009i \(-0.710076\pi\)
−0.613095 + 0.790009i \(0.710076\pi\)
\(840\) −245.086 −8.45626
\(841\) 63.6313 2.19418
\(842\) −59.8540 −2.06270
\(843\) 70.1980 2.41775
\(844\) −45.8591 −1.57853
\(845\) 104.996 3.61196
\(846\) −66.5373 −2.28760
\(847\) −36.4881 −1.25375
\(848\) −6.80456 −0.233670
\(849\) −32.2223 −1.10587
\(850\) 44.7365 1.53445
\(851\) 1.93861 0.0664546
\(852\) 189.729 6.50000
\(853\) 30.6390 1.04906 0.524529 0.851393i \(-0.324241\pi\)
0.524529 + 0.851393i \(0.324241\pi\)
\(854\) −104.609 −3.57965
\(855\) −115.229 −3.94076
\(856\) −107.516 −3.67481
\(857\) 26.7959 0.915332 0.457666 0.889124i \(-0.348686\pi\)
0.457666 + 0.889124i \(0.348686\pi\)
\(858\) −208.827 −7.12923
\(859\) 44.1114 1.50506 0.752531 0.658557i \(-0.228833\pi\)
0.752531 + 0.658557i \(0.228833\pi\)
\(860\) −78.5233 −2.67762
\(861\) −64.2986 −2.19129
\(862\) 20.7554 0.706932
\(863\) −21.1381 −0.719548 −0.359774 0.933040i \(-0.617146\pi\)
−0.359774 + 0.933040i \(0.617146\pi\)
\(864\) 24.4289 0.831087
\(865\) −28.1084 −0.955713
\(866\) −30.1150 −1.02335
\(867\) 24.1180 0.819092
\(868\) −166.106 −5.63800
\(869\) 3.30339 0.112060
\(870\) −226.980 −7.69535
\(871\) −33.5188 −1.13574
\(872\) 44.6642 1.51252
\(873\) 57.8728 1.95870
\(874\) −57.7378 −1.95301
\(875\) −15.6416 −0.528781
\(876\) 33.2917 1.12482
\(877\) 13.3385 0.450409 0.225205 0.974311i \(-0.427695\pi\)
0.225205 + 0.974311i \(0.427695\pi\)
\(878\) −97.8372 −3.30185
\(879\) −4.45757 −0.150350
\(880\) −100.246 −3.37929
\(881\) −25.9543 −0.874421 −0.437211 0.899359i \(-0.644034\pi\)
−0.437211 + 0.899359i \(0.644034\pi\)
\(882\) −136.004 −4.57949
\(883\) 41.7160 1.40385 0.701927 0.712248i \(-0.252323\pi\)
0.701927 + 0.712248i \(0.252323\pi\)
\(884\) −85.5506 −2.87738
\(885\) 81.1934 2.72929
\(886\) −6.08782 −0.204524
\(887\) −5.28684 −0.177515 −0.0887573 0.996053i \(-0.528290\pi\)
−0.0887573 + 0.996053i \(0.528290\pi\)
\(888\) −10.6142 −0.356188
\(889\) 33.8376 1.13488
\(890\) 104.108 3.48970
\(891\) 2.01766 0.0675941
\(892\) 35.4142 1.18576
\(893\) −39.6120 −1.32557
\(894\) 105.758 3.53706
\(895\) −4.11619 −0.137589
\(896\) −54.4940 −1.82052
\(897\) 58.6231 1.95737
\(898\) 16.3173 0.544515
\(899\) −84.4738 −2.81736
\(900\) 129.492 4.31639
\(901\) 2.89072 0.0963038
\(902\) −60.5883 −2.01737
\(903\) −63.2516 −2.10488
\(904\) 100.766 3.35141
\(905\) 38.4647 1.27861
\(906\) 7.07848 0.235167
\(907\) −7.12151 −0.236466 −0.118233 0.992986i \(-0.537723\pi\)
−0.118233 + 0.992986i \(0.537723\pi\)
\(908\) −58.1776 −1.93069
\(909\) 53.4045 1.77132
\(910\) 240.596 7.97569
\(911\) −55.5357 −1.83998 −0.919990 0.391941i \(-0.871804\pi\)
−0.919990 + 0.391941i \(0.871804\pi\)
\(912\) 137.220 4.54382
\(913\) −9.52964 −0.315385
\(914\) 34.0867 1.12749
\(915\) 89.8475 2.97027
\(916\) −67.8177 −2.24076
\(917\) 7.38186 0.243771
\(918\) −36.5322 −1.20574
\(919\) 21.9205 0.723090 0.361545 0.932355i \(-0.382249\pi\)
0.361545 + 0.932355i \(0.382249\pi\)
\(920\) 64.8318 2.13744
\(921\) −6.20889 −0.204590
\(922\) 89.4868 2.94709
\(923\) −102.276 −3.36644
\(924\) −233.496 −7.68145
\(925\) −3.75547 −0.123479
\(926\) −7.00307 −0.230135
\(927\) 22.6763 0.744788
\(928\) 47.1968 1.54931
\(929\) 44.6819 1.46597 0.732983 0.680247i \(-0.238128\pi\)
0.732983 + 0.680247i \(0.238128\pi\)
\(930\) 206.991 6.78752
\(931\) −80.9681 −2.65362
\(932\) −86.0089 −2.81731
\(933\) 86.0625 2.81756
\(934\) 91.0005 2.97763
\(935\) 42.5866 1.39273
\(936\) −197.289 −6.44858
\(937\) 16.1922 0.528975 0.264488 0.964389i \(-0.414797\pi\)
0.264488 + 0.964389i \(0.414797\pi\)
\(938\) −54.3767 −1.77546
\(939\) 72.5907 2.36891
\(940\) 81.0004 2.64194
\(941\) 17.6100 0.574069 0.287034 0.957920i \(-0.407331\pi\)
0.287034 + 0.957920i \(0.407331\pi\)
\(942\) 10.0776 0.328346
\(943\) 17.0087 0.553880
\(944\) −59.4309 −1.93431
\(945\) 70.8125 2.30353
\(946\) −59.6017 −1.93782
\(947\) −37.0787 −1.20490 −0.602448 0.798158i \(-0.705808\pi\)
−0.602448 + 0.798158i \(0.705808\pi\)
\(948\) 9.24638 0.300308
\(949\) −17.9463 −0.582561
\(950\) 111.850 3.62889
\(951\) 38.0810 1.23486
\(952\) −76.2106 −2.47000
\(953\) −14.9504 −0.484290 −0.242145 0.970240i \(-0.577851\pi\)
−0.242145 + 0.970240i \(0.577851\pi\)
\(954\) 12.1399 0.393045
\(955\) 54.1233 1.75139
\(956\) 14.0590 0.454700
\(957\) −118.745 −3.83849
\(958\) 19.7804 0.639074
\(959\) −6.66103 −0.215096
\(960\) 10.8647 0.350658
\(961\) 46.0347 1.48499
\(962\) 10.4197 0.335946
\(963\) 83.2626 2.68310
\(964\) −88.9084 −2.86355
\(965\) −62.3634 −2.00755
\(966\) 95.1028 3.05988
\(967\) −51.6886 −1.66219 −0.831097 0.556128i \(-0.812286\pi\)
−0.831097 + 0.556128i \(0.812286\pi\)
\(968\) −52.8467 −1.69856
\(969\) −58.2940 −1.87267
\(970\) −102.218 −3.28203
\(971\) −10.3711 −0.332824 −0.166412 0.986056i \(-0.553218\pi\)
−0.166412 + 0.986056i \(0.553218\pi\)
\(972\) 71.9395 2.30746
\(973\) 1.04653 0.0335502
\(974\) −56.6065 −1.81379
\(975\) −113.565 −3.63699
\(976\) −65.7654 −2.10510
\(977\) 45.5204 1.45633 0.728163 0.685403i \(-0.240374\pi\)
0.728163 + 0.685403i \(0.240374\pi\)
\(978\) 118.907 3.80223
\(979\) 54.4643 1.74069
\(980\) 165.567 5.28884
\(981\) −34.5890 −1.10434
\(982\) −1.93561 −0.0617679
\(983\) 3.73183 0.119027 0.0595134 0.998228i \(-0.481045\pi\)
0.0595134 + 0.998228i \(0.481045\pi\)
\(984\) −93.1253 −2.96873
\(985\) 24.9716 0.795663
\(986\) −70.5805 −2.24774
\(987\) 65.2469 2.07683
\(988\) −213.893 −6.80484
\(989\) 16.7318 0.532039
\(990\) 178.848 5.68416
\(991\) 21.8638 0.694527 0.347264 0.937768i \(-0.387111\pi\)
0.347264 + 0.937768i \(0.387111\pi\)
\(992\) −43.0405 −1.36654
\(993\) −11.1703 −0.354479
\(994\) −165.919 −5.26263
\(995\) 29.5753 0.937602
\(996\) −26.6740 −0.845197
\(997\) 31.1409 0.986242 0.493121 0.869961i \(-0.335856\pi\)
0.493121 + 0.869961i \(0.335856\pi\)
\(998\) 10.7863 0.341434
\(999\) 3.06675 0.0970276
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 \(a_p\))