Properties

Label 8021.2.a.a.1.10
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.45973 q^{2}\) \(-2.31536 q^{3}\) \(+4.05029 q^{4}\) \(-2.20524 q^{5}\) \(+5.69516 q^{6}\) \(-0.890619 q^{7}\) \(-5.04316 q^{8}\) \(+2.36088 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.45973 q^{2}\) \(-2.31536 q^{3}\) \(+4.05029 q^{4}\) \(-2.20524 q^{5}\) \(+5.69516 q^{6}\) \(-0.890619 q^{7}\) \(-5.04316 q^{8}\) \(+2.36088 q^{9}\) \(+5.42429 q^{10}\) \(-1.81246 q^{11}\) \(-9.37786 q^{12}\) \(+1.00000 q^{13}\) \(+2.19069 q^{14}\) \(+5.10591 q^{15}\) \(+4.30426 q^{16}\) \(-2.96099 q^{17}\) \(-5.80714 q^{18}\) \(-7.45390 q^{19}\) \(-8.93184 q^{20}\) \(+2.06210 q^{21}\) \(+4.45818 q^{22}\) \(-8.54775 q^{23}\) \(+11.6767 q^{24}\) \(-0.136930 q^{25}\) \(-2.45973 q^{26}\) \(+1.47979 q^{27}\) \(-3.60726 q^{28}\) \(+10.0296 q^{29}\) \(-12.5592 q^{30}\) \(-7.75715 q^{31}\) \(-0.500998 q^{32}\) \(+4.19650 q^{33}\) \(+7.28324 q^{34}\) \(+1.96403 q^{35}\) \(+9.56225 q^{36}\) \(+7.12117 q^{37}\) \(+18.3346 q^{38}\) \(-2.31536 q^{39}\) \(+11.1214 q^{40}\) \(+1.41132 q^{41}\) \(-5.07222 q^{42}\) \(+4.26646 q^{43}\) \(-7.34100 q^{44}\) \(-5.20630 q^{45}\) \(+21.0252 q^{46}\) \(+8.74552 q^{47}\) \(-9.96589 q^{48}\) \(-6.20680 q^{49}\) \(+0.336812 q^{50}\) \(+6.85575 q^{51}\) \(+4.05029 q^{52}\) \(+2.66520 q^{53}\) \(-3.63989 q^{54}\) \(+3.99691 q^{55}\) \(+4.49153 q^{56}\) \(+17.2585 q^{57}\) \(-24.6702 q^{58}\) \(-4.22538 q^{59}\) \(+20.6804 q^{60}\) \(-15.1537 q^{61}\) \(+19.0805 q^{62}\) \(-2.10265 q^{63}\) \(-7.37619 q^{64}\) \(-2.20524 q^{65}\) \(-10.3223 q^{66}\) \(-12.7596 q^{67}\) \(-11.9929 q^{68}\) \(+19.7911 q^{69}\) \(-4.83098 q^{70}\) \(+15.0852 q^{71}\) \(-11.9063 q^{72}\) \(+9.95574 q^{73}\) \(-17.5162 q^{74}\) \(+0.317043 q^{75}\) \(-30.1905 q^{76}\) \(+1.61421 q^{77}\) \(+5.69516 q^{78}\) \(-6.85303 q^{79}\) \(-9.49190 q^{80}\) \(-10.5089 q^{81}\) \(-3.47147 q^{82}\) \(-5.19063 q^{83}\) \(+8.35210 q^{84}\) \(+6.52968 q^{85}\) \(-10.4943 q^{86}\) \(-23.2221 q^{87}\) \(+9.14055 q^{88}\) \(+9.77411 q^{89}\) \(+12.8061 q^{90}\) \(-0.890619 q^{91}\) \(-34.6209 q^{92}\) \(+17.9606 q^{93}\) \(-21.5116 q^{94}\) \(+16.4376 q^{95}\) \(+1.15999 q^{96}\) \(+1.22167 q^{97}\) \(+15.2671 q^{98}\) \(-4.27901 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(134q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 33q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 47q^{11} \) \(\mathstrut -\mathstrut 53q^{12} \) \(\mathstrut +\mathstrut 134q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 30q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 87q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 52q^{22} \) \(\mathstrut -\mathstrut 44q^{23} \) \(\mathstrut -\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 58q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 117q^{27} \) \(\mathstrut -\mathstrut 71q^{28} \) \(\mathstrut -\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 21q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 30q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 32q^{36} \) \(\mathstrut -\mathstrut 55q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 86q^{40} \) \(\mathstrut -\mathstrut 16q^{41} \) \(\mathstrut +\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 148q^{43} \) \(\mathstrut -\mathstrut 54q^{44} \) \(\mathstrut -\mathstrut 24q^{45} \) \(\mathstrut -\mathstrut 57q^{46} \) \(\mathstrut -\mathstrut 21q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 17q^{50} \) \(\mathstrut -\mathstrut 123q^{51} \) \(\mathstrut +\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 17q^{53} \) \(\mathstrut -\mathstrut 10q^{54} \) \(\mathstrut -\mathstrut 148q^{55} \) \(\mathstrut -\mathstrut 47q^{56} \) \(\mathstrut -\mathstrut q^{57} \) \(\mathstrut -\mathstrut 58q^{58} \) \(\mathstrut -\mathstrut 64q^{59} \) \(\mathstrut -\mathstrut 16q^{60} \) \(\mathstrut -\mathstrut 112q^{61} \) \(\mathstrut -\mathstrut 15q^{62} \) \(\mathstrut -\mathstrut 58q^{63} \) \(\mathstrut -\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 20q^{66} \) \(\mathstrut -\mathstrut 110q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 57q^{69} \) \(\mathstrut -\mathstrut 40q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 28q^{72} \) \(\mathstrut -\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 52q^{74} \) \(\mathstrut -\mathstrut 150q^{75} \) \(\mathstrut -\mathstrut 96q^{76} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 228q^{79} \) \(\mathstrut +\mathstrut 20q^{80} \) \(\mathstrut +\mathstrut 54q^{81} \) \(\mathstrut -\mathstrut 89q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 77q^{87} \) \(\mathstrut -\mathstrut 95q^{88} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 46q^{90} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 62q^{92} \) \(\mathstrut -\mathstrut 9q^{93} \) \(\mathstrut -\mathstrut 87q^{94} \) \(\mathstrut -\mathstrut 61q^{95} \) \(\mathstrut -\mathstrut 54q^{96} \) \(\mathstrut -\mathstrut 38q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 193q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.45973 −1.73929 −0.869647 0.493674i \(-0.835654\pi\)
−0.869647 + 0.493674i \(0.835654\pi\)
\(3\) −2.31536 −1.33677 −0.668386 0.743814i \(-0.733015\pi\)
−0.668386 + 0.743814i \(0.733015\pi\)
\(4\) 4.05029 2.02514
\(5\) −2.20524 −0.986212 −0.493106 0.869969i \(-0.664139\pi\)
−0.493106 + 0.869969i \(0.664139\pi\)
\(6\) 5.69516 2.32504
\(7\) −0.890619 −0.336622 −0.168311 0.985734i \(-0.553831\pi\)
−0.168311 + 0.985734i \(0.553831\pi\)
\(8\) −5.04316 −1.78303
\(9\) 2.36088 0.786960
\(10\) 5.42429 1.71531
\(11\) −1.81246 −0.546478 −0.273239 0.961946i \(-0.588095\pi\)
−0.273239 + 0.961946i \(0.588095\pi\)
\(12\) −9.37786 −2.70716
\(13\) 1.00000 0.277350
\(14\) 2.19069 0.585485
\(15\) 5.10591 1.31834
\(16\) 4.30426 1.07606
\(17\) −2.96099 −0.718145 −0.359073 0.933310i \(-0.616907\pi\)
−0.359073 + 0.933310i \(0.616907\pi\)
\(18\) −5.80714 −1.36876
\(19\) −7.45390 −1.71004 −0.855021 0.518593i \(-0.826456\pi\)
−0.855021 + 0.518593i \(0.826456\pi\)
\(20\) −8.93184 −1.99722
\(21\) 2.06210 0.449987
\(22\) 4.45818 0.950487
\(23\) −8.54775 −1.78233 −0.891165 0.453679i \(-0.850111\pi\)
−0.891165 + 0.453679i \(0.850111\pi\)
\(24\) 11.6767 2.38350
\(25\) −0.136930 −0.0273861
\(26\) −2.45973 −0.482393
\(27\) 1.47979 0.284786
\(28\) −3.60726 −0.681709
\(29\) 10.0296 1.86245 0.931226 0.364443i \(-0.118741\pi\)
0.931226 + 0.364443i \(0.118741\pi\)
\(30\) −12.5592 −2.29298
\(31\) −7.75715 −1.39322 −0.696612 0.717448i \(-0.745310\pi\)
−0.696612 + 0.717448i \(0.745310\pi\)
\(32\) −0.500998 −0.0885647
\(33\) 4.19650 0.730517
\(34\) 7.28324 1.24907
\(35\) 1.96403 0.331981
\(36\) 9.56225 1.59371
\(37\) 7.12117 1.17071 0.585356 0.810776i \(-0.300955\pi\)
0.585356 + 0.810776i \(0.300955\pi\)
\(38\) 18.3346 2.97427
\(39\) −2.31536 −0.370754
\(40\) 11.1214 1.75844
\(41\) 1.41132 0.220411 0.110206 0.993909i \(-0.464849\pi\)
0.110206 + 0.993909i \(0.464849\pi\)
\(42\) −5.07222 −0.782660
\(43\) 4.26646 0.650628 0.325314 0.945606i \(-0.394530\pi\)
0.325314 + 0.945606i \(0.394530\pi\)
\(44\) −7.34100 −1.10670
\(45\) −5.20630 −0.776110
\(46\) 21.0252 3.10000
\(47\) 8.74552 1.27566 0.637832 0.770175i \(-0.279831\pi\)
0.637832 + 0.770175i \(0.279831\pi\)
\(48\) −9.96589 −1.43845
\(49\) −6.20680 −0.886685
\(50\) 0.336812 0.0476324
\(51\) 6.85575 0.959997
\(52\) 4.05029 0.561674
\(53\) 2.66520 0.366093 0.183047 0.983104i \(-0.441404\pi\)
0.183047 + 0.983104i \(0.441404\pi\)
\(54\) −3.63989 −0.495326
\(55\) 3.99691 0.538943
\(56\) 4.49153 0.600207
\(57\) 17.2585 2.28594
\(58\) −24.6702 −3.23935
\(59\) −4.22538 −0.550097 −0.275049 0.961430i \(-0.588694\pi\)
−0.275049 + 0.961430i \(0.588694\pi\)
\(60\) 20.6804 2.66983
\(61\) −15.1537 −1.94023 −0.970117 0.242636i \(-0.921988\pi\)
−0.970117 + 0.242636i \(0.921988\pi\)
\(62\) 19.0805 2.42323
\(63\) −2.10265 −0.264908
\(64\) −7.37619 −0.922024
\(65\) −2.20524 −0.273526
\(66\) −10.3223 −1.27058
\(67\) −12.7596 −1.55883 −0.779415 0.626508i \(-0.784483\pi\)
−0.779415 + 0.626508i \(0.784483\pi\)
\(68\) −11.9929 −1.45435
\(69\) 19.7911 2.38257
\(70\) −4.83098 −0.577413
\(71\) 15.0852 1.79028 0.895142 0.445781i \(-0.147074\pi\)
0.895142 + 0.445781i \(0.147074\pi\)
\(72\) −11.9063 −1.40317
\(73\) 9.95574 1.16523 0.582616 0.812748i \(-0.302029\pi\)
0.582616 + 0.812748i \(0.302029\pi\)
\(74\) −17.5162 −2.03621
\(75\) 0.317043 0.0366089
\(76\) −30.1905 −3.46308
\(77\) 1.61421 0.183957
\(78\) 5.69516 0.644850
\(79\) −6.85303 −0.771027 −0.385513 0.922702i \(-0.625976\pi\)
−0.385513 + 0.922702i \(0.625976\pi\)
\(80\) −9.49190 −1.06123
\(81\) −10.5089 −1.16765
\(82\) −3.47147 −0.383360
\(83\) −5.19063 −0.569745 −0.284873 0.958565i \(-0.591951\pi\)
−0.284873 + 0.958565i \(0.591951\pi\)
\(84\) 8.35210 0.911289
\(85\) 6.52968 0.708243
\(86\) −10.4943 −1.13163
\(87\) −23.2221 −2.48967
\(88\) 9.14055 0.974385
\(89\) 9.77411 1.03605 0.518027 0.855365i \(-0.326667\pi\)
0.518027 + 0.855365i \(0.326667\pi\)
\(90\) 12.8061 1.34988
\(91\) −0.890619 −0.0933622
\(92\) −34.6209 −3.60947
\(93\) 17.9606 1.86242
\(94\) −21.5116 −2.21876
\(95\) 16.4376 1.68646
\(96\) 1.15999 0.118391
\(97\) 1.22167 0.124041 0.0620206 0.998075i \(-0.480246\pi\)
0.0620206 + 0.998075i \(0.480246\pi\)
\(98\) 15.2671 1.54221
\(99\) −4.27901 −0.430057
\(100\) −0.554607 −0.0554607
\(101\) 17.0169 1.69325 0.846625 0.532190i \(-0.178631\pi\)
0.846625 + 0.532190i \(0.178631\pi\)
\(102\) −16.8633 −1.66972
\(103\) −12.2122 −1.20331 −0.601653 0.798758i \(-0.705491\pi\)
−0.601653 + 0.798758i \(0.705491\pi\)
\(104\) −5.04316 −0.494523
\(105\) −4.54742 −0.443783
\(106\) −6.55568 −0.636744
\(107\) −6.94824 −0.671712 −0.335856 0.941913i \(-0.609025\pi\)
−0.335856 + 0.941913i \(0.609025\pi\)
\(108\) 5.99358 0.576732
\(109\) −3.21713 −0.308145 −0.154073 0.988060i \(-0.549239\pi\)
−0.154073 + 0.988060i \(0.549239\pi\)
\(110\) −9.83134 −0.937381
\(111\) −16.4880 −1.56498
\(112\) −3.83345 −0.362227
\(113\) −10.1700 −0.956714 −0.478357 0.878165i \(-0.658768\pi\)
−0.478357 + 0.878165i \(0.658768\pi\)
\(114\) −42.4512 −3.97592
\(115\) 18.8498 1.75776
\(116\) 40.6228 3.77173
\(117\) 2.36088 0.218263
\(118\) 10.3933 0.956781
\(119\) 2.63711 0.241744
\(120\) −25.7499 −2.35064
\(121\) −7.71498 −0.701361
\(122\) 37.2741 3.37464
\(123\) −3.26771 −0.294639
\(124\) −31.4187 −2.82148
\(125\) 11.3281 1.01322
\(126\) 5.17195 0.460754
\(127\) −3.24902 −0.288304 −0.144152 0.989556i \(-0.546045\pi\)
−0.144152 + 0.989556i \(0.546045\pi\)
\(128\) 19.1455 1.69224
\(129\) −9.87837 −0.869742
\(130\) 5.42429 0.475742
\(131\) 0.584395 0.0510588 0.0255294 0.999674i \(-0.491873\pi\)
0.0255294 + 0.999674i \(0.491873\pi\)
\(132\) 16.9970 1.47940
\(133\) 6.63859 0.575639
\(134\) 31.3851 2.71126
\(135\) −3.26329 −0.280859
\(136\) 14.9327 1.28047
\(137\) 18.6969 1.59739 0.798693 0.601739i \(-0.205525\pi\)
0.798693 + 0.601739i \(0.205525\pi\)
\(138\) −48.6808 −4.14399
\(139\) 10.6147 0.900330 0.450165 0.892945i \(-0.351365\pi\)
0.450165 + 0.892945i \(0.351365\pi\)
\(140\) 7.95487 0.672309
\(141\) −20.2490 −1.70527
\(142\) −37.1056 −3.11383
\(143\) −1.81246 −0.151566
\(144\) 10.1618 0.846819
\(145\) −22.1177 −1.83677
\(146\) −24.4885 −2.02668
\(147\) 14.3710 1.18530
\(148\) 28.8428 2.37086
\(149\) 7.38236 0.604787 0.302393 0.953183i \(-0.402214\pi\)
0.302393 + 0.953183i \(0.402214\pi\)
\(150\) −0.779841 −0.0636737
\(151\) −2.15205 −0.175131 −0.0875655 0.996159i \(-0.527909\pi\)
−0.0875655 + 0.996159i \(0.527909\pi\)
\(152\) 37.5912 3.04905
\(153\) −6.99054 −0.565152
\(154\) −3.97054 −0.319955
\(155\) 17.1063 1.37401
\(156\) −9.37786 −0.750830
\(157\) 15.1555 1.20954 0.604771 0.796399i \(-0.293264\pi\)
0.604771 + 0.796399i \(0.293264\pi\)
\(158\) 16.8566 1.34104
\(159\) −6.17089 −0.489383
\(160\) 1.10482 0.0873436
\(161\) 7.61279 0.599972
\(162\) 25.8491 2.03089
\(163\) 17.5376 1.37365 0.686824 0.726824i \(-0.259004\pi\)
0.686824 + 0.726824i \(0.259004\pi\)
\(164\) 5.71625 0.446364
\(165\) −9.25428 −0.720445
\(166\) 12.7676 0.990955
\(167\) −11.8794 −0.919254 −0.459627 0.888112i \(-0.652017\pi\)
−0.459627 + 0.888112i \(0.652017\pi\)
\(168\) −10.3995 −0.802340
\(169\) 1.00000 0.0769231
\(170\) −16.0613 −1.23184
\(171\) −17.5978 −1.34574
\(172\) 17.2804 1.31762
\(173\) 5.65748 0.430130 0.215065 0.976600i \(-0.431004\pi\)
0.215065 + 0.976600i \(0.431004\pi\)
\(174\) 57.1202 4.33027
\(175\) 0.121953 0.00921877
\(176\) −7.80131 −0.588046
\(177\) 9.78326 0.735355
\(178\) −24.0417 −1.80200
\(179\) −18.0100 −1.34613 −0.673065 0.739583i \(-0.735023\pi\)
−0.673065 + 0.739583i \(0.735023\pi\)
\(180\) −21.0870 −1.57173
\(181\) −9.24275 −0.687008 −0.343504 0.939151i \(-0.611614\pi\)
−0.343504 + 0.939151i \(0.611614\pi\)
\(182\) 2.19069 0.162384
\(183\) 35.0863 2.59365
\(184\) 43.1077 3.17794
\(185\) −15.7039 −1.15457
\(186\) −44.1782 −3.23930
\(187\) 5.36668 0.392451
\(188\) 35.4219 2.58340
\(189\) −1.31793 −0.0958652
\(190\) −40.4322 −2.93326
\(191\) 7.75719 0.561291 0.280645 0.959812i \(-0.409451\pi\)
0.280645 + 0.959812i \(0.409451\pi\)
\(192\) 17.0785 1.23254
\(193\) 2.77310 0.199612 0.0998060 0.995007i \(-0.468178\pi\)
0.0998060 + 0.995007i \(0.468178\pi\)
\(194\) −3.00497 −0.215744
\(195\) 5.10591 0.365642
\(196\) −25.1393 −1.79567
\(197\) 26.4317 1.88318 0.941590 0.336762i \(-0.109332\pi\)
0.941590 + 0.336762i \(0.109332\pi\)
\(198\) 10.5252 0.747995
\(199\) 7.12132 0.504817 0.252409 0.967621i \(-0.418777\pi\)
0.252409 + 0.967621i \(0.418777\pi\)
\(200\) 0.690562 0.0488301
\(201\) 29.5430 2.08380
\(202\) −41.8571 −2.94506
\(203\) −8.93256 −0.626943
\(204\) 27.7677 1.94413
\(205\) −3.11229 −0.217372
\(206\) 30.0388 2.09290
\(207\) −20.1802 −1.40262
\(208\) 4.30426 0.298446
\(209\) 13.5099 0.934501
\(210\) 11.1854 0.771869
\(211\) −8.40753 −0.578798 −0.289399 0.957209i \(-0.593455\pi\)
−0.289399 + 0.957209i \(0.593455\pi\)
\(212\) 10.7948 0.741392
\(213\) −34.9276 −2.39320
\(214\) 17.0908 1.16830
\(215\) −9.40855 −0.641657
\(216\) −7.46282 −0.507781
\(217\) 6.90866 0.468990
\(218\) 7.91329 0.535955
\(219\) −23.0511 −1.55765
\(220\) 16.1886 1.09144
\(221\) −2.96099 −0.199178
\(222\) 40.5562 2.72195
\(223\) 20.2523 1.35619 0.678096 0.734974i \(-0.262805\pi\)
0.678096 + 0.734974i \(0.262805\pi\)
\(224\) 0.446198 0.0298129
\(225\) −0.323276 −0.0215518
\(226\) 25.0155 1.66401
\(227\) 15.2853 1.01452 0.507261 0.861792i \(-0.330658\pi\)
0.507261 + 0.861792i \(0.330658\pi\)
\(228\) 69.9017 4.62935
\(229\) −8.46059 −0.559092 −0.279546 0.960132i \(-0.590184\pi\)
−0.279546 + 0.960132i \(0.590184\pi\)
\(230\) −46.3655 −3.05725
\(231\) −3.73748 −0.245908
\(232\) −50.5809 −3.32080
\(233\) −10.9903 −0.719997 −0.359999 0.932953i \(-0.617223\pi\)
−0.359999 + 0.932953i \(0.617223\pi\)
\(234\) −5.80714 −0.379624
\(235\) −19.2859 −1.25808
\(236\) −17.1140 −1.11403
\(237\) 15.8672 1.03069
\(238\) −6.48659 −0.420463
\(239\) −28.6596 −1.85383 −0.926917 0.375267i \(-0.877551\pi\)
−0.926917 + 0.375267i \(0.877551\pi\)
\(240\) 21.9771 1.41862
\(241\) 29.7098 1.91378 0.956889 0.290452i \(-0.0938058\pi\)
0.956889 + 0.290452i \(0.0938058\pi\)
\(242\) 18.9768 1.21987
\(243\) 19.8925 1.27610
\(244\) −61.3769 −3.92925
\(245\) 13.6875 0.874460
\(246\) 8.03769 0.512465
\(247\) −7.45390 −0.474281
\(248\) 39.1205 2.48416
\(249\) 12.0182 0.761620
\(250\) −27.8642 −1.76229
\(251\) 13.9902 0.883054 0.441527 0.897248i \(-0.354437\pi\)
0.441527 + 0.897248i \(0.354437\pi\)
\(252\) −8.51632 −0.536478
\(253\) 15.4925 0.974005
\(254\) 7.99173 0.501446
\(255\) −15.1185 −0.946760
\(256\) −32.3403 −2.02127
\(257\) −4.79895 −0.299350 −0.149675 0.988735i \(-0.547823\pi\)
−0.149675 + 0.988735i \(0.547823\pi\)
\(258\) 24.2982 1.51274
\(259\) −6.34225 −0.394088
\(260\) −8.93184 −0.553929
\(261\) 23.6787 1.46567
\(262\) −1.43746 −0.0888063
\(263\) −6.88841 −0.424758 −0.212379 0.977187i \(-0.568121\pi\)
−0.212379 + 0.977187i \(0.568121\pi\)
\(264\) −21.1636 −1.30253
\(265\) −5.87740 −0.361046
\(266\) −16.3292 −1.00120
\(267\) −22.6305 −1.38497
\(268\) −51.6799 −3.15685
\(269\) −2.83799 −0.173036 −0.0865178 0.996250i \(-0.527574\pi\)
−0.0865178 + 0.996250i \(0.527574\pi\)
\(270\) 8.02682 0.488497
\(271\) 14.8386 0.901384 0.450692 0.892680i \(-0.351177\pi\)
0.450692 + 0.892680i \(0.351177\pi\)
\(272\) −12.7448 −0.772770
\(273\) 2.06210 0.124804
\(274\) −45.9894 −2.77832
\(275\) 0.248181 0.0149659
\(276\) 80.1597 4.82505
\(277\) −10.6353 −0.639012 −0.319506 0.947584i \(-0.603517\pi\)
−0.319506 + 0.947584i \(0.603517\pi\)
\(278\) −26.1094 −1.56594
\(279\) −18.3137 −1.09641
\(280\) −9.90490 −0.591931
\(281\) 4.98660 0.297475 0.148738 0.988877i \(-0.452479\pi\)
0.148738 + 0.988877i \(0.452479\pi\)
\(282\) 49.8071 2.96597
\(283\) 6.45551 0.383740 0.191870 0.981420i \(-0.438545\pi\)
0.191870 + 0.981420i \(0.438545\pi\)
\(284\) 61.0994 3.62558
\(285\) −38.0590 −2.25442
\(286\) 4.45818 0.263618
\(287\) −1.25695 −0.0741953
\(288\) −1.18280 −0.0696969
\(289\) −8.23255 −0.484267
\(290\) 54.4035 3.19469
\(291\) −2.82859 −0.165815
\(292\) 40.3236 2.35976
\(293\) 7.30332 0.426664 0.213332 0.976980i \(-0.431568\pi\)
0.213332 + 0.976980i \(0.431568\pi\)
\(294\) −35.3487 −2.06158
\(295\) 9.31796 0.542513
\(296\) −35.9132 −2.08741
\(297\) −2.68207 −0.155629
\(298\) −18.1586 −1.05190
\(299\) −8.54775 −0.494329
\(300\) 1.28411 0.0741384
\(301\) −3.79979 −0.219016
\(302\) 5.29346 0.304604
\(303\) −39.4003 −2.26349
\(304\) −32.0835 −1.84012
\(305\) 33.4175 1.91348
\(306\) 17.1949 0.982965
\(307\) 18.6079 1.06201 0.531005 0.847369i \(-0.321814\pi\)
0.531005 + 0.847369i \(0.321814\pi\)
\(308\) 6.53803 0.372539
\(309\) 28.2756 1.60855
\(310\) −42.0770 −2.38982
\(311\) 11.9235 0.676122 0.338061 0.941124i \(-0.390229\pi\)
0.338061 + 0.941124i \(0.390229\pi\)
\(312\) 11.6767 0.661064
\(313\) 31.3740 1.77336 0.886681 0.462381i \(-0.153005\pi\)
0.886681 + 0.462381i \(0.153005\pi\)
\(314\) −37.2786 −2.10375
\(315\) 4.63683 0.261256
\(316\) −27.7568 −1.56144
\(317\) −21.2251 −1.19212 −0.596059 0.802940i \(-0.703268\pi\)
−0.596059 + 0.802940i \(0.703268\pi\)
\(318\) 15.1787 0.851182
\(319\) −18.1783 −1.01779
\(320\) 16.2662 0.909311
\(321\) 16.0877 0.897926
\(322\) −18.7254 −1.04353
\(323\) 22.0709 1.22806
\(324\) −42.5640 −2.36467
\(325\) −0.136930 −0.00759553
\(326\) −43.1377 −2.38918
\(327\) 7.44881 0.411920
\(328\) −7.11751 −0.392999
\(329\) −7.78892 −0.429417
\(330\) 22.7631 1.25307
\(331\) 8.37205 0.460170 0.230085 0.973171i \(-0.426100\pi\)
0.230085 + 0.973171i \(0.426100\pi\)
\(332\) −21.0235 −1.15382
\(333\) 16.8122 0.921304
\(334\) 29.2201 1.59885
\(335\) 28.1379 1.53734
\(336\) 8.87581 0.484215
\(337\) 15.8145 0.861472 0.430736 0.902478i \(-0.358254\pi\)
0.430736 + 0.902478i \(0.358254\pi\)
\(338\) −2.45973 −0.133792
\(339\) 23.5472 1.27891
\(340\) 26.4471 1.43429
\(341\) 14.0595 0.761367
\(342\) 43.2858 2.34063
\(343\) 11.7622 0.635100
\(344\) −21.5164 −1.16009
\(345\) −43.6441 −2.34972
\(346\) −13.9159 −0.748123
\(347\) 16.8612 0.905156 0.452578 0.891725i \(-0.350504\pi\)
0.452578 + 0.891725i \(0.350504\pi\)
\(348\) −94.0563 −5.04195
\(349\) −4.53306 −0.242649 −0.121325 0.992613i \(-0.538714\pi\)
−0.121325 + 0.992613i \(0.538714\pi\)
\(350\) −0.299971 −0.0160341
\(351\) 1.47979 0.0789853
\(352\) 0.908040 0.0483987
\(353\) −16.4652 −0.876352 −0.438176 0.898889i \(-0.644375\pi\)
−0.438176 + 0.898889i \(0.644375\pi\)
\(354\) −24.0642 −1.27900
\(355\) −33.2664 −1.76560
\(356\) 39.5879 2.09816
\(357\) −6.10586 −0.323156
\(358\) 44.2998 2.34132
\(359\) −27.4609 −1.44933 −0.724666 0.689100i \(-0.758006\pi\)
−0.724666 + 0.689100i \(0.758006\pi\)
\(360\) 26.2562 1.38382
\(361\) 36.5607 1.92425
\(362\) 22.7347 1.19491
\(363\) 17.8629 0.937560
\(364\) −3.60726 −0.189072
\(365\) −21.9548 −1.14917
\(366\) −86.3029 −4.51112
\(367\) 17.8711 0.932866 0.466433 0.884557i \(-0.345539\pi\)
0.466433 + 0.884557i \(0.345539\pi\)
\(368\) −36.7917 −1.91790
\(369\) 3.33196 0.173455
\(370\) 38.6273 2.00814
\(371\) −2.37368 −0.123235
\(372\) 72.7455 3.77168
\(373\) 4.28436 0.221836 0.110918 0.993830i \(-0.464621\pi\)
0.110918 + 0.993830i \(0.464621\pi\)
\(374\) −13.2006 −0.682587
\(375\) −26.2287 −1.35444
\(376\) −44.1051 −2.27454
\(377\) 10.0296 0.516551
\(378\) 3.24175 0.166738
\(379\) 3.97270 0.204064 0.102032 0.994781i \(-0.467466\pi\)
0.102032 + 0.994781i \(0.467466\pi\)
\(380\) 66.5771 3.41533
\(381\) 7.52265 0.385397
\(382\) −19.0806 −0.976250
\(383\) 22.0070 1.12450 0.562252 0.826966i \(-0.309935\pi\)
0.562252 + 0.826966i \(0.309935\pi\)
\(384\) −44.3286 −2.26213
\(385\) −3.55973 −0.181420
\(386\) −6.82108 −0.347184
\(387\) 10.0726 0.512019
\(388\) 4.94810 0.251201
\(389\) −24.4752 −1.24094 −0.620470 0.784230i \(-0.713058\pi\)
−0.620470 + 0.784230i \(0.713058\pi\)
\(390\) −12.5592 −0.635959
\(391\) 25.3098 1.27997
\(392\) 31.3019 1.58098
\(393\) −1.35308 −0.0682540
\(394\) −65.0149 −3.27540
\(395\) 15.1126 0.760396
\(396\) −17.3312 −0.870927
\(397\) −27.6171 −1.38606 −0.693030 0.720909i \(-0.743725\pi\)
−0.693030 + 0.720909i \(0.743725\pi\)
\(398\) −17.5165 −0.878025
\(399\) −15.3707 −0.769498
\(400\) −0.589383 −0.0294692
\(401\) 5.75345 0.287313 0.143657 0.989628i \(-0.454114\pi\)
0.143657 + 0.989628i \(0.454114\pi\)
\(402\) −72.6678 −3.62434
\(403\) −7.75715 −0.386411
\(404\) 68.9235 3.42907
\(405\) 23.1746 1.15155
\(406\) 21.9717 1.09044
\(407\) −12.9069 −0.639769
\(408\) −34.5746 −1.71170
\(409\) 5.05537 0.249972 0.124986 0.992159i \(-0.460111\pi\)
0.124986 + 0.992159i \(0.460111\pi\)
\(410\) 7.65541 0.378074
\(411\) −43.2900 −2.13534
\(412\) −49.4630 −2.43687
\(413\) 3.76320 0.185175
\(414\) 49.6380 2.43957
\(415\) 11.4466 0.561890
\(416\) −0.500998 −0.0245634
\(417\) −24.5769 −1.20354
\(418\) −33.2308 −1.62537
\(419\) 6.58860 0.321874 0.160937 0.986965i \(-0.448548\pi\)
0.160937 + 0.986965i \(0.448548\pi\)
\(420\) −18.4184 −0.898724
\(421\) −10.2150 −0.497848 −0.248924 0.968523i \(-0.580077\pi\)
−0.248924 + 0.968523i \(0.580077\pi\)
\(422\) 20.6803 1.00670
\(423\) 20.6471 1.00390
\(424\) −13.4410 −0.652754
\(425\) 0.405449 0.0196672
\(426\) 85.9127 4.16248
\(427\) 13.4962 0.653126
\(428\) −28.1424 −1.36031
\(429\) 4.19650 0.202609
\(430\) 23.1425 1.11603
\(431\) −17.3046 −0.833531 −0.416765 0.909014i \(-0.636836\pi\)
−0.416765 + 0.909014i \(0.636836\pi\)
\(432\) 6.36939 0.306448
\(433\) 30.5560 1.46843 0.734214 0.678918i \(-0.237551\pi\)
0.734214 + 0.678918i \(0.237551\pi\)
\(434\) −16.9935 −0.815712
\(435\) 51.2103 2.45535
\(436\) −13.0303 −0.624039
\(437\) 63.7141 3.04786
\(438\) 56.6996 2.70921
\(439\) 17.1881 0.820342 0.410171 0.912009i \(-0.365469\pi\)
0.410171 + 0.912009i \(0.365469\pi\)
\(440\) −20.1571 −0.960951
\(441\) −14.6535 −0.697786
\(442\) 7.28324 0.346428
\(443\) 28.0979 1.33497 0.667486 0.744622i \(-0.267370\pi\)
0.667486 + 0.744622i \(0.267370\pi\)
\(444\) −66.7813 −3.16930
\(445\) −21.5542 −1.02177
\(446\) −49.8152 −2.35882
\(447\) −17.0928 −0.808462
\(448\) 6.56937 0.310374
\(449\) −2.46234 −0.116205 −0.0581024 0.998311i \(-0.518505\pi\)
−0.0581024 + 0.998311i \(0.518505\pi\)
\(450\) 0.795173 0.0374848
\(451\) −2.55797 −0.120450
\(452\) −41.1915 −1.93748
\(453\) 4.98276 0.234110
\(454\) −37.5978 −1.76455
\(455\) 1.96403 0.0920749
\(456\) −87.0372 −4.07589
\(457\) 31.5335 1.47507 0.737537 0.675307i \(-0.235989\pi\)
0.737537 + 0.675307i \(0.235989\pi\)
\(458\) 20.8108 0.972425
\(459\) −4.38164 −0.204517
\(460\) 76.3472 3.55971
\(461\) −6.25599 −0.291371 −0.145685 0.989331i \(-0.546539\pi\)
−0.145685 + 0.989331i \(0.546539\pi\)
\(462\) 9.19321 0.427707
\(463\) 2.24515 0.104341 0.0521706 0.998638i \(-0.483386\pi\)
0.0521706 + 0.998638i \(0.483386\pi\)
\(464\) 43.1700 2.00412
\(465\) −39.6073 −1.83674
\(466\) 27.0332 1.25229
\(467\) 27.4655 1.27095 0.635477 0.772120i \(-0.280804\pi\)
0.635477 + 0.772120i \(0.280804\pi\)
\(468\) 9.56225 0.442015
\(469\) 11.3639 0.524737
\(470\) 47.4383 2.18816
\(471\) −35.0905 −1.61688
\(472\) 21.3093 0.980838
\(473\) −7.73280 −0.355554
\(474\) −39.0291 −1.79267
\(475\) 1.02067 0.0468314
\(476\) 10.6811 0.489566
\(477\) 6.29222 0.288101
\(478\) 70.4949 3.22436
\(479\) 21.8531 0.998493 0.499246 0.866460i \(-0.333610\pi\)
0.499246 + 0.866460i \(0.333610\pi\)
\(480\) −2.55805 −0.116759
\(481\) 7.12117 0.324697
\(482\) −73.0783 −3.32862
\(483\) −17.6263 −0.802026
\(484\) −31.2479 −1.42036
\(485\) −2.69406 −0.122331
\(486\) −48.9301 −2.21952
\(487\) 38.2254 1.73216 0.866078 0.499909i \(-0.166633\pi\)
0.866078 + 0.499909i \(0.166633\pi\)
\(488\) 76.4226 3.45949
\(489\) −40.6057 −1.83625
\(490\) −33.6675 −1.52094
\(491\) 4.63653 0.209244 0.104622 0.994512i \(-0.466637\pi\)
0.104622 + 0.994512i \(0.466637\pi\)
\(492\) −13.2352 −0.596687
\(493\) −29.6975 −1.33751
\(494\) 18.3346 0.824913
\(495\) 9.43623 0.424127
\(496\) −33.3887 −1.49920
\(497\) −13.4352 −0.602650
\(498\) −29.5615 −1.32468
\(499\) −40.0348 −1.79220 −0.896101 0.443850i \(-0.853612\pi\)
−0.896101 + 0.443850i \(0.853612\pi\)
\(500\) 45.8823 2.05192
\(501\) 27.5050 1.22883
\(502\) −34.4122 −1.53589
\(503\) −36.6435 −1.63385 −0.816926 0.576743i \(-0.804323\pi\)
−0.816926 + 0.576743i \(0.804323\pi\)
\(504\) 10.6040 0.472339
\(505\) −37.5264 −1.66990
\(506\) −38.1074 −1.69408
\(507\) −2.31536 −0.102829
\(508\) −13.1595 −0.583857
\(509\) 4.76700 0.211294 0.105647 0.994404i \(-0.466309\pi\)
0.105647 + 0.994404i \(0.466309\pi\)
\(510\) 37.1876 1.64669
\(511\) −8.86677 −0.392243
\(512\) 41.2577 1.82335
\(513\) −11.0302 −0.486996
\(514\) 11.8041 0.520658
\(515\) 26.9308 1.18671
\(516\) −40.0102 −1.76135
\(517\) −15.8509 −0.697123
\(518\) 15.6002 0.685435
\(519\) −13.0991 −0.574986
\(520\) 11.1214 0.487704
\(521\) −21.6942 −0.950441 −0.475221 0.879867i \(-0.657632\pi\)
−0.475221 + 0.879867i \(0.657632\pi\)
\(522\) −58.2433 −2.54924
\(523\) 0.412057 0.0180180 0.00900900 0.999959i \(-0.497132\pi\)
0.00900900 + 0.999959i \(0.497132\pi\)
\(524\) 2.36697 0.103401
\(525\) −0.282364 −0.0123234
\(526\) 16.9437 0.738778
\(527\) 22.9688 1.00054
\(528\) 18.0628 0.786083
\(529\) 50.0641 2.17670
\(530\) 14.4568 0.627965
\(531\) −9.97561 −0.432905
\(532\) 26.8882 1.16575
\(533\) 1.41132 0.0611310
\(534\) 55.6651 2.40887
\(535\) 15.3225 0.662450
\(536\) 64.3486 2.77943
\(537\) 41.6996 1.79947
\(538\) 6.98071 0.300960
\(539\) 11.2496 0.484554
\(540\) −13.2173 −0.568780
\(541\) −40.5964 −1.74538 −0.872688 0.488278i \(-0.837625\pi\)
−0.872688 + 0.488278i \(0.837625\pi\)
\(542\) −36.4991 −1.56777
\(543\) 21.4003 0.918374
\(544\) 1.48345 0.0636023
\(545\) 7.09454 0.303897
\(546\) −5.07222 −0.217071
\(547\) −32.2489 −1.37886 −0.689432 0.724351i \(-0.742140\pi\)
−0.689432 + 0.724351i \(0.742140\pi\)
\(548\) 75.7279 3.23493
\(549\) −35.7761 −1.52689
\(550\) −0.610460 −0.0260301
\(551\) −74.7597 −3.18487
\(552\) −99.8097 −4.24818
\(553\) 6.10344 0.259545
\(554\) 26.1599 1.11143
\(555\) 36.3600 1.54340
\(556\) 42.9927 1.82330
\(557\) 22.9535 0.972572 0.486286 0.873800i \(-0.338351\pi\)
0.486286 + 0.873800i \(0.338351\pi\)
\(558\) 45.0468 1.90698
\(559\) 4.26646 0.180452
\(560\) 8.45367 0.357233
\(561\) −12.4258 −0.524617
\(562\) −12.2657 −0.517397
\(563\) 33.7985 1.42444 0.712218 0.701958i \(-0.247691\pi\)
0.712218 + 0.701958i \(0.247691\pi\)
\(564\) −82.0143 −3.45342
\(565\) 22.4273 0.943523
\(566\) −15.8788 −0.667437
\(567\) 9.35941 0.393058
\(568\) −76.0771 −3.19212
\(569\) 33.4822 1.40365 0.701824 0.712350i \(-0.252369\pi\)
0.701824 + 0.712350i \(0.252369\pi\)
\(570\) 93.6149 3.92110
\(571\) −20.0288 −0.838178 −0.419089 0.907945i \(-0.637651\pi\)
−0.419089 + 0.907945i \(0.637651\pi\)
\(572\) −7.34100 −0.306943
\(573\) −17.9607 −0.750318
\(574\) 3.09176 0.129047
\(575\) 1.17045 0.0488110
\(576\) −17.4143 −0.725596
\(577\) 4.19287 0.174551 0.0872757 0.996184i \(-0.472184\pi\)
0.0872757 + 0.996184i \(0.472184\pi\)
\(578\) 20.2499 0.842284
\(579\) −6.42072 −0.266836
\(580\) −89.5829 −3.71973
\(581\) 4.62287 0.191789
\(582\) 6.95758 0.288401
\(583\) −4.83058 −0.200062
\(584\) −50.2084 −2.07764
\(585\) −5.20630 −0.215254
\(586\) −17.9642 −0.742095
\(587\) −16.1367 −0.666034 −0.333017 0.942921i \(-0.608067\pi\)
−0.333017 + 0.942921i \(0.608067\pi\)
\(588\) 58.2065 2.40040
\(589\) 57.8210 2.38247
\(590\) −22.9197 −0.943589
\(591\) −61.1988 −2.51738
\(592\) 30.6513 1.25976
\(593\) 6.91404 0.283926 0.141963 0.989872i \(-0.454659\pi\)
0.141963 + 0.989872i \(0.454659\pi\)
\(594\) 6.59717 0.270685
\(595\) −5.81546 −0.238411
\(596\) 29.9007 1.22478
\(597\) −16.4884 −0.674825
\(598\) 21.0252 0.859784
\(599\) −25.3985 −1.03776 −0.518878 0.854849i \(-0.673650\pi\)
−0.518878 + 0.854849i \(0.673650\pi\)
\(600\) −1.59890 −0.0652747
\(601\) −40.6374 −1.65763 −0.828816 0.559521i \(-0.810985\pi\)
−0.828816 + 0.559521i \(0.810985\pi\)
\(602\) 9.34646 0.380933
\(603\) −30.1238 −1.22674
\(604\) −8.71640 −0.354665
\(605\) 17.0133 0.691691
\(606\) 96.9143 3.93687
\(607\) −13.3117 −0.540304 −0.270152 0.962818i \(-0.587074\pi\)
−0.270152 + 0.962818i \(0.587074\pi\)
\(608\) 3.73439 0.151449
\(609\) 20.6821 0.838080
\(610\) −82.1982 −3.32811
\(611\) 8.74552 0.353806
\(612\) −28.3137 −1.14451
\(613\) −19.2654 −0.778121 −0.389061 0.921212i \(-0.627200\pi\)
−0.389061 + 0.921212i \(0.627200\pi\)
\(614\) −45.7705 −1.84715
\(615\) 7.20607 0.290577
\(616\) −8.14074 −0.328000
\(617\) 1.00000 0.0402585
\(618\) −69.5506 −2.79773
\(619\) −24.7192 −0.993548 −0.496774 0.867880i \(-0.665482\pi\)
−0.496774 + 0.867880i \(0.665482\pi\)
\(620\) 69.2856 2.78258
\(621\) −12.6489 −0.507582
\(622\) −29.3287 −1.17597
\(623\) −8.70500 −0.348759
\(624\) −9.96589 −0.398955
\(625\) −24.2966 −0.971864
\(626\) −77.1716 −3.08440
\(627\) −31.2803 −1.24922
\(628\) 61.3843 2.44950
\(629\) −21.0857 −0.840742
\(630\) −11.4054 −0.454401
\(631\) −2.30893 −0.0919172 −0.0459586 0.998943i \(-0.514634\pi\)
−0.0459586 + 0.998943i \(0.514634\pi\)
\(632\) 34.5610 1.37476
\(633\) 19.4664 0.773722
\(634\) 52.2080 2.07345
\(635\) 7.16487 0.284329
\(636\) −24.9939 −0.991072
\(637\) −6.20680 −0.245922
\(638\) 44.7138 1.77023
\(639\) 35.6144 1.40888
\(640\) −42.2203 −1.66890
\(641\) 3.14795 0.124337 0.0621683 0.998066i \(-0.480198\pi\)
0.0621683 + 0.998066i \(0.480198\pi\)
\(642\) −39.5713 −1.56176
\(643\) 29.8323 1.17647 0.588236 0.808689i \(-0.299823\pi\)
0.588236 + 0.808689i \(0.299823\pi\)
\(644\) 30.8340 1.21503
\(645\) 21.7841 0.857750
\(646\) −54.2886 −2.13596
\(647\) −19.8551 −0.780583 −0.390292 0.920691i \(-0.627626\pi\)
−0.390292 + 0.920691i \(0.627626\pi\)
\(648\) 52.9980 2.08196
\(649\) 7.65834 0.300616
\(650\) 0.336812 0.0132109
\(651\) −15.9960 −0.626933
\(652\) 71.0322 2.78184
\(653\) −41.3645 −1.61872 −0.809360 0.587313i \(-0.800186\pi\)
−0.809360 + 0.587313i \(0.800186\pi\)
\(654\) −18.3221 −0.716450
\(655\) −1.28873 −0.0503548
\(656\) 6.07468 0.237176
\(657\) 23.5043 0.916991
\(658\) 19.1587 0.746883
\(659\) −32.9092 −1.28196 −0.640980 0.767558i \(-0.721472\pi\)
−0.640980 + 0.767558i \(0.721472\pi\)
\(660\) −37.4825 −1.45900
\(661\) 0.619072 0.0240791 0.0120395 0.999928i \(-0.496168\pi\)
0.0120395 + 0.999928i \(0.496168\pi\)
\(662\) −20.5930 −0.800370
\(663\) 6.85575 0.266255
\(664\) 26.1772 1.01587
\(665\) −14.6397 −0.567702
\(666\) −41.3536 −1.60242
\(667\) −85.7306 −3.31950
\(668\) −48.1149 −1.86162
\(669\) −46.8912 −1.81292
\(670\) −69.2117 −2.67388
\(671\) 27.4656 1.06030
\(672\) −1.03311 −0.0398530
\(673\) −41.2780 −1.59115 −0.795575 0.605855i \(-0.792831\pi\)
−0.795575 + 0.605855i \(0.792831\pi\)
\(674\) −38.8995 −1.49835
\(675\) −0.202628 −0.00779916
\(676\) 4.05029 0.155780
\(677\) −19.0264 −0.731244 −0.365622 0.930763i \(-0.619144\pi\)
−0.365622 + 0.930763i \(0.619144\pi\)
\(678\) −57.9199 −2.22440
\(679\) −1.08804 −0.0417551
\(680\) −32.9302 −1.26282
\(681\) −35.3910 −1.35619
\(682\) −34.5827 −1.32424
\(683\) −15.9486 −0.610255 −0.305128 0.952311i \(-0.598699\pi\)
−0.305128 + 0.952311i \(0.598699\pi\)
\(684\) −71.2761 −2.72531
\(685\) −41.2311 −1.57536
\(686\) −28.9319 −1.10463
\(687\) 19.5893 0.747378
\(688\) 18.3639 0.700118
\(689\) 2.66520 0.101536
\(690\) 107.353 4.08685
\(691\) 2.57120 0.0978132 0.0489066 0.998803i \(-0.484426\pi\)
0.0489066 + 0.998803i \(0.484426\pi\)
\(692\) 22.9144 0.871075
\(693\) 3.81097 0.144767
\(694\) −41.4740 −1.57433
\(695\) −23.4080 −0.887916
\(696\) 117.113 4.43915
\(697\) −4.17890 −0.158287
\(698\) 11.1501 0.422038
\(699\) 25.4464 0.962472
\(700\) 0.493944 0.0186693
\(701\) −1.16647 −0.0440569 −0.0220285 0.999757i \(-0.507012\pi\)
−0.0220285 + 0.999757i \(0.507012\pi\)
\(702\) −3.63989 −0.137379
\(703\) −53.0805 −2.00197
\(704\) 13.3691 0.503866
\(705\) 44.6538 1.68176
\(706\) 40.4999 1.52423
\(707\) −15.1556 −0.569986
\(708\) 39.6250 1.48920
\(709\) 23.0279 0.864831 0.432416 0.901674i \(-0.357661\pi\)
0.432416 + 0.901674i \(0.357661\pi\)
\(710\) 81.8266 3.07090
\(711\) −16.1792 −0.606767
\(712\) −49.2924 −1.84731
\(713\) 66.3062 2.48319
\(714\) 15.0188 0.562064
\(715\) 3.99691 0.149476
\(716\) −72.9457 −2.72611
\(717\) 66.3571 2.47815
\(718\) 67.5466 2.52082
\(719\) 51.4729 1.91962 0.959808 0.280657i \(-0.0905522\pi\)
0.959808 + 0.280657i \(0.0905522\pi\)
\(720\) −22.4092 −0.835143
\(721\) 10.8764 0.405059
\(722\) −89.9295 −3.34683
\(723\) −68.7889 −2.55829
\(724\) −37.4358 −1.39129
\(725\) −1.37336 −0.0510052
\(726\) −43.9380 −1.63069
\(727\) 10.8698 0.403138 0.201569 0.979474i \(-0.435396\pi\)
0.201569 + 0.979474i \(0.435396\pi\)
\(728\) 4.49153 0.166467
\(729\) −14.5315 −0.538203
\(730\) 54.0029 1.99874
\(731\) −12.6329 −0.467246
\(732\) 142.109 5.25252
\(733\) 6.00526 0.221809 0.110905 0.993831i \(-0.464625\pi\)
0.110905 + 0.993831i \(0.464625\pi\)
\(734\) −43.9582 −1.62253
\(735\) −31.6914 −1.16895
\(736\) 4.28241 0.157852
\(737\) 23.1263 0.851867
\(738\) −8.19573 −0.301689
\(739\) −18.0170 −0.662767 −0.331383 0.943496i \(-0.607515\pi\)
−0.331383 + 0.943496i \(0.607515\pi\)
\(740\) −63.6051 −2.33817
\(741\) 17.2585 0.634005
\(742\) 5.83861 0.214342
\(743\) −41.0540 −1.50613 −0.753063 0.657948i \(-0.771425\pi\)
−0.753063 + 0.657948i \(0.771425\pi\)
\(744\) −90.5780 −3.32075
\(745\) −16.2799 −0.596448
\(746\) −10.5384 −0.385838
\(747\) −12.2544 −0.448367
\(748\) 21.7366 0.794769
\(749\) 6.18823 0.226113
\(750\) 64.5156 2.35578
\(751\) 31.7225 1.15757 0.578784 0.815481i \(-0.303527\pi\)
0.578784 + 0.815481i \(0.303527\pi\)
\(752\) 37.6429 1.37270
\(753\) −32.3923 −1.18044
\(754\) −24.6702 −0.898434
\(755\) 4.74577 0.172716
\(756\) −5.33799 −0.194141
\(757\) 31.7079 1.15244 0.576221 0.817294i \(-0.304527\pi\)
0.576221 + 0.817294i \(0.304527\pi\)
\(758\) −9.77177 −0.354927
\(759\) −35.8707 −1.30202
\(760\) −82.8976 −3.00701
\(761\) −31.1860 −1.13049 −0.565246 0.824923i \(-0.691219\pi\)
−0.565246 + 0.824923i \(0.691219\pi\)
\(762\) −18.5037 −0.670319
\(763\) 2.86524 0.103729
\(764\) 31.4189 1.13669
\(765\) 15.4158 0.557359
\(766\) −54.1313 −1.95584
\(767\) −4.22538 −0.152570
\(768\) 74.8794 2.70198
\(769\) 32.8316 1.18394 0.591969 0.805960i \(-0.298351\pi\)
0.591969 + 0.805960i \(0.298351\pi\)
\(770\) 8.75598 0.315543
\(771\) 11.1113 0.400163
\(772\) 11.2318 0.404243
\(773\) 15.3649 0.552636 0.276318 0.961066i \(-0.410886\pi\)
0.276318 + 0.961066i \(0.410886\pi\)
\(774\) −24.7759 −0.890551
\(775\) 1.06219 0.0381550
\(776\) −6.16105 −0.221169
\(777\) 14.6846 0.526806
\(778\) 60.2024 2.15836
\(779\) −10.5198 −0.376912
\(780\) 20.6804 0.740478
\(781\) −27.3414 −0.978352
\(782\) −62.2554 −2.22625
\(783\) 14.8417 0.530399
\(784\) −26.7156 −0.954130
\(785\) −33.4215 −1.19287
\(786\) 3.32822 0.118714
\(787\) 12.8898 0.459472 0.229736 0.973253i \(-0.426214\pi\)
0.229736 + 0.973253i \(0.426214\pi\)
\(788\) 107.056 3.81371
\(789\) 15.9491 0.567804
\(790\) −37.1729 −1.32255
\(791\) 9.05761 0.322051
\(792\) 21.5797 0.766803
\(793\) −15.1537 −0.538124
\(794\) 67.9306 2.41077
\(795\) 13.6083 0.482636
\(796\) 28.8434 1.02233
\(797\) 12.2711 0.434665 0.217333 0.976098i \(-0.430264\pi\)
0.217333 + 0.976098i \(0.430264\pi\)
\(798\) 37.8078 1.33838
\(799\) −25.8954 −0.916113
\(800\) 0.0686018 0.00242544
\(801\) 23.0755 0.815333
\(802\) −14.1519 −0.499723
\(803\) −18.0444 −0.636774
\(804\) 119.658 4.21999
\(805\) −16.7880 −0.591700
\(806\) 19.0805 0.672082
\(807\) 6.57097 0.231309
\(808\) −85.8192 −3.01911
\(809\) −36.3989 −1.27972 −0.639858 0.768493i \(-0.721007\pi\)
−0.639858 + 0.768493i \(0.721007\pi\)
\(810\) −57.0033 −2.00289
\(811\) 14.2993 0.502117 0.251059 0.967972i \(-0.419221\pi\)
0.251059 + 0.967972i \(0.419221\pi\)
\(812\) −36.1794 −1.26965
\(813\) −34.3568 −1.20494
\(814\) 31.7474 1.11275
\(815\) −38.6745 −1.35471
\(816\) 29.5089 1.03302
\(817\) −31.8018 −1.11260
\(818\) −12.4349 −0.434775
\(819\) −2.10265 −0.0734724
\(820\) −12.6057 −0.440210
\(821\) −2.40556 −0.0839547 −0.0419773 0.999119i \(-0.513366\pi\)
−0.0419773 + 0.999119i \(0.513366\pi\)
\(822\) 106.482 3.71398
\(823\) −3.90643 −0.136170 −0.0680849 0.997680i \(-0.521689\pi\)
−0.0680849 + 0.997680i \(0.521689\pi\)
\(824\) 61.5882 2.14553
\(825\) −0.574629 −0.0200060
\(826\) −9.25647 −0.322074
\(827\) −9.73334 −0.338461 −0.169231 0.985576i \(-0.554128\pi\)
−0.169231 + 0.985576i \(0.554128\pi\)
\(828\) −81.7357 −2.84051
\(829\) −35.7167 −1.24049 −0.620246 0.784407i \(-0.712967\pi\)
−0.620246 + 0.784407i \(0.712967\pi\)
\(830\) −28.1555 −0.977291
\(831\) 24.6245 0.854213
\(832\) −7.37619 −0.255723
\(833\) 18.3783 0.636769
\(834\) 60.4526 2.09330
\(835\) 26.1969 0.906580
\(836\) 54.7191 1.89250
\(837\) −11.4789 −0.396770
\(838\) −16.2062 −0.559834
\(839\) −17.3033 −0.597377 −0.298688 0.954351i \(-0.596549\pi\)
−0.298688 + 0.954351i \(0.596549\pi\)
\(840\) 22.9334 0.791277
\(841\) 71.5930 2.46872
\(842\) 25.1261 0.865904
\(843\) −11.5458 −0.397657
\(844\) −34.0529 −1.17215
\(845\) −2.20524 −0.0758625
\(846\) −50.7864 −1.74607
\(847\) 6.87110 0.236094
\(848\) 11.4717 0.393940
\(849\) −14.9468 −0.512973
\(850\) −0.997297 −0.0342070
\(851\) −60.8700 −2.08660
\(852\) −141.467 −4.84658
\(853\) 41.2758 1.41326 0.706628 0.707585i \(-0.250215\pi\)
0.706628 + 0.707585i \(0.250215\pi\)
\(854\) −33.1970 −1.13598
\(855\) 38.8073 1.32718
\(856\) 35.0411 1.19768
\(857\) −6.77866 −0.231554 −0.115777 0.993275i \(-0.536936\pi\)
−0.115777 + 0.993275i \(0.536936\pi\)
\(858\) −10.3223 −0.352397
\(859\) 10.1715 0.347049 0.173524 0.984830i \(-0.444484\pi\)
0.173524 + 0.984830i \(0.444484\pi\)
\(860\) −38.1073 −1.29945
\(861\) 2.91028 0.0991822
\(862\) 42.5646 1.44976
\(863\) 4.42072 0.150483 0.0752415 0.997165i \(-0.476027\pi\)
0.0752415 + 0.997165i \(0.476027\pi\)
\(864\) −0.741372 −0.0252220
\(865\) −12.4761 −0.424199
\(866\) −75.1596 −2.55403
\(867\) 19.0613 0.647355
\(868\) 27.9821 0.949773
\(869\) 12.4209 0.421349
\(870\) −125.964 −4.27057
\(871\) −12.7596 −0.432341
\(872\) 16.2245 0.549431
\(873\) 2.88421 0.0976156
\(874\) −156.720 −5.30113
\(875\) −10.0891 −0.341073
\(876\) −93.3636 −3.15446
\(877\) −49.1833 −1.66080 −0.830400 0.557167i \(-0.811888\pi\)
−0.830400 + 0.557167i \(0.811888\pi\)
\(878\) −42.2781 −1.42682
\(879\) −16.9098 −0.570353
\(880\) 17.2037 0.579938
\(881\) 18.1714 0.612209 0.306104 0.951998i \(-0.400974\pi\)
0.306104 + 0.951998i \(0.400974\pi\)
\(882\) 36.0437 1.21366
\(883\) −47.9800 −1.61466 −0.807328 0.590103i \(-0.799087\pi\)
−0.807328 + 0.590103i \(0.799087\pi\)
\(884\) −11.9929 −0.403363
\(885\) −21.5744 −0.725216
\(886\) −69.1134 −2.32191
\(887\) 12.8607 0.431820 0.215910 0.976413i \(-0.430728\pi\)
0.215910 + 0.976413i \(0.430728\pi\)
\(888\) 83.1519 2.79039
\(889\) 2.89364 0.0970496
\(890\) 53.0176 1.77715
\(891\) 19.0470 0.638098
\(892\) 82.0275 2.74648
\(893\) −65.1883 −2.18144
\(894\) 42.0437 1.40615
\(895\) 39.7163 1.32757
\(896\) −17.0513 −0.569644
\(897\) 19.7911 0.660806
\(898\) 6.05669 0.202114
\(899\) −77.8011 −2.59481
\(900\) −1.30936 −0.0436454
\(901\) −7.89163 −0.262908
\(902\) 6.29191 0.209498
\(903\) 8.79786 0.292775
\(904\) 51.2890 1.70585
\(905\) 20.3825 0.677536
\(906\) −12.2562 −0.407187
\(907\) 14.9157 0.495267 0.247633 0.968854i \(-0.420347\pi\)
0.247633 + 0.968854i \(0.420347\pi\)
\(908\) 61.9099 2.05455
\(909\) 40.1750 1.33252
\(910\) −4.83098 −0.160145
\(911\) 3.64159 0.120651 0.0603257 0.998179i \(-0.480786\pi\)
0.0603257 + 0.998179i \(0.480786\pi\)
\(912\) 74.2848 2.45982
\(913\) 9.40782 0.311353
\(914\) −77.5639 −2.56559
\(915\) −77.3735 −2.55789
\(916\) −34.2678 −1.13224
\(917\) −0.520473 −0.0171875
\(918\) 10.7777 0.355716
\(919\) −53.4146 −1.76199 −0.880993 0.473130i \(-0.843124\pi\)
−0.880993 + 0.473130i \(0.843124\pi\)
\(920\) −95.0627 −3.13412
\(921\) −43.0840 −1.41967
\(922\) 15.3881 0.506779
\(923\) 15.0852 0.496535
\(924\) −15.1379 −0.498000
\(925\) −0.975104 −0.0320612
\(926\) −5.52248 −0.181480
\(927\) −28.8316 −0.946953
\(928\) −5.02481 −0.164947
\(929\) 7.09091 0.232645 0.116323 0.993211i \(-0.462889\pi\)
0.116323 + 0.993211i \(0.462889\pi\)
\(930\) 97.4234 3.19464
\(931\) 46.2649 1.51627
\(932\) −44.5138 −1.45810
\(933\) −27.6073 −0.903821
\(934\) −67.5579 −2.21056
\(935\) −11.8348 −0.387040
\(936\) −11.9063 −0.389170
\(937\) −20.9720 −0.685124 −0.342562 0.939495i \(-0.611295\pi\)
−0.342562 + 0.939495i \(0.611295\pi\)
\(938\) −27.9522 −0.912672
\(939\) −72.6420 −2.37058
\(940\) −78.1136 −2.54778
\(941\) −6.76739 −0.220611 −0.110305 0.993898i \(-0.535183\pi\)
−0.110305 + 0.993898i \(0.535183\pi\)
\(942\) 86.3132 2.81224
\(943\) −12.0636 −0.392845
\(944\) −18.1871 −0.591940
\(945\) 2.90635 0.0945434
\(946\) 19.0206 0.618414
\(947\) 33.1589 1.07752 0.538760 0.842459i \(-0.318893\pi\)
0.538760 + 0.842459i \(0.318893\pi\)
\(948\) 64.2668 2.08729
\(949\) 9.95574 0.323177
\(950\) −2.51057 −0.0814535
\(951\) 49.1436 1.59359
\(952\) −13.2994 −0.431035
\(953\) −10.8799 −0.352434 −0.176217 0.984351i \(-0.556386\pi\)
−0.176217 + 0.984351i \(0.556386\pi\)
\(954\) −15.4772 −0.501092
\(955\) −17.1065 −0.553552
\(956\) −116.079 −3.75428
\(957\) 42.0893 1.36055
\(958\) −53.7527 −1.73667
\(959\) −16.6518 −0.537716
\(960\) −37.6622 −1.21554
\(961\) 29.1733 0.941074
\(962\) −17.5162 −0.564744
\(963\) −16.4040 −0.528610
\(964\) 120.333 3.87568
\(965\) −6.11534 −0.196860
\(966\) 43.3561 1.39496
\(967\) −37.2375 −1.19748 −0.598738 0.800945i \(-0.704331\pi\)
−0.598738 + 0.800945i \(0.704331\pi\)
\(968\) 38.9079 1.25055
\(969\) −51.1021 −1.64164
\(970\) 6.62667 0.212770
\(971\) 54.8554 1.76039 0.880197 0.474609i \(-0.157411\pi\)
0.880197 + 0.474609i \(0.157411\pi\)
\(972\) 80.5702 2.58429
\(973\) −9.45368 −0.303071
\(974\) −94.0242 −3.01273
\(975\) 0.317043 0.0101535
\(976\) −65.2255 −2.08782
\(977\) 14.8009 0.473523 0.236762 0.971568i \(-0.423914\pi\)
0.236762 + 0.971568i \(0.423914\pi\)
\(978\) 99.8793 3.19379
\(979\) −17.7152 −0.566181
\(980\) 55.4381 1.77091
\(981\) −7.59526 −0.242498
\(982\) −11.4046 −0.363936
\(983\) −18.8218 −0.600322 −0.300161 0.953889i \(-0.597040\pi\)
−0.300161 + 0.953889i \(0.597040\pi\)
\(984\) 16.4796 0.525350
\(985\) −58.2881 −1.85721
\(986\) 73.0480 2.32632
\(987\) 18.0341 0.574033
\(988\) −30.1905 −0.960486
\(989\) −36.4686 −1.15963
\(990\) −23.2106 −0.737682
\(991\) −36.1415 −1.14807 −0.574036 0.818830i \(-0.694623\pi\)
−0.574036 + 0.818830i \(0.694623\pi\)
\(992\) 3.88631 0.123391
\(993\) −19.3843 −0.615142
\(994\) 33.0469 1.04818
\(995\) −15.7042 −0.497857
\(996\) 48.6770 1.54239
\(997\) 27.0461 0.856559 0.428279 0.903646i \(-0.359120\pi\)
0.428279 + 0.903646i \(0.359120\pi\)
\(998\) 98.4748 3.11717
\(999\) 10.5378 0.333402
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 \(a_p\))