Properties

Label 6019.2.a.c.1.9
Level 6019
Weight 2
Character 6019.1
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM No

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.56322 q^{2}\) \(-2.39331 q^{3}\) \(+4.57009 q^{4}\) \(+1.98047 q^{5}\) \(+6.13457 q^{6}\) \(+1.46442 q^{7}\) \(-6.58772 q^{8}\) \(+2.72791 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.56322 q^{2}\) \(-2.39331 q^{3}\) \(+4.57009 q^{4}\) \(+1.98047 q^{5}\) \(+6.13457 q^{6}\) \(+1.46442 q^{7}\) \(-6.58772 q^{8}\) \(+2.72791 q^{9}\) \(-5.07639 q^{10}\) \(-1.05309 q^{11}\) \(-10.9376 q^{12}\) \(-1.00000 q^{13}\) \(-3.75364 q^{14}\) \(-4.73988 q^{15}\) \(+7.74558 q^{16}\) \(-4.51135 q^{17}\) \(-6.99224 q^{18}\) \(-0.322065 q^{19}\) \(+9.05095 q^{20}\) \(-3.50481 q^{21}\) \(+2.69929 q^{22}\) \(-0.436369 q^{23}\) \(+15.7664 q^{24}\) \(-1.07772 q^{25}\) \(+2.56322 q^{26}\) \(+0.651184 q^{27}\) \(+6.69255 q^{28}\) \(+1.24674 q^{29}\) \(+12.1494 q^{30}\) \(-6.86552 q^{31}\) \(-6.67818 q^{32}\) \(+2.52036 q^{33}\) \(+11.5636 q^{34}\) \(+2.90025 q^{35}\) \(+12.4668 q^{36}\) \(+8.21223 q^{37}\) \(+0.825524 q^{38}\) \(+2.39331 q^{39}\) \(-13.0468 q^{40}\) \(-7.30907 q^{41}\) \(+8.98361 q^{42}\) \(+10.9795 q^{43}\) \(-4.81270 q^{44}\) \(+5.40256 q^{45}\) \(+1.11851 q^{46}\) \(+2.66041 q^{47}\) \(-18.5375 q^{48}\) \(-4.85546 q^{49}\) \(+2.76244 q^{50}\) \(+10.7970 q^{51}\) \(-4.57009 q^{52}\) \(+6.07930 q^{53}\) \(-1.66913 q^{54}\) \(-2.08561 q^{55}\) \(-9.64721 q^{56}\) \(+0.770801 q^{57}\) \(-3.19566 q^{58}\) \(+7.73857 q^{59}\) \(-21.6617 q^{60}\) \(+9.88157 q^{61}\) \(+17.5978 q^{62}\) \(+3.99482 q^{63}\) \(+1.62649 q^{64}\) \(-1.98047 q^{65}\) \(-6.46023 q^{66}\) \(+11.0843 q^{67}\) \(-20.6173 q^{68}\) \(+1.04436 q^{69}\) \(-7.43398 q^{70}\) \(-12.4574 q^{71}\) \(-17.9707 q^{72}\) \(-3.30899 q^{73}\) \(-21.0497 q^{74}\) \(+2.57932 q^{75}\) \(-1.47187 q^{76}\) \(-1.54216 q^{77}\) \(-6.13457 q^{78}\) \(-0.210549 q^{79}\) \(+15.3399 q^{80}\) \(-9.74223 q^{81}\) \(+18.7348 q^{82}\) \(-9.57254 q^{83}\) \(-16.0173 q^{84}\) \(-8.93460 q^{85}\) \(-28.1429 q^{86}\) \(-2.98383 q^{87}\) \(+6.93743 q^{88}\) \(+18.4974 q^{89}\) \(-13.8480 q^{90}\) \(-1.46442 q^{91}\) \(-1.99425 q^{92}\) \(+16.4313 q^{93}\) \(-6.81922 q^{94}\) \(-0.637842 q^{95}\) \(+15.9829 q^{96}\) \(-1.36389 q^{97}\) \(+12.4456 q^{98}\) \(-2.87273 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56322 −1.81247 −0.906235 0.422774i \(-0.861056\pi\)
−0.906235 + 0.422774i \(0.861056\pi\)
\(3\) −2.39331 −1.38178 −0.690888 0.722962i \(-0.742780\pi\)
−0.690888 + 0.722962i \(0.742780\pi\)
\(4\) 4.57009 2.28505
\(5\) 1.98047 0.885695 0.442847 0.896597i \(-0.353968\pi\)
0.442847 + 0.896597i \(0.353968\pi\)
\(6\) 6.13457 2.50443
\(7\) 1.46442 0.553500 0.276750 0.960942i \(-0.410743\pi\)
0.276750 + 0.960942i \(0.410743\pi\)
\(8\) −6.58772 −2.32911
\(9\) 2.72791 0.909305
\(10\) −5.07639 −1.60530
\(11\) −1.05309 −0.317517 −0.158759 0.987317i \(-0.550749\pi\)
−0.158759 + 0.987317i \(0.550749\pi\)
\(12\) −10.9376 −3.15742
\(13\) −1.00000 −0.277350
\(14\) −3.75364 −1.00320
\(15\) −4.73988 −1.22383
\(16\) 7.74558 1.93639
\(17\) −4.51135 −1.09416 −0.547081 0.837080i \(-0.684261\pi\)
−0.547081 + 0.837080i \(0.684261\pi\)
\(18\) −6.99224 −1.64809
\(19\) −0.322065 −0.0738868 −0.0369434 0.999317i \(-0.511762\pi\)
−0.0369434 + 0.999317i \(0.511762\pi\)
\(20\) 9.05095 2.02385
\(21\) −3.50481 −0.764813
\(22\) 2.69929 0.575491
\(23\) −0.436369 −0.0909892 −0.0454946 0.998965i \(-0.514486\pi\)
−0.0454946 + 0.998965i \(0.514486\pi\)
\(24\) 15.7664 3.21831
\(25\) −1.07772 −0.215545
\(26\) 2.56322 0.502689
\(27\) 0.651184 0.125320
\(28\) 6.69255 1.26477
\(29\) 1.24674 0.231514 0.115757 0.993278i \(-0.463071\pi\)
0.115757 + 0.993278i \(0.463071\pi\)
\(30\) 12.1494 2.21816
\(31\) −6.86552 −1.23308 −0.616542 0.787322i \(-0.711467\pi\)
−0.616542 + 0.787322i \(0.711467\pi\)
\(32\) −6.67818 −1.18055
\(33\) 2.52036 0.438738
\(34\) 11.5636 1.98314
\(35\) 2.90025 0.490232
\(36\) 12.4668 2.07780
\(37\) 8.21223 1.35008 0.675041 0.737780i \(-0.264126\pi\)
0.675041 + 0.737780i \(0.264126\pi\)
\(38\) 0.825524 0.133918
\(39\) 2.39331 0.383236
\(40\) −13.0468 −2.06288
\(41\) −7.30907 −1.14149 −0.570743 0.821129i \(-0.693345\pi\)
−0.570743 + 0.821129i \(0.693345\pi\)
\(42\) 8.98361 1.38620
\(43\) 10.9795 1.67436 0.837180 0.546928i \(-0.184203\pi\)
0.837180 + 0.546928i \(0.184203\pi\)
\(44\) −4.81270 −0.725542
\(45\) 5.40256 0.805367
\(46\) 1.11851 0.164915
\(47\) 2.66041 0.388061 0.194031 0.980995i \(-0.437844\pi\)
0.194031 + 0.980995i \(0.437844\pi\)
\(48\) −18.5375 −2.67566
\(49\) −4.85546 −0.693638
\(50\) 2.76244 0.390668
\(51\) 10.7970 1.51189
\(52\) −4.57009 −0.633758
\(53\) 6.07930 0.835055 0.417528 0.908664i \(-0.362897\pi\)
0.417528 + 0.908664i \(0.362897\pi\)
\(54\) −1.66913 −0.227140
\(55\) −2.08561 −0.281224
\(56\) −9.64721 −1.28916
\(57\) 0.770801 0.102095
\(58\) −3.19566 −0.419611
\(59\) 7.73857 1.00748 0.503738 0.863856i \(-0.331958\pi\)
0.503738 + 0.863856i \(0.331958\pi\)
\(60\) −21.6617 −2.79651
\(61\) 9.88157 1.26521 0.632603 0.774476i \(-0.281987\pi\)
0.632603 + 0.774476i \(0.281987\pi\)
\(62\) 17.5978 2.23493
\(63\) 3.99482 0.503300
\(64\) 1.62649 0.203311
\(65\) −1.98047 −0.245648
\(66\) −6.46023 −0.795199
\(67\) 11.0843 1.35417 0.677084 0.735906i \(-0.263243\pi\)
0.677084 + 0.735906i \(0.263243\pi\)
\(68\) −20.6173 −2.50021
\(69\) 1.04436 0.125727
\(70\) −7.43398 −0.888531
\(71\) −12.4574 −1.47842 −0.739212 0.673473i \(-0.764802\pi\)
−0.739212 + 0.673473i \(0.764802\pi\)
\(72\) −17.9707 −2.11787
\(73\) −3.30899 −0.387288 −0.193644 0.981072i \(-0.562031\pi\)
−0.193644 + 0.981072i \(0.562031\pi\)
\(74\) −21.0497 −2.44698
\(75\) 2.57932 0.297834
\(76\) −1.47187 −0.168835
\(77\) −1.54216 −0.175746
\(78\) −6.13457 −0.694603
\(79\) −0.210549 −0.0236886 −0.0118443 0.999930i \(-0.503770\pi\)
−0.0118443 + 0.999930i \(0.503770\pi\)
\(80\) 15.3399 1.71505
\(81\) −9.74223 −1.08247
\(82\) 18.7348 2.06891
\(83\) −9.57254 −1.05072 −0.525361 0.850879i \(-0.676070\pi\)
−0.525361 + 0.850879i \(0.676070\pi\)
\(84\) −16.0173 −1.74763
\(85\) −8.93460 −0.969094
\(86\) −28.1429 −3.03473
\(87\) −2.98383 −0.319900
\(88\) 6.93743 0.739533
\(89\) 18.4974 1.96072 0.980359 0.197220i \(-0.0631914\pi\)
0.980359 + 0.197220i \(0.0631914\pi\)
\(90\) −13.8480 −1.45970
\(91\) −1.46442 −0.153513
\(92\) −1.99425 −0.207915
\(93\) 16.4313 1.70385
\(94\) −6.81922 −0.703349
\(95\) −0.637842 −0.0654412
\(96\) 15.9829 1.63125
\(97\) −1.36389 −0.138482 −0.0692410 0.997600i \(-0.522058\pi\)
−0.0692410 + 0.997600i \(0.522058\pi\)
\(98\) 12.4456 1.25720
\(99\) −2.87273 −0.288720
\(100\) −4.92529 −0.492529
\(101\) 2.37426 0.236248 0.118124 0.992999i \(-0.462312\pi\)
0.118124 + 0.992999i \(0.462312\pi\)
\(102\) −27.6752 −2.74025
\(103\) −4.07504 −0.401525 −0.200763 0.979640i \(-0.564342\pi\)
−0.200763 + 0.979640i \(0.564342\pi\)
\(104\) 6.58772 0.645979
\(105\) −6.94119 −0.677391
\(106\) −15.5826 −1.51351
\(107\) −9.50627 −0.919006 −0.459503 0.888176i \(-0.651972\pi\)
−0.459503 + 0.888176i \(0.651972\pi\)
\(108\) 2.97597 0.286363
\(109\) −1.55811 −0.149239 −0.0746197 0.997212i \(-0.523774\pi\)
−0.0746197 + 0.997212i \(0.523774\pi\)
\(110\) 5.34588 0.509709
\(111\) −19.6544 −1.86551
\(112\) 11.3428 1.07179
\(113\) −16.1939 −1.52340 −0.761699 0.647931i \(-0.775634\pi\)
−0.761699 + 0.647931i \(0.775634\pi\)
\(114\) −1.97573 −0.185044
\(115\) −0.864218 −0.0805887
\(116\) 5.69771 0.529019
\(117\) −2.72791 −0.252196
\(118\) −19.8357 −1.82602
\(119\) −6.60652 −0.605619
\(120\) 31.2250 2.85044
\(121\) −9.89101 −0.899183
\(122\) −25.3286 −2.29315
\(123\) 17.4928 1.57728
\(124\) −31.3761 −2.81765
\(125\) −12.0368 −1.07660
\(126\) −10.2396 −0.912217
\(127\) 11.7252 1.04044 0.520221 0.854032i \(-0.325850\pi\)
0.520221 + 0.854032i \(0.325850\pi\)
\(128\) 9.18731 0.812052
\(129\) −26.2773 −2.31359
\(130\) 5.07639 0.445229
\(131\) −16.8443 −1.47169 −0.735846 0.677149i \(-0.763215\pi\)
−0.735846 + 0.677149i \(0.763215\pi\)
\(132\) 11.5183 1.00254
\(133\) −0.471640 −0.0408964
\(134\) −28.4116 −2.45439
\(135\) 1.28965 0.110996
\(136\) 29.7195 2.54842
\(137\) 2.46142 0.210293 0.105147 0.994457i \(-0.466469\pi\)
0.105147 + 0.994457i \(0.466469\pi\)
\(138\) −2.67694 −0.227876
\(139\) −2.43010 −0.206118 −0.103059 0.994675i \(-0.532863\pi\)
−0.103059 + 0.994675i \(0.532863\pi\)
\(140\) 13.2544 1.12020
\(141\) −6.36718 −0.536214
\(142\) 31.9311 2.67960
\(143\) 1.05309 0.0880635
\(144\) 21.1293 1.76077
\(145\) 2.46913 0.205050
\(146\) 8.48166 0.701947
\(147\) 11.6206 0.958452
\(148\) 37.5307 3.08500
\(149\) 0.102314 0.00838193 0.00419096 0.999991i \(-0.498666\pi\)
0.00419096 + 0.999991i \(0.498666\pi\)
\(150\) −6.61136 −0.539816
\(151\) 13.5004 1.09865 0.549323 0.835610i \(-0.314886\pi\)
0.549323 + 0.835610i \(0.314886\pi\)
\(152\) 2.12167 0.172091
\(153\) −12.3066 −0.994927
\(154\) 3.95290 0.318534
\(155\) −13.5970 −1.09214
\(156\) 10.9376 0.875712
\(157\) 10.9947 0.877469 0.438735 0.898617i \(-0.355427\pi\)
0.438735 + 0.898617i \(0.355427\pi\)
\(158\) 0.539682 0.0429348
\(159\) −14.5496 −1.15386
\(160\) −13.2260 −1.04560
\(161\) −0.639029 −0.0503625
\(162\) 24.9715 1.96194
\(163\) −7.46943 −0.585051 −0.292525 0.956258i \(-0.594496\pi\)
−0.292525 + 0.956258i \(0.594496\pi\)
\(164\) −33.4031 −2.60835
\(165\) 4.99150 0.388588
\(166\) 24.5365 1.90440
\(167\) 8.32006 0.643826 0.321913 0.946769i \(-0.395674\pi\)
0.321913 + 0.946769i \(0.395674\pi\)
\(168\) 23.0887 1.78133
\(169\) 1.00000 0.0769231
\(170\) 22.9014 1.75645
\(171\) −0.878566 −0.0671856
\(172\) 50.1774 3.82599
\(173\) 19.4403 1.47802 0.739008 0.673697i \(-0.235295\pi\)
0.739008 + 0.673697i \(0.235295\pi\)
\(174\) 7.64820 0.579809
\(175\) −1.57824 −0.119304
\(176\) −8.15676 −0.614839
\(177\) −18.5208 −1.39211
\(178\) −47.4128 −3.55374
\(179\) 10.8513 0.811061 0.405530 0.914082i \(-0.367087\pi\)
0.405530 + 0.914082i \(0.367087\pi\)
\(180\) 24.6902 1.84030
\(181\) −24.2764 −1.80445 −0.902224 0.431268i \(-0.858066\pi\)
−0.902224 + 0.431268i \(0.858066\pi\)
\(182\) 3.75364 0.278238
\(183\) −23.6496 −1.74823
\(184\) 2.87468 0.211924
\(185\) 16.2641 1.19576
\(186\) −42.1170 −3.08817
\(187\) 4.75084 0.347416
\(188\) 12.1583 0.886738
\(189\) 0.953609 0.0693649
\(190\) 1.63493 0.118610
\(191\) −25.9256 −1.87591 −0.937957 0.346752i \(-0.887285\pi\)
−0.937957 + 0.346752i \(0.887285\pi\)
\(192\) −3.89268 −0.280930
\(193\) −3.71707 −0.267560 −0.133780 0.991011i \(-0.542712\pi\)
−0.133780 + 0.991011i \(0.542712\pi\)
\(194\) 3.49595 0.250994
\(195\) 4.73988 0.339430
\(196\) −22.1899 −1.58500
\(197\) 15.3897 1.09647 0.548236 0.836323i \(-0.315299\pi\)
0.548236 + 0.836323i \(0.315299\pi\)
\(198\) 7.36343 0.523297
\(199\) 23.9721 1.69934 0.849670 0.527315i \(-0.176801\pi\)
0.849670 + 0.527315i \(0.176801\pi\)
\(200\) 7.09973 0.502027
\(201\) −26.5282 −1.87116
\(202\) −6.08575 −0.428192
\(203\) 1.82575 0.128143
\(204\) 49.3435 3.45473
\(205\) −14.4754 −1.01101
\(206\) 10.4452 0.727753
\(207\) −1.19038 −0.0827370
\(208\) −7.74558 −0.537059
\(209\) 0.339162 0.0234603
\(210\) 17.7918 1.22775
\(211\) 0.375711 0.0258650 0.0129325 0.999916i \(-0.495883\pi\)
0.0129325 + 0.999916i \(0.495883\pi\)
\(212\) 27.7830 1.90814
\(213\) 29.8144 2.04285
\(214\) 24.3667 1.66567
\(215\) 21.7446 1.48297
\(216\) −4.28982 −0.291885
\(217\) −10.0540 −0.682512
\(218\) 3.99377 0.270492
\(219\) 7.91942 0.535145
\(220\) −9.53143 −0.642609
\(221\) 4.51135 0.303466
\(222\) 50.3785 3.38118
\(223\) 1.58502 0.106141 0.0530705 0.998591i \(-0.483099\pi\)
0.0530705 + 0.998591i \(0.483099\pi\)
\(224\) −9.77968 −0.653433
\(225\) −2.93994 −0.195996
\(226\) 41.5086 2.76111
\(227\) −20.2927 −1.34687 −0.673437 0.739245i \(-0.735183\pi\)
−0.673437 + 0.739245i \(0.735183\pi\)
\(228\) 3.52263 0.233292
\(229\) −5.18866 −0.342877 −0.171438 0.985195i \(-0.554841\pi\)
−0.171438 + 0.985195i \(0.554841\pi\)
\(230\) 2.21518 0.146065
\(231\) 3.69087 0.242841
\(232\) −8.21316 −0.539220
\(233\) −16.2291 −1.06320 −0.531601 0.846995i \(-0.678410\pi\)
−0.531601 + 0.846995i \(0.678410\pi\)
\(234\) 6.99224 0.457097
\(235\) 5.26888 0.343704
\(236\) 35.3660 2.30213
\(237\) 0.503907 0.0327323
\(238\) 16.9340 1.09767
\(239\) −21.7085 −1.40421 −0.702103 0.712075i \(-0.747755\pi\)
−0.702103 + 0.712075i \(0.747755\pi\)
\(240\) −36.7131 −2.36982
\(241\) 11.0353 0.710847 0.355423 0.934705i \(-0.384337\pi\)
0.355423 + 0.934705i \(0.384337\pi\)
\(242\) 25.3528 1.62974
\(243\) 21.3626 1.37041
\(244\) 45.1597 2.89106
\(245\) −9.61612 −0.614351
\(246\) −44.8380 −2.85877
\(247\) 0.322065 0.0204925
\(248\) 45.2281 2.87199
\(249\) 22.9100 1.45186
\(250\) 30.8529 1.95131
\(251\) 24.2143 1.52839 0.764197 0.644983i \(-0.223135\pi\)
0.764197 + 0.644983i \(0.223135\pi\)
\(252\) 18.2567 1.15006
\(253\) 0.459534 0.0288907
\(254\) −30.0542 −1.88577
\(255\) 21.3832 1.33907
\(256\) −26.8021 −1.67513
\(257\) −17.1349 −1.06884 −0.534422 0.845218i \(-0.679471\pi\)
−0.534422 + 0.845218i \(0.679471\pi\)
\(258\) 67.3546 4.19331
\(259\) 12.0262 0.747271
\(260\) −9.05095 −0.561316
\(261\) 3.40100 0.210516
\(262\) 43.1756 2.66740
\(263\) 18.6865 1.15226 0.576128 0.817360i \(-0.304563\pi\)
0.576128 + 0.817360i \(0.304563\pi\)
\(264\) −16.6034 −1.02187
\(265\) 12.0399 0.739604
\(266\) 1.20892 0.0741234
\(267\) −44.2699 −2.70927
\(268\) 50.6565 3.09434
\(269\) −15.4148 −0.939859 −0.469930 0.882704i \(-0.655721\pi\)
−0.469930 + 0.882704i \(0.655721\pi\)
\(270\) −3.30566 −0.201176
\(271\) 1.03181 0.0626781 0.0313390 0.999509i \(-0.490023\pi\)
0.0313390 + 0.999509i \(0.490023\pi\)
\(272\) −34.9430 −2.11873
\(273\) 3.50481 0.212121
\(274\) −6.30916 −0.381150
\(275\) 1.13493 0.0684391
\(276\) 4.77285 0.287292
\(277\) 13.9223 0.836509 0.418255 0.908330i \(-0.362642\pi\)
0.418255 + 0.908330i \(0.362642\pi\)
\(278\) 6.22887 0.373583
\(279\) −18.7286 −1.12125
\(280\) −19.1060 −1.14180
\(281\) −21.8732 −1.30485 −0.652424 0.757854i \(-0.726248\pi\)
−0.652424 + 0.757854i \(0.726248\pi\)
\(282\) 16.3205 0.971871
\(283\) 17.3719 1.03265 0.516327 0.856392i \(-0.327299\pi\)
0.516327 + 0.856392i \(0.327299\pi\)
\(284\) −56.9316 −3.37827
\(285\) 1.52655 0.0904250
\(286\) −2.69929 −0.159612
\(287\) −10.7036 −0.631812
\(288\) −18.2175 −1.07348
\(289\) 3.35225 0.197191
\(290\) −6.32893 −0.371648
\(291\) 3.26420 0.191351
\(292\) −15.1224 −0.884971
\(293\) 30.8755 1.80377 0.901884 0.431978i \(-0.142184\pi\)
0.901884 + 0.431978i \(0.142184\pi\)
\(294\) −29.7862 −1.73717
\(295\) 15.3260 0.892317
\(296\) −54.0998 −3.14449
\(297\) −0.685753 −0.0397914
\(298\) −0.262254 −0.0151920
\(299\) 0.436369 0.0252359
\(300\) 11.7877 0.680565
\(301\) 16.0787 0.926758
\(302\) −34.6045 −1.99126
\(303\) −5.68233 −0.326441
\(304\) −2.49458 −0.143074
\(305\) 19.5702 1.12059
\(306\) 31.5444 1.80328
\(307\) 19.0131 1.08513 0.542567 0.840013i \(-0.317452\pi\)
0.542567 + 0.840013i \(0.317452\pi\)
\(308\) −7.04784 −0.401588
\(309\) 9.75281 0.554818
\(310\) 34.8521 1.97946
\(311\) −27.5211 −1.56058 −0.780290 0.625418i \(-0.784928\pi\)
−0.780290 + 0.625418i \(0.784928\pi\)
\(312\) −15.7664 −0.892598
\(313\) −21.8496 −1.23501 −0.617505 0.786567i \(-0.711856\pi\)
−0.617505 + 0.786567i \(0.711856\pi\)
\(314\) −28.1817 −1.59039
\(315\) 7.91164 0.445770
\(316\) −0.962227 −0.0541295
\(317\) −14.4644 −0.812400 −0.406200 0.913784i \(-0.633146\pi\)
−0.406200 + 0.913784i \(0.633146\pi\)
\(318\) 37.2939 2.09134
\(319\) −1.31292 −0.0735096
\(320\) 3.22122 0.180071
\(321\) 22.7514 1.26986
\(322\) 1.63797 0.0912806
\(323\) 1.45295 0.0808442
\(324\) −44.5229 −2.47349
\(325\) 1.07772 0.0597813
\(326\) 19.1458 1.06039
\(327\) 3.72902 0.206215
\(328\) 48.1501 2.65864
\(329\) 3.89597 0.214792
\(330\) −12.7943 −0.704304
\(331\) 23.9420 1.31597 0.657986 0.753030i \(-0.271408\pi\)
0.657986 + 0.753030i \(0.271408\pi\)
\(332\) −43.7474 −2.40095
\(333\) 22.4023 1.22764
\(334\) −21.3261 −1.16691
\(335\) 21.9522 1.19938
\(336\) −27.1468 −1.48098
\(337\) −3.02838 −0.164966 −0.0824831 0.996592i \(-0.526285\pi\)
−0.0824831 + 0.996592i \(0.526285\pi\)
\(338\) −2.56322 −0.139421
\(339\) 38.7570 2.10499
\(340\) −40.8320 −2.21443
\(341\) 7.22998 0.391526
\(342\) 2.25196 0.121772
\(343\) −17.3614 −0.937429
\(344\) −72.3299 −3.89977
\(345\) 2.06834 0.111356
\(346\) −49.8296 −2.67886
\(347\) −8.26574 −0.443728 −0.221864 0.975078i \(-0.571214\pi\)
−0.221864 + 0.975078i \(0.571214\pi\)
\(348\) −13.6364 −0.730986
\(349\) −30.5334 −1.63442 −0.817208 0.576342i \(-0.804479\pi\)
−0.817208 + 0.576342i \(0.804479\pi\)
\(350\) 4.04538 0.216235
\(351\) −0.651184 −0.0347576
\(352\) 7.03270 0.374844
\(353\) 3.32339 0.176886 0.0884432 0.996081i \(-0.471811\pi\)
0.0884432 + 0.996081i \(0.471811\pi\)
\(354\) 47.4728 2.52315
\(355\) −24.6716 −1.30943
\(356\) 84.5348 4.48033
\(357\) 15.8114 0.836830
\(358\) −27.8141 −1.47002
\(359\) −19.0599 −1.00594 −0.502971 0.864303i \(-0.667760\pi\)
−0.502971 + 0.864303i \(0.667760\pi\)
\(360\) −35.5906 −1.87579
\(361\) −18.8963 −0.994541
\(362\) 62.2256 3.27051
\(363\) 23.6722 1.24247
\(364\) −6.69255 −0.350785
\(365\) −6.55336 −0.343019
\(366\) 60.6192 3.16862
\(367\) 32.9275 1.71880 0.859401 0.511303i \(-0.170837\pi\)
0.859401 + 0.511303i \(0.170837\pi\)
\(368\) −3.37993 −0.176191
\(369\) −19.9385 −1.03796
\(370\) −41.6885 −2.16728
\(371\) 8.90266 0.462203
\(372\) 75.0926 3.89337
\(373\) −24.5068 −1.26891 −0.634456 0.772959i \(-0.718776\pi\)
−0.634456 + 0.772959i \(0.718776\pi\)
\(374\) −12.1774 −0.629680
\(375\) 28.8077 1.48762
\(376\) −17.5261 −0.903837
\(377\) −1.24674 −0.0642103
\(378\) −2.44431 −0.125722
\(379\) −13.1778 −0.676897 −0.338449 0.940985i \(-0.609902\pi\)
−0.338449 + 0.940985i \(0.609902\pi\)
\(380\) −2.91500 −0.149536
\(381\) −28.0620 −1.43766
\(382\) 66.4531 3.40004
\(383\) −33.6940 −1.72168 −0.860842 0.508872i \(-0.830063\pi\)
−0.860842 + 0.508872i \(0.830063\pi\)
\(384\) −21.9881 −1.12207
\(385\) −3.05422 −0.155657
\(386\) 9.52766 0.484945
\(387\) 29.9512 1.52250
\(388\) −6.23310 −0.316438
\(389\) −21.1426 −1.07197 −0.535987 0.844226i \(-0.680061\pi\)
−0.535987 + 0.844226i \(0.680061\pi\)
\(390\) −12.1494 −0.615207
\(391\) 1.96861 0.0995570
\(392\) 31.9864 1.61556
\(393\) 40.3135 2.03355
\(394\) −39.4473 −1.98732
\(395\) −0.416986 −0.0209808
\(396\) −13.1286 −0.659739
\(397\) −7.22916 −0.362821 −0.181411 0.983407i \(-0.558066\pi\)
−0.181411 + 0.983407i \(0.558066\pi\)
\(398\) −61.4459 −3.08000
\(399\) 1.12878 0.0565096
\(400\) −8.34758 −0.417379
\(401\) −3.15229 −0.157418 −0.0787090 0.996898i \(-0.525080\pi\)
−0.0787090 + 0.996898i \(0.525080\pi\)
\(402\) 67.9976 3.39141
\(403\) 6.86552 0.341996
\(404\) 10.8506 0.539837
\(405\) −19.2942 −0.958738
\(406\) −4.67981 −0.232255
\(407\) −8.64818 −0.428675
\(408\) −71.1278 −3.52135
\(409\) −7.74633 −0.383031 −0.191516 0.981490i \(-0.561340\pi\)
−0.191516 + 0.981490i \(0.561340\pi\)
\(410\) 37.1037 1.83242
\(411\) −5.89093 −0.290578
\(412\) −18.6233 −0.917504
\(413\) 11.3325 0.557638
\(414\) 3.05120 0.149958
\(415\) −18.9582 −0.930620
\(416\) 6.67818 0.327425
\(417\) 5.81597 0.284809
\(418\) −0.869348 −0.0425212
\(419\) −4.12325 −0.201434 −0.100717 0.994915i \(-0.532114\pi\)
−0.100717 + 0.994915i \(0.532114\pi\)
\(420\) −31.7219 −1.54787
\(421\) −3.74617 −0.182577 −0.0912885 0.995824i \(-0.529099\pi\)
−0.0912885 + 0.995824i \(0.529099\pi\)
\(422\) −0.963031 −0.0468796
\(423\) 7.25738 0.352866
\(424\) −40.0487 −1.94494
\(425\) 4.86198 0.235841
\(426\) −76.4209 −3.70260
\(427\) 14.4708 0.700291
\(428\) −43.4445 −2.09997
\(429\) −2.52036 −0.121684
\(430\) −55.7363 −2.68784
\(431\) 20.3700 0.981186 0.490593 0.871389i \(-0.336780\pi\)
0.490593 + 0.871389i \(0.336780\pi\)
\(432\) 5.04380 0.242670
\(433\) 0.407658 0.0195908 0.00979540 0.999952i \(-0.496882\pi\)
0.00979540 + 0.999952i \(0.496882\pi\)
\(434\) 25.7707 1.23703
\(435\) −5.90939 −0.283334
\(436\) −7.12069 −0.341019
\(437\) 0.140539 0.00672291
\(438\) −20.2992 −0.969934
\(439\) 21.9928 1.04966 0.524830 0.851207i \(-0.324129\pi\)
0.524830 + 0.851207i \(0.324129\pi\)
\(440\) 13.7394 0.655001
\(441\) −13.2453 −0.630728
\(442\) −11.5636 −0.550023
\(443\) −3.63646 −0.172774 −0.0863868 0.996262i \(-0.527532\pi\)
−0.0863868 + 0.996262i \(0.527532\pi\)
\(444\) −89.8224 −4.26278
\(445\) 36.6336 1.73660
\(446\) −4.06276 −0.192377
\(447\) −0.244870 −0.0115819
\(448\) 2.38187 0.112533
\(449\) 5.33266 0.251664 0.125832 0.992052i \(-0.459840\pi\)
0.125832 + 0.992052i \(0.459840\pi\)
\(450\) 7.53570 0.355236
\(451\) 7.69708 0.362441
\(452\) −74.0078 −3.48104
\(453\) −32.3106 −1.51808
\(454\) 52.0146 2.44117
\(455\) −2.90025 −0.135966
\(456\) −5.07782 −0.237791
\(457\) −18.0640 −0.844997 −0.422498 0.906364i \(-0.638847\pi\)
−0.422498 + 0.906364i \(0.638847\pi\)
\(458\) 13.2997 0.621453
\(459\) −2.93772 −0.137121
\(460\) −3.94956 −0.184149
\(461\) −17.7094 −0.824811 −0.412406 0.911000i \(-0.635311\pi\)
−0.412406 + 0.911000i \(0.635311\pi\)
\(462\) −9.46051 −0.440143
\(463\) −1.00000 −0.0464739
\(464\) 9.65671 0.448301
\(465\) 32.5417 1.50909
\(466\) 41.5987 1.92702
\(467\) 22.7457 1.05255 0.526273 0.850316i \(-0.323589\pi\)
0.526273 + 0.850316i \(0.323589\pi\)
\(468\) −12.4668 −0.576279
\(469\) 16.2322 0.749532
\(470\) −13.5053 −0.622953
\(471\) −26.3136 −1.21247
\(472\) −50.9795 −2.34652
\(473\) −11.5624 −0.531638
\(474\) −1.29163 −0.0593263
\(475\) 0.347097 0.0159259
\(476\) −30.1924 −1.38387
\(477\) 16.5838 0.759320
\(478\) 55.6437 2.54508
\(479\) 3.71595 0.169786 0.0848930 0.996390i \(-0.472945\pi\)
0.0848930 + 0.996390i \(0.472945\pi\)
\(480\) 31.6538 1.44479
\(481\) −8.21223 −0.374445
\(482\) −28.2859 −1.28839
\(483\) 1.52939 0.0695898
\(484\) −45.2029 −2.05468
\(485\) −2.70115 −0.122653
\(486\) −54.7570 −2.48383
\(487\) 35.7140 1.61835 0.809177 0.587565i \(-0.199913\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(488\) −65.0970 −2.94680
\(489\) 17.8766 0.808409
\(490\) 24.6482 1.11349
\(491\) 3.51616 0.158682 0.0793411 0.996848i \(-0.474718\pi\)
0.0793411 + 0.996848i \(0.474718\pi\)
\(492\) 79.9440 3.60415
\(493\) −5.62447 −0.253313
\(494\) −0.825524 −0.0371421
\(495\) −5.68936 −0.255718
\(496\) −53.1774 −2.38774
\(497\) −18.2429 −0.818308
\(498\) −58.7234 −2.63146
\(499\) 17.8697 0.799956 0.399978 0.916525i \(-0.369018\pi\)
0.399978 + 0.916525i \(0.369018\pi\)
\(500\) −55.0092 −2.46009
\(501\) −19.9125 −0.889623
\(502\) −62.0666 −2.77017
\(503\) −1.99613 −0.0890030 −0.0445015 0.999009i \(-0.514170\pi\)
−0.0445015 + 0.999009i \(0.514170\pi\)
\(504\) −26.3168 −1.17224
\(505\) 4.70216 0.209243
\(506\) −1.17789 −0.0523635
\(507\) −2.39331 −0.106290
\(508\) 53.5852 2.37746
\(509\) −29.9226 −1.32630 −0.663148 0.748488i \(-0.730780\pi\)
−0.663148 + 0.748488i \(0.730780\pi\)
\(510\) −54.8100 −2.42703
\(511\) −4.84576 −0.214364
\(512\) 50.3250 2.22407
\(513\) −0.209724 −0.00925953
\(514\) 43.9204 1.93725
\(515\) −8.07051 −0.355629
\(516\) −120.090 −5.28666
\(517\) −2.80164 −0.123216
\(518\) −30.8257 −1.35441
\(519\) −46.5265 −2.04229
\(520\) 13.0468 0.572140
\(521\) 5.65157 0.247600 0.123800 0.992307i \(-0.460492\pi\)
0.123800 + 0.992307i \(0.460492\pi\)
\(522\) −8.71750 −0.381555
\(523\) −22.8950 −1.00113 −0.500564 0.865700i \(-0.666874\pi\)
−0.500564 + 0.865700i \(0.666874\pi\)
\(524\) −76.9800 −3.36289
\(525\) 3.77722 0.164851
\(526\) −47.8975 −2.08843
\(527\) 30.9727 1.34919
\(528\) 19.5216 0.849570
\(529\) −22.8096 −0.991721
\(530\) −30.8609 −1.34051
\(531\) 21.1102 0.916103
\(532\) −2.15544 −0.0934501
\(533\) 7.30907 0.316591
\(534\) 113.473 4.91048
\(535\) −18.8269 −0.813959
\(536\) −73.0205 −3.15400
\(537\) −25.9704 −1.12070
\(538\) 39.5116 1.70347
\(539\) 5.11322 0.220242
\(540\) 5.89384 0.253630
\(541\) 23.3275 1.00293 0.501464 0.865178i \(-0.332795\pi\)
0.501464 + 0.865178i \(0.332795\pi\)
\(542\) −2.64476 −0.113602
\(543\) 58.1008 2.49334
\(544\) 30.1276 1.29171
\(545\) −3.08579 −0.132181
\(546\) −8.98361 −0.384463
\(547\) −26.0532 −1.11395 −0.556977 0.830528i \(-0.688039\pi\)
−0.556977 + 0.830528i \(0.688039\pi\)
\(548\) 11.2489 0.480530
\(549\) 26.9561 1.15046
\(550\) −2.90909 −0.124044
\(551\) −0.401531 −0.0171058
\(552\) −6.87998 −0.292831
\(553\) −0.308332 −0.0131116
\(554\) −35.6859 −1.51615
\(555\) −38.9250 −1.65227
\(556\) −11.1058 −0.470990
\(557\) −23.5669 −0.998562 −0.499281 0.866440i \(-0.666403\pi\)
−0.499281 + 0.866440i \(0.666403\pi\)
\(558\) 48.0054 2.03223
\(559\) −10.9795 −0.464384
\(560\) 22.4641 0.949283
\(561\) −11.3702 −0.480050
\(562\) 56.0659 2.36500
\(563\) 23.7893 1.00260 0.501300 0.865273i \(-0.332855\pi\)
0.501300 + 0.865273i \(0.332855\pi\)
\(564\) −29.0986 −1.22527
\(565\) −32.0717 −1.34927
\(566\) −44.5280 −1.87165
\(567\) −14.2667 −0.599147
\(568\) 82.0660 3.44341
\(569\) −28.5800 −1.19814 −0.599069 0.800698i \(-0.704462\pi\)
−0.599069 + 0.800698i \(0.704462\pi\)
\(570\) −3.91288 −0.163893
\(571\) 13.6238 0.570139 0.285069 0.958507i \(-0.407983\pi\)
0.285069 + 0.958507i \(0.407983\pi\)
\(572\) 4.81270 0.201229
\(573\) 62.0480 2.59209
\(574\) 27.4356 1.14514
\(575\) 0.470285 0.0196122
\(576\) 4.43692 0.184872
\(577\) −30.6388 −1.27551 −0.637755 0.770239i \(-0.720137\pi\)
−0.637755 + 0.770239i \(0.720137\pi\)
\(578\) −8.59255 −0.357403
\(579\) 8.89608 0.369709
\(580\) 11.2842 0.468550
\(581\) −14.0183 −0.581575
\(582\) −8.36687 −0.346818
\(583\) −6.40202 −0.265145
\(584\) 21.7987 0.902036
\(585\) −5.40256 −0.223369
\(586\) −79.1408 −3.26928
\(587\) −16.8905 −0.697144 −0.348572 0.937282i \(-0.613333\pi\)
−0.348572 + 0.937282i \(0.613333\pi\)
\(588\) 53.1073 2.19011
\(589\) 2.21114 0.0911086
\(590\) −39.2840 −1.61730
\(591\) −36.8323 −1.51508
\(592\) 63.6085 2.61429
\(593\) −14.3521 −0.589370 −0.294685 0.955594i \(-0.595215\pi\)
−0.294685 + 0.955594i \(0.595215\pi\)
\(594\) 1.75774 0.0721207
\(595\) −13.0840 −0.536394
\(596\) 0.467587 0.0191531
\(597\) −57.3727 −2.34811
\(598\) −1.11851 −0.0457393
\(599\) 43.5647 1.78001 0.890004 0.455953i \(-0.150702\pi\)
0.890004 + 0.455953i \(0.150702\pi\)
\(600\) −16.9918 −0.693689
\(601\) 32.7379 1.33541 0.667703 0.744427i \(-0.267277\pi\)
0.667703 + 0.744427i \(0.267277\pi\)
\(602\) −41.2131 −1.67972
\(603\) 30.2371 1.23135
\(604\) 61.6981 2.51046
\(605\) −19.5889 −0.796402
\(606\) 14.5651 0.591665
\(607\) 37.2769 1.51302 0.756512 0.653979i \(-0.226902\pi\)
0.756512 + 0.653979i \(0.226902\pi\)
\(608\) 2.15081 0.0872268
\(609\) −4.36959 −0.177065
\(610\) −50.1627 −2.03103
\(611\) −2.66041 −0.107629
\(612\) −56.2422 −2.27346
\(613\) −40.7834 −1.64723 −0.823613 0.567152i \(-0.808045\pi\)
−0.823613 + 0.567152i \(0.808045\pi\)
\(614\) −48.7347 −1.96677
\(615\) 34.6441 1.39699
\(616\) 10.1593 0.409331
\(617\) −14.5704 −0.586583 −0.293292 0.956023i \(-0.594751\pi\)
−0.293292 + 0.956023i \(0.594751\pi\)
\(618\) −24.9986 −1.00559
\(619\) −8.38533 −0.337035 −0.168517 0.985699i \(-0.553898\pi\)
−0.168517 + 0.985699i \(0.553898\pi\)
\(620\) −62.1395 −2.49558
\(621\) −0.284157 −0.0114028
\(622\) 70.5427 2.82850
\(623\) 27.0880 1.08526
\(624\) 18.5375 0.742095
\(625\) −18.4499 −0.737996
\(626\) 56.0052 2.23842
\(627\) −0.811719 −0.0324169
\(628\) 50.2466 2.00506
\(629\) −37.0482 −1.47721
\(630\) −20.2793 −0.807946
\(631\) −31.8311 −1.26717 −0.633587 0.773671i \(-0.718418\pi\)
−0.633587 + 0.773671i \(0.718418\pi\)
\(632\) 1.38703 0.0551733
\(633\) −0.899192 −0.0357397
\(634\) 37.0754 1.47245
\(635\) 23.2214 0.921514
\(636\) −66.4931 −2.63662
\(637\) 4.85546 0.192380
\(638\) 3.36531 0.133234
\(639\) −33.9828 −1.34434
\(640\) 18.1952 0.719230
\(641\) −1.07310 −0.0423851 −0.0211925 0.999775i \(-0.506746\pi\)
−0.0211925 + 0.999775i \(0.506746\pi\)
\(642\) −58.3169 −2.30158
\(643\) 10.9677 0.432523 0.216262 0.976335i \(-0.430614\pi\)
0.216262 + 0.976335i \(0.430614\pi\)
\(644\) −2.92042 −0.115081
\(645\) −52.0416 −2.04913
\(646\) −3.72422 −0.146528
\(647\) −25.3715 −0.997458 −0.498729 0.866758i \(-0.666200\pi\)
−0.498729 + 0.866758i \(0.666200\pi\)
\(648\) 64.1790 2.52119
\(649\) −8.14938 −0.319891
\(650\) −2.76244 −0.108352
\(651\) 24.0624 0.943079
\(652\) −34.1360 −1.33687
\(653\) −36.5957 −1.43210 −0.716049 0.698050i \(-0.754051\pi\)
−0.716049 + 0.698050i \(0.754051\pi\)
\(654\) −9.55831 −0.373759
\(655\) −33.3597 −1.30347
\(656\) −56.6130 −2.21037
\(657\) −9.02663 −0.352163
\(658\) −9.98623 −0.389304
\(659\) 33.5190 1.30572 0.652858 0.757480i \(-0.273570\pi\)
0.652858 + 0.757480i \(0.273570\pi\)
\(660\) 22.8116 0.887942
\(661\) 12.6134 0.490605 0.245303 0.969447i \(-0.421113\pi\)
0.245303 + 0.969447i \(0.421113\pi\)
\(662\) −61.3687 −2.38516
\(663\) −10.7970 −0.419322
\(664\) 63.0612 2.44725
\(665\) −0.934070 −0.0362217
\(666\) −57.4219 −2.22505
\(667\) −0.544038 −0.0210652
\(668\) 38.0235 1.47117
\(669\) −3.79345 −0.146663
\(670\) −56.2684 −2.17384
\(671\) −10.4061 −0.401725
\(672\) 23.4058 0.902897
\(673\) −37.6582 −1.45162 −0.725808 0.687897i \(-0.758534\pi\)
−0.725808 + 0.687897i \(0.758534\pi\)
\(674\) 7.76240 0.298996
\(675\) −0.701796 −0.0270121
\(676\) 4.57009 0.175773
\(677\) 20.5046 0.788056 0.394028 0.919098i \(-0.371081\pi\)
0.394028 + 0.919098i \(0.371081\pi\)
\(678\) −99.3428 −3.81524
\(679\) −1.99731 −0.0766498
\(680\) 58.8587 2.25713
\(681\) 48.5666 1.86108
\(682\) −18.5320 −0.709628
\(683\) −37.6491 −1.44060 −0.720300 0.693662i \(-0.755996\pi\)
−0.720300 + 0.693662i \(0.755996\pi\)
\(684\) −4.01513 −0.153522
\(685\) 4.87478 0.186256
\(686\) 44.5011 1.69906
\(687\) 12.4181 0.473779
\(688\) 85.0426 3.24222
\(689\) −6.07930 −0.231603
\(690\) −5.30160 −0.201829
\(691\) 6.90301 0.262603 0.131301 0.991342i \(-0.458084\pi\)
0.131301 + 0.991342i \(0.458084\pi\)
\(692\) 88.8438 3.37734
\(693\) −4.20689 −0.159807
\(694\) 21.1869 0.804244
\(695\) −4.81274 −0.182558
\(696\) 19.6566 0.745082
\(697\) 32.9738 1.24897
\(698\) 78.2639 2.96233
\(699\) 38.8412 1.46911
\(700\) −7.21272 −0.272615
\(701\) 24.7946 0.936478 0.468239 0.883602i \(-0.344889\pi\)
0.468239 + 0.883602i \(0.344889\pi\)
\(702\) 1.66913 0.0629972
\(703\) −2.64487 −0.0997533
\(704\) −1.71283 −0.0645548
\(705\) −12.6100 −0.474922
\(706\) −8.51858 −0.320601
\(707\) 3.47692 0.130763
\(708\) −84.6417 −3.18103
\(709\) 18.8353 0.707373 0.353687 0.935364i \(-0.384928\pi\)
0.353687 + 0.935364i \(0.384928\pi\)
\(710\) 63.2387 2.37331
\(711\) −0.574359 −0.0215401
\(712\) −121.856 −4.56673
\(713\) 2.99590 0.112197
\(714\) −40.5282 −1.51673
\(715\) 2.08561 0.0779974
\(716\) 49.5912 1.85331
\(717\) 51.9551 1.94030
\(718\) 48.8546 1.82324
\(719\) 20.3520 0.759002 0.379501 0.925191i \(-0.376096\pi\)
0.379501 + 0.925191i \(0.376096\pi\)
\(720\) 41.8460 1.55951
\(721\) −5.96758 −0.222244
\(722\) 48.4353 1.80258
\(723\) −26.4109 −0.982231
\(724\) −110.945 −4.12325
\(725\) −1.34364 −0.0499015
\(726\) −60.6771 −2.25194
\(727\) −49.0613 −1.81958 −0.909791 0.415067i \(-0.863758\pi\)
−0.909791 + 0.415067i \(0.863758\pi\)
\(728\) 9.64721 0.357549
\(729\) −21.9005 −0.811130
\(730\) 16.7977 0.621711
\(731\) −49.5324 −1.83202
\(732\) −108.081 −3.99479
\(733\) −2.27043 −0.0838601 −0.0419301 0.999121i \(-0.513351\pi\)
−0.0419301 + 0.999121i \(0.513351\pi\)
\(734\) −84.4004 −3.11528
\(735\) 23.0143 0.848896
\(736\) 2.91415 0.107417
\(737\) −11.6728 −0.429972
\(738\) 51.1068 1.88127
\(739\) −22.1241 −0.813850 −0.406925 0.913462i \(-0.633399\pi\)
−0.406925 + 0.913462i \(0.633399\pi\)
\(740\) 74.3285 2.73237
\(741\) −0.770801 −0.0283161
\(742\) −22.8195 −0.837729
\(743\) −37.9916 −1.39378 −0.696888 0.717180i \(-0.745432\pi\)
−0.696888 + 0.717180i \(0.745432\pi\)
\(744\) −108.245 −3.96844
\(745\) 0.202631 0.00742383
\(746\) 62.8162 2.29986
\(747\) −26.1131 −0.955427
\(748\) 21.7118 0.793861
\(749\) −13.9212 −0.508670
\(750\) −73.8404 −2.69627
\(751\) −43.4343 −1.58494 −0.792471 0.609910i \(-0.791206\pi\)
−0.792471 + 0.609910i \(0.791206\pi\)
\(752\) 20.6064 0.751439
\(753\) −57.9523 −2.11190
\(754\) 3.19566 0.116379
\(755\) 26.7372 0.973066
\(756\) 4.35808 0.158502
\(757\) −46.7084 −1.69765 −0.848823 0.528676i \(-0.822689\pi\)
−0.848823 + 0.528676i \(0.822689\pi\)
\(758\) 33.7776 1.22686
\(759\) −1.09981 −0.0399204
\(760\) 4.20192 0.152420
\(761\) −23.2379 −0.842373 −0.421186 0.906974i \(-0.638386\pi\)
−0.421186 + 0.906974i \(0.638386\pi\)
\(762\) 71.9290 2.60571
\(763\) −2.28173 −0.0826040
\(764\) −118.483 −4.28655
\(765\) −24.3728 −0.881202
\(766\) 86.3652 3.12050
\(767\) −7.73857 −0.279424
\(768\) 64.1456 2.31465
\(769\) 48.8205 1.76051 0.880255 0.474500i \(-0.157371\pi\)
0.880255 + 0.474500i \(0.157371\pi\)
\(770\) 7.82863 0.282124
\(771\) 41.0090 1.47690
\(772\) −16.9874 −0.611388
\(773\) −31.0947 −1.11840 −0.559199 0.829033i \(-0.688891\pi\)
−0.559199 + 0.829033i \(0.688891\pi\)
\(774\) −76.7714 −2.75949
\(775\) 7.39913 0.265784
\(776\) 8.98492 0.322540
\(777\) −28.7823 −1.03256
\(778\) 54.1932 1.94292
\(779\) 2.35400 0.0843407
\(780\) 21.6617 0.775613
\(781\) 13.1187 0.469425
\(782\) −5.04599 −0.180444
\(783\) 0.811856 0.0290134
\(784\) −37.6084 −1.34316
\(785\) 21.7746 0.777170
\(786\) −103.332 −3.68575
\(787\) −40.6300 −1.44830 −0.724151 0.689642i \(-0.757768\pi\)
−0.724151 + 0.689642i \(0.757768\pi\)
\(788\) 70.3325 2.50549
\(789\) −44.7224 −1.59216
\(790\) 1.06883 0.0380272
\(791\) −23.7148 −0.843201
\(792\) 18.9247 0.672461
\(793\) −9.88157 −0.350905
\(794\) 18.5299 0.657603
\(795\) −28.8151 −1.02197
\(796\) 109.555 3.88307
\(797\) 49.6548 1.75886 0.879431 0.476027i \(-0.157923\pi\)
0.879431 + 0.476027i \(0.157923\pi\)
\(798\) −2.89331 −0.102422
\(799\) −12.0020 −0.424602
\(800\) 7.19723 0.254460
\(801\) 50.4593 1.78289
\(802\) 8.08002 0.285315
\(803\) 3.48465 0.122971
\(804\) −121.236 −4.27568
\(805\) −1.26558 −0.0446059
\(806\) −17.5978 −0.619857
\(807\) 36.8924 1.29868
\(808\) −15.6410 −0.550247
\(809\) −7.12548 −0.250518 −0.125259 0.992124i \(-0.539976\pi\)
−0.125259 + 0.992124i \(0.539976\pi\)
\(810\) 49.4553 1.73768
\(811\) 20.1584 0.707857 0.353928 0.935273i \(-0.384846\pi\)
0.353928 + 0.935273i \(0.384846\pi\)
\(812\) 8.34386 0.292812
\(813\) −2.46944 −0.0866070
\(814\) 22.1672 0.776960
\(815\) −14.7930 −0.518176
\(816\) 83.6293 2.92761
\(817\) −3.53612 −0.123713
\(818\) 19.8555 0.694233
\(819\) −3.99482 −0.139590
\(820\) −66.1541 −2.31020
\(821\) −29.2926 −1.02232 −0.511159 0.859486i \(-0.670784\pi\)
−0.511159 + 0.859486i \(0.670784\pi\)
\(822\) 15.0998 0.526665
\(823\) 52.1349 1.81731 0.908654 0.417550i \(-0.137111\pi\)
0.908654 + 0.417550i \(0.137111\pi\)
\(824\) 26.8452 0.935197
\(825\) −2.71625 −0.0945676
\(826\) −29.0478 −1.01070
\(827\) −40.9040 −1.42237 −0.711185 0.703005i \(-0.751841\pi\)
−0.711185 + 0.703005i \(0.751841\pi\)
\(828\) −5.44014 −0.189058
\(829\) −12.4958 −0.433999 −0.216999 0.976172i \(-0.569627\pi\)
−0.216999 + 0.976172i \(0.569627\pi\)
\(830\) 48.5939 1.68672
\(831\) −33.3203 −1.15587
\(832\) −1.62649 −0.0563883
\(833\) 21.9047 0.758952
\(834\) −14.9076 −0.516208
\(835\) 16.4777 0.570233
\(836\) 1.55000 0.0536080
\(837\) −4.47072 −0.154531
\(838\) 10.5688 0.365093
\(839\) 45.4987 1.57079 0.785395 0.618995i \(-0.212460\pi\)
0.785395 + 0.618995i \(0.212460\pi\)
\(840\) 45.7266 1.57772
\(841\) −27.4456 −0.946401
\(842\) 9.60225 0.330915
\(843\) 52.3494 1.80301
\(844\) 1.71704 0.0591028
\(845\) 1.98047 0.0681304
\(846\) −18.6023 −0.639559
\(847\) −14.4846 −0.497698
\(848\) 47.0877 1.61700
\(849\) −41.5763 −1.42690
\(850\) −12.4623 −0.427454
\(851\) −3.58356 −0.122843
\(852\) 136.255 4.66801
\(853\) 17.0490 0.583748 0.291874 0.956457i \(-0.405721\pi\)
0.291874 + 0.956457i \(0.405721\pi\)
\(854\) −37.0919 −1.26926
\(855\) −1.73998 −0.0595060
\(856\) 62.6246 2.14046
\(857\) 12.0689 0.412265 0.206133 0.978524i \(-0.433912\pi\)
0.206133 + 0.978524i \(0.433912\pi\)
\(858\) 6.46023 0.220549
\(859\) 8.47756 0.289251 0.144625 0.989486i \(-0.453802\pi\)
0.144625 + 0.989486i \(0.453802\pi\)
\(860\) 99.3750 3.38866
\(861\) 25.6169 0.873023
\(862\) −52.2127 −1.77837
\(863\) 25.7290 0.875824 0.437912 0.899018i \(-0.355718\pi\)
0.437912 + 0.899018i \(0.355718\pi\)
\(864\) −4.34872 −0.147947
\(865\) 38.5009 1.30907
\(866\) −1.04492 −0.0355077
\(867\) −8.02296 −0.272474
\(868\) −45.9479 −1.55957
\(869\) 0.221726 0.00752153
\(870\) 15.1471 0.513534
\(871\) −11.0843 −0.375578
\(872\) 10.2644 0.347595
\(873\) −3.72057 −0.125922
\(874\) −0.360233 −0.0121851
\(875\) −17.6269 −0.595899
\(876\) 36.1925 1.22283
\(877\) −0.274544 −0.00927070 −0.00463535 0.999989i \(-0.501475\pi\)
−0.00463535 + 0.999989i \(0.501475\pi\)
\(878\) −56.3725 −1.90248
\(879\) −73.8946 −2.49240
\(880\) −16.1542 −0.544560
\(881\) −9.70484 −0.326964 −0.163482 0.986546i \(-0.552273\pi\)
−0.163482 + 0.986546i \(0.552273\pi\)
\(882\) 33.9506 1.14318
\(883\) 29.2003 0.982670 0.491335 0.870971i \(-0.336509\pi\)
0.491335 + 0.870971i \(0.336509\pi\)
\(884\) 20.6173 0.693434
\(885\) −36.6799 −1.23298
\(886\) 9.32105 0.313147
\(887\) 39.5210 1.32699 0.663493 0.748182i \(-0.269073\pi\)
0.663493 + 0.748182i \(0.269073\pi\)
\(888\) 129.477 4.34498
\(889\) 17.1706 0.575885
\(890\) −93.8999 −3.14753
\(891\) 10.2594 0.343703
\(892\) 7.24371 0.242537
\(893\) −0.856826 −0.0286726
\(894\) 0.627655 0.0209919
\(895\) 21.4906 0.718352
\(896\) 13.4541 0.449471
\(897\) −1.04436 −0.0348703
\(898\) −13.6688 −0.456133
\(899\) −8.55951 −0.285476
\(900\) −13.4358 −0.447859
\(901\) −27.4258 −0.913686
\(902\) −19.7293 −0.656914
\(903\) −38.4811 −1.28057
\(904\) 106.681 3.54816
\(905\) −48.0787 −1.59819
\(906\) 82.8191 2.75148
\(907\) 12.8140 0.425482 0.212741 0.977109i \(-0.431761\pi\)
0.212741 + 0.977109i \(0.431761\pi\)
\(908\) −92.7395 −3.07767
\(909\) 6.47678 0.214821
\(910\) 7.43398 0.246434
\(911\) −16.2102 −0.537069 −0.268534 0.963270i \(-0.586539\pi\)
−0.268534 + 0.963270i \(0.586539\pi\)
\(912\) 5.97029 0.197696
\(913\) 10.0807 0.333623
\(914\) 46.3019 1.53153
\(915\) −46.8375 −1.54840
\(916\) −23.7127 −0.783489
\(917\) −24.6672 −0.814582
\(918\) 7.53001 0.248527
\(919\) 51.4103 1.69587 0.847934 0.530101i \(-0.177846\pi\)
0.847934 + 0.530101i \(0.177846\pi\)
\(920\) 5.69322 0.187700
\(921\) −45.5041 −1.49941
\(922\) 45.3932 1.49495
\(923\) 12.4574 0.410041
\(924\) 16.8676 0.554904
\(925\) −8.85050 −0.291003
\(926\) 2.56322 0.0842326
\(927\) −11.1164 −0.365109
\(928\) −8.32594 −0.273312
\(929\) 3.90109 0.127990 0.0639952 0.997950i \(-0.479616\pi\)
0.0639952 + 0.997950i \(0.479616\pi\)
\(930\) −83.4116 −2.73518
\(931\) 1.56378 0.0512507
\(932\) −74.1685 −2.42947
\(933\) 65.8665 2.15637
\(934\) −58.3022 −1.90771
\(935\) 9.40891 0.307704
\(936\) 17.9707 0.587392
\(937\) 25.1619 0.822004 0.411002 0.911634i \(-0.365179\pi\)
0.411002 + 0.911634i \(0.365179\pi\)
\(938\) −41.6066 −1.35850
\(939\) 52.2927 1.70651
\(940\) 24.0793 0.785380
\(941\) 8.97743 0.292656 0.146328 0.989236i \(-0.453255\pi\)
0.146328 + 0.989236i \(0.453255\pi\)
\(942\) 67.4475 2.19756
\(943\) 3.18945 0.103863
\(944\) 59.9397 1.95087
\(945\) 1.88860 0.0614361
\(946\) 29.6369 0.963579
\(947\) −18.3014 −0.594715 −0.297358 0.954766i \(-0.596105\pi\)
−0.297358 + 0.954766i \(0.596105\pi\)
\(948\) 2.30290 0.0747949
\(949\) 3.30899 0.107414
\(950\) −0.889686 −0.0288652
\(951\) 34.6177 1.12256
\(952\) 43.5219 1.41055
\(953\) −43.4432 −1.40726 −0.703632 0.710565i \(-0.748440\pi\)
−0.703632 + 0.710565i \(0.748440\pi\)
\(954\) −42.5079 −1.37624
\(955\) −51.3451 −1.66149
\(956\) −99.2099 −3.20868
\(957\) 3.14223 0.101574
\(958\) −9.52479 −0.307732
\(959\) 3.60456 0.116397
\(960\) −7.70936 −0.248818
\(961\) 16.1354 0.520496
\(962\) 21.0497 0.678671
\(963\) −25.9323 −0.835656
\(964\) 50.4324 1.62432
\(965\) −7.36156 −0.236977
\(966\) −3.92017 −0.126129
\(967\) 23.0283 0.740541 0.370271 0.928924i \(-0.379265\pi\)
0.370271 + 0.928924i \(0.379265\pi\)
\(968\) 65.1592 2.09430
\(969\) −3.47735 −0.111709
\(970\) 6.92363 0.222304
\(971\) −35.2808 −1.13221 −0.566107 0.824331i \(-0.691551\pi\)
−0.566107 + 0.824331i \(0.691551\pi\)
\(972\) 97.6290 3.13145
\(973\) −3.55869 −0.114086
\(974\) −91.5427 −2.93322
\(975\) −2.57932 −0.0826044
\(976\) 76.5385 2.44994
\(977\) −45.9431 −1.46985 −0.734924 0.678149i \(-0.762782\pi\)
−0.734924 + 0.678149i \(0.762782\pi\)
\(978\) −45.8217 −1.46522
\(979\) −19.4793 −0.622562
\(980\) −43.9466 −1.40382
\(981\) −4.25038 −0.135704
\(982\) −9.01269 −0.287607
\(983\) 44.1189 1.40717 0.703586 0.710610i \(-0.251581\pi\)
0.703586 + 0.710610i \(0.251581\pi\)
\(984\) −115.238 −3.67365
\(985\) 30.4790 0.971140
\(986\) 14.4167 0.459123
\(987\) −9.32425 −0.296794
\(988\) 1.47187 0.0468264
\(989\) −4.79112 −0.152349
\(990\) 14.5831 0.463481
\(991\) −17.9541 −0.570329 −0.285165 0.958479i \(-0.592048\pi\)
−0.285165 + 0.958479i \(0.592048\pi\)
\(992\) 45.8492 1.45571
\(993\) −57.3006 −1.81838
\(994\) 46.7607 1.48316
\(995\) 47.4762 1.50510
\(996\) 104.701 3.31758
\(997\) 13.6148 0.431184 0.215592 0.976484i \(-0.430832\pi\)
0.215592 + 0.976484i \(0.430832\pi\)
\(998\) −45.8039 −1.44990
\(999\) 5.34767 0.169193
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 \(a_p\))