Properties

Label 4019.2.a.b.1.10
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.60285 q^{2}\) \(-0.581840 q^{3}\) \(+4.77483 q^{4}\) \(+3.23074 q^{5}\) \(+1.51444 q^{6}\) \(-2.22687 q^{7}\) \(-7.22248 q^{8}\) \(-2.66146 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.60285 q^{2}\) \(-0.581840 q^{3}\) \(+4.77483 q^{4}\) \(+3.23074 q^{5}\) \(+1.51444 q^{6}\) \(-2.22687 q^{7}\) \(-7.22248 q^{8}\) \(-2.66146 q^{9}\) \(-8.40914 q^{10}\) \(+4.03329 q^{11}\) \(-2.77819 q^{12}\) \(-4.71429 q^{13}\) \(+5.79620 q^{14}\) \(-1.87978 q^{15}\) \(+9.24938 q^{16}\) \(-2.68900 q^{17}\) \(+6.92739 q^{18}\) \(+5.82926 q^{19}\) \(+15.4263 q^{20}\) \(+1.29568 q^{21}\) \(-10.4981 q^{22}\) \(-3.12196 q^{23}\) \(+4.20233 q^{24}\) \(+5.43770 q^{25}\) \(+12.2706 q^{26}\) \(+3.29407 q^{27}\) \(-10.6329 q^{28}\) \(+3.30779 q^{29}\) \(+4.89278 q^{30}\) \(-9.01132 q^{31}\) \(-9.62979 q^{32}\) \(-2.34673 q^{33}\) \(+6.99906 q^{34}\) \(-7.19443 q^{35}\) \(-12.7080 q^{36}\) \(+4.13158 q^{37}\) \(-15.1727 q^{38}\) \(+2.74296 q^{39}\) \(-23.3340 q^{40}\) \(+2.52193 q^{41}\) \(-3.37246 q^{42}\) \(-8.22725 q^{43}\) \(+19.2583 q^{44}\) \(-8.59850 q^{45}\) \(+8.12600 q^{46}\) \(+3.83412 q^{47}\) \(-5.38166 q^{48}\) \(-2.04106 q^{49}\) \(-14.1535 q^{50}\) \(+1.56457 q^{51}\) \(-22.5099 q^{52}\) \(-5.42870 q^{53}\) \(-8.57396 q^{54}\) \(+13.0305 q^{55}\) \(+16.0835 q^{56}\) \(-3.39170 q^{57}\) \(-8.60970 q^{58}\) \(+3.04539 q^{59}\) \(-8.97562 q^{60}\) \(+5.32069 q^{61}\) \(+23.4551 q^{62}\) \(+5.92672 q^{63}\) \(+6.56615 q^{64}\) \(-15.2307 q^{65}\) \(+6.10819 q^{66}\) \(-4.67358 q^{67}\) \(-12.8395 q^{68}\) \(+1.81648 q^{69}\) \(+18.7260 q^{70}\) \(+7.47704 q^{71}\) \(+19.2224 q^{72}\) \(+0.456568 q^{73}\) \(-10.7539 q^{74}\) \(-3.16387 q^{75}\) \(+27.8337 q^{76}\) \(-8.98161 q^{77}\) \(-7.13952 q^{78}\) \(+8.71123 q^{79}\) \(+29.8824 q^{80}\) \(+6.06777 q^{81}\) \(-6.56422 q^{82}\) \(+13.8724 q^{83}\) \(+6.18666 q^{84}\) \(-8.68745 q^{85}\) \(+21.4143 q^{86}\) \(-1.92461 q^{87}\) \(-29.1304 q^{88}\) \(-12.9690 q^{89}\) \(+22.3806 q^{90}\) \(+10.4981 q^{91}\) \(-14.9068 q^{92}\) \(+5.24315 q^{93}\) \(-9.97966 q^{94}\) \(+18.8328 q^{95}\) \(+5.60300 q^{96}\) \(+13.8494 q^{97}\) \(+5.31258 q^{98}\) \(-10.7345 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60285 −1.84049 −0.920247 0.391338i \(-0.872012\pi\)
−0.920247 + 0.391338i \(0.872012\pi\)
\(3\) −0.581840 −0.335926 −0.167963 0.985793i \(-0.553719\pi\)
−0.167963 + 0.985793i \(0.553719\pi\)
\(4\) 4.77483 2.38742
\(5\) 3.23074 1.44483 0.722416 0.691459i \(-0.243032\pi\)
0.722416 + 0.691459i \(0.243032\pi\)
\(6\) 1.51444 0.618269
\(7\) −2.22687 −0.841677 −0.420838 0.907136i \(-0.638264\pi\)
−0.420838 + 0.907136i \(0.638264\pi\)
\(8\) −7.22248 −2.55353
\(9\) −2.66146 −0.887154
\(10\) −8.40914 −2.65920
\(11\) 4.03329 1.21608 0.608042 0.793905i \(-0.291955\pi\)
0.608042 + 0.793905i \(0.291955\pi\)
\(12\) −2.77819 −0.801995
\(13\) −4.71429 −1.30751 −0.653754 0.756707i \(-0.726807\pi\)
−0.653754 + 0.756707i \(0.726807\pi\)
\(14\) 5.79620 1.54910
\(15\) −1.87978 −0.485356
\(16\) 9.24938 2.31234
\(17\) −2.68900 −0.652177 −0.326089 0.945339i \(-0.605731\pi\)
−0.326089 + 0.945339i \(0.605731\pi\)
\(18\) 6.92739 1.63280
\(19\) 5.82926 1.33732 0.668661 0.743567i \(-0.266868\pi\)
0.668661 + 0.743567i \(0.266868\pi\)
\(20\) 15.4263 3.44942
\(21\) 1.29568 0.282741
\(22\) −10.4981 −2.23819
\(23\) −3.12196 −0.650974 −0.325487 0.945547i \(-0.605528\pi\)
−0.325487 + 0.945547i \(0.605528\pi\)
\(24\) 4.20233 0.857797
\(25\) 5.43770 1.08754
\(26\) 12.2706 2.40646
\(27\) 3.29407 0.633943
\(28\) −10.6329 −2.00943
\(29\) 3.30779 0.614242 0.307121 0.951670i \(-0.400634\pi\)
0.307121 + 0.951670i \(0.400634\pi\)
\(30\) 4.89278 0.893295
\(31\) −9.01132 −1.61848 −0.809241 0.587477i \(-0.800121\pi\)
−0.809241 + 0.587477i \(0.800121\pi\)
\(32\) −9.62979 −1.70232
\(33\) −2.34673 −0.408514
\(34\) 6.99906 1.20033
\(35\) −7.19443 −1.21608
\(36\) −12.7080 −2.11801
\(37\) 4.13158 0.679228 0.339614 0.940565i \(-0.389704\pi\)
0.339614 + 0.940565i \(0.389704\pi\)
\(38\) −15.1727 −2.46133
\(39\) 2.74296 0.439226
\(40\) −23.3340 −3.68943
\(41\) 2.52193 0.393860 0.196930 0.980418i \(-0.436903\pi\)
0.196930 + 0.980418i \(0.436903\pi\)
\(42\) −3.37246 −0.520383
\(43\) −8.22725 −1.25464 −0.627322 0.778760i \(-0.715849\pi\)
−0.627322 + 0.778760i \(0.715849\pi\)
\(44\) 19.2583 2.90330
\(45\) −8.59850 −1.28179
\(46\) 8.12600 1.19811
\(47\) 3.83412 0.559265 0.279632 0.960107i \(-0.409787\pi\)
0.279632 + 0.960107i \(0.409787\pi\)
\(48\) −5.38166 −0.776776
\(49\) −2.04106 −0.291580
\(50\) −14.1535 −2.00161
\(51\) 1.56457 0.219083
\(52\) −22.5099 −3.12157
\(53\) −5.42870 −0.745689 −0.372844 0.927894i \(-0.621617\pi\)
−0.372844 + 0.927894i \(0.621617\pi\)
\(54\) −8.57396 −1.16677
\(55\) 13.0305 1.75704
\(56\) 16.0835 2.14925
\(57\) −3.39170 −0.449241
\(58\) −8.60970 −1.13051
\(59\) 3.04539 0.396477 0.198238 0.980154i \(-0.436478\pi\)
0.198238 + 0.980154i \(0.436478\pi\)
\(60\) −8.97562 −1.15875
\(61\) 5.32069 0.681245 0.340622 0.940200i \(-0.389362\pi\)
0.340622 + 0.940200i \(0.389362\pi\)
\(62\) 23.4551 2.97881
\(63\) 5.92672 0.746697
\(64\) 6.56615 0.820769
\(65\) −15.2307 −1.88913
\(66\) 6.10819 0.751867
\(67\) −4.67358 −0.570968 −0.285484 0.958383i \(-0.592154\pi\)
−0.285484 + 0.958383i \(0.592154\pi\)
\(68\) −12.8395 −1.55702
\(69\) 1.81648 0.218679
\(70\) 18.7260 2.23819
\(71\) 7.47704 0.887361 0.443680 0.896185i \(-0.353673\pi\)
0.443680 + 0.896185i \(0.353673\pi\)
\(72\) 19.2224 2.26538
\(73\) 0.456568 0.0534372 0.0267186 0.999643i \(-0.491494\pi\)
0.0267186 + 0.999643i \(0.491494\pi\)
\(74\) −10.7539 −1.25011
\(75\) −3.16387 −0.365332
\(76\) 27.8337 3.19275
\(77\) −8.98161 −1.02355
\(78\) −7.13952 −0.808392
\(79\) 8.71123 0.980090 0.490045 0.871697i \(-0.336980\pi\)
0.490045 + 0.871697i \(0.336980\pi\)
\(80\) 29.8824 3.34095
\(81\) 6.06777 0.674196
\(82\) −6.56422 −0.724897
\(83\) 13.8724 1.52269 0.761344 0.648348i \(-0.224540\pi\)
0.761344 + 0.648348i \(0.224540\pi\)
\(84\) 6.18666 0.675020
\(85\) −8.68745 −0.942286
\(86\) 21.4143 2.30916
\(87\) −1.92461 −0.206340
\(88\) −29.1304 −3.10531
\(89\) −12.9690 −1.37471 −0.687355 0.726322i \(-0.741228\pi\)
−0.687355 + 0.726322i \(0.741228\pi\)
\(90\) 22.3806 2.35912
\(91\) 10.4981 1.10050
\(92\) −14.9068 −1.55415
\(93\) 5.24315 0.543689
\(94\) −9.97966 −1.02932
\(95\) 18.8328 1.93221
\(96\) 5.60300 0.571853
\(97\) 13.8494 1.40619 0.703095 0.711096i \(-0.251801\pi\)
0.703095 + 0.711096i \(0.251801\pi\)
\(98\) 5.31258 0.536652
\(99\) −10.7345 −1.07885
\(100\) 25.9641 2.59641
\(101\) 1.37992 0.137307 0.0686537 0.997641i \(-0.478130\pi\)
0.0686537 + 0.997641i \(0.478130\pi\)
\(102\) −4.07233 −0.403221
\(103\) −1.24334 −0.122510 −0.0612552 0.998122i \(-0.519510\pi\)
−0.0612552 + 0.998122i \(0.519510\pi\)
\(104\) 34.0489 3.33877
\(105\) 4.18601 0.408513
\(106\) 14.1301 1.37244
\(107\) 18.3026 1.76938 0.884688 0.466184i \(-0.154371\pi\)
0.884688 + 0.466184i \(0.154371\pi\)
\(108\) 15.7286 1.51349
\(109\) 13.9954 1.34052 0.670259 0.742127i \(-0.266183\pi\)
0.670259 + 0.742127i \(0.266183\pi\)
\(110\) −33.9165 −3.23381
\(111\) −2.40392 −0.228170
\(112\) −20.5971 −1.94625
\(113\) 4.25192 0.399987 0.199994 0.979797i \(-0.435908\pi\)
0.199994 + 0.979797i \(0.435908\pi\)
\(114\) 8.82808 0.826825
\(115\) −10.0863 −0.940548
\(116\) 15.7942 1.46645
\(117\) 12.5469 1.15996
\(118\) −7.92671 −0.729713
\(119\) 5.98804 0.548922
\(120\) 13.5766 1.23937
\(121\) 5.26746 0.478860
\(122\) −13.8490 −1.25383
\(123\) −1.46736 −0.132308
\(124\) −43.0276 −3.86399
\(125\) 1.41408 0.126479
\(126\) −15.4264 −1.37429
\(127\) −4.89422 −0.434292 −0.217146 0.976139i \(-0.569675\pi\)
−0.217146 + 0.976139i \(0.569675\pi\)
\(128\) 2.16886 0.191702
\(129\) 4.78695 0.421467
\(130\) 39.6431 3.47693
\(131\) −3.00785 −0.262797 −0.131399 0.991330i \(-0.541947\pi\)
−0.131399 + 0.991330i \(0.541947\pi\)
\(132\) −11.2053 −0.975293
\(133\) −12.9810 −1.12559
\(134\) 12.1646 1.05086
\(135\) 10.6423 0.915942
\(136\) 19.4212 1.66536
\(137\) −14.1715 −1.21075 −0.605376 0.795939i \(-0.706977\pi\)
−0.605376 + 0.795939i \(0.706977\pi\)
\(138\) −4.72803 −0.402477
\(139\) 18.1021 1.53540 0.767698 0.640812i \(-0.221402\pi\)
0.767698 + 0.640812i \(0.221402\pi\)
\(140\) −34.3522 −2.90329
\(141\) −2.23085 −0.187871
\(142\) −19.4616 −1.63318
\(143\) −19.0141 −1.59004
\(144\) −24.6169 −2.05141
\(145\) 10.6866 0.887476
\(146\) −1.18838 −0.0983509
\(147\) 1.18757 0.0979493
\(148\) 19.7276 1.62160
\(149\) −4.87781 −0.399606 −0.199803 0.979836i \(-0.564030\pi\)
−0.199803 + 0.979836i \(0.564030\pi\)
\(150\) 8.23508 0.672392
\(151\) −6.22854 −0.506871 −0.253436 0.967352i \(-0.581561\pi\)
−0.253436 + 0.967352i \(0.581561\pi\)
\(152\) −42.1017 −3.41490
\(153\) 7.15666 0.578582
\(154\) 23.3778 1.88384
\(155\) −29.1133 −2.33843
\(156\) 13.0972 1.04861
\(157\) 13.4908 1.07668 0.538342 0.842727i \(-0.319051\pi\)
0.538342 + 0.842727i \(0.319051\pi\)
\(158\) −22.6740 −1.80385
\(159\) 3.15863 0.250496
\(160\) −31.1114 −2.45957
\(161\) 6.95219 0.547910
\(162\) −15.7935 −1.24085
\(163\) 8.83059 0.691665 0.345833 0.938296i \(-0.387596\pi\)
0.345833 + 0.938296i \(0.387596\pi\)
\(164\) 12.0418 0.940308
\(165\) −7.58169 −0.590234
\(166\) −36.1077 −2.80250
\(167\) −24.2090 −1.87335 −0.936674 0.350203i \(-0.886113\pi\)
−0.936674 + 0.350203i \(0.886113\pi\)
\(168\) −9.35803 −0.721988
\(169\) 9.22452 0.709578
\(170\) 22.6121 1.73427
\(171\) −15.5143 −1.18641
\(172\) −39.2838 −2.99536
\(173\) 14.8883 1.13193 0.565967 0.824428i \(-0.308503\pi\)
0.565967 + 0.824428i \(0.308503\pi\)
\(174\) 5.00947 0.379767
\(175\) −12.1090 −0.915356
\(176\) 37.3054 2.81200
\(177\) −1.77193 −0.133187
\(178\) 33.7563 2.53014
\(179\) −4.44169 −0.331987 −0.165994 0.986127i \(-0.553083\pi\)
−0.165994 + 0.986127i \(0.553083\pi\)
\(180\) −41.0564 −3.06016
\(181\) 22.8415 1.69779 0.848897 0.528558i \(-0.177267\pi\)
0.848897 + 0.528558i \(0.177267\pi\)
\(182\) −27.3250 −2.02546
\(183\) −3.09579 −0.228848
\(184\) 22.5483 1.66228
\(185\) 13.3481 0.981370
\(186\) −13.6471 −1.00066
\(187\) −10.8455 −0.793102
\(188\) 18.3073 1.33520
\(189\) −7.33545 −0.533575
\(190\) −49.0190 −3.55621
\(191\) −22.7265 −1.64443 −0.822217 0.569174i \(-0.807263\pi\)
−0.822217 + 0.569174i \(0.807263\pi\)
\(192\) −3.82045 −0.275717
\(193\) 5.43609 0.391298 0.195649 0.980674i \(-0.437319\pi\)
0.195649 + 0.980674i \(0.437319\pi\)
\(194\) −36.0478 −2.58808
\(195\) 8.86181 0.634607
\(196\) −9.74574 −0.696124
\(197\) 8.67401 0.617998 0.308999 0.951062i \(-0.400006\pi\)
0.308999 + 0.951062i \(0.400006\pi\)
\(198\) 27.9402 1.98562
\(199\) −0.295069 −0.0209169 −0.0104584 0.999945i \(-0.503329\pi\)
−0.0104584 + 0.999945i \(0.503329\pi\)
\(200\) −39.2737 −2.77707
\(201\) 2.71927 0.191803
\(202\) −3.59173 −0.252713
\(203\) −7.36602 −0.516993
\(204\) 7.47054 0.523043
\(205\) 8.14772 0.569061
\(206\) 3.23624 0.225479
\(207\) 8.30898 0.577514
\(208\) −43.6042 −3.02341
\(209\) 23.5111 1.62630
\(210\) −10.8956 −0.751865
\(211\) 19.1222 1.31643 0.658214 0.752831i \(-0.271312\pi\)
0.658214 + 0.752831i \(0.271312\pi\)
\(212\) −25.9211 −1.78027
\(213\) −4.35044 −0.298087
\(214\) −47.6389 −3.25653
\(215\) −26.5801 −1.81275
\(216\) −23.7913 −1.61880
\(217\) 20.0670 1.36224
\(218\) −36.4280 −2.46722
\(219\) −0.265650 −0.0179509
\(220\) 62.2186 4.19478
\(221\) 12.6767 0.852727
\(222\) 6.25705 0.419945
\(223\) −23.2979 −1.56014 −0.780072 0.625690i \(-0.784818\pi\)
−0.780072 + 0.625690i \(0.784818\pi\)
\(224\) 21.4443 1.43280
\(225\) −14.4722 −0.964815
\(226\) −11.0671 −0.736174
\(227\) −5.74978 −0.381627 −0.190813 0.981626i \(-0.561113\pi\)
−0.190813 + 0.981626i \(0.561113\pi\)
\(228\) −16.1948 −1.07253
\(229\) 0.0805382 0.00532211 0.00266106 0.999996i \(-0.499153\pi\)
0.00266106 + 0.999996i \(0.499153\pi\)
\(230\) 26.2530 1.73107
\(231\) 5.22586 0.343836
\(232\) −23.8905 −1.56849
\(233\) 1.96070 0.128450 0.0642250 0.997935i \(-0.479542\pi\)
0.0642250 + 0.997935i \(0.479542\pi\)
\(234\) −32.6577 −2.13490
\(235\) 12.3871 0.808043
\(236\) 14.5413 0.946555
\(237\) −5.06854 −0.329237
\(238\) −15.5860 −1.01029
\(239\) 30.2860 1.95904 0.979518 0.201358i \(-0.0645353\pi\)
0.979518 + 0.201358i \(0.0645353\pi\)
\(240\) −17.3868 −1.12231
\(241\) 1.44120 0.0928356 0.0464178 0.998922i \(-0.485219\pi\)
0.0464178 + 0.998922i \(0.485219\pi\)
\(242\) −13.7104 −0.881338
\(243\) −13.4127 −0.860423
\(244\) 25.4054 1.62642
\(245\) −6.59415 −0.421285
\(246\) 3.81933 0.243511
\(247\) −27.4808 −1.74856
\(248\) 65.0841 4.13285
\(249\) −8.07149 −0.511510
\(250\) −3.68065 −0.232785
\(251\) −2.99460 −0.189017 −0.0945087 0.995524i \(-0.530128\pi\)
−0.0945087 + 0.995524i \(0.530128\pi\)
\(252\) 28.2991 1.78268
\(253\) −12.5918 −0.791639
\(254\) 12.7389 0.799311
\(255\) 5.05471 0.316538
\(256\) −18.7775 −1.17360
\(257\) 10.6987 0.667368 0.333684 0.942685i \(-0.391708\pi\)
0.333684 + 0.942685i \(0.391708\pi\)
\(258\) −12.4597 −0.775707
\(259\) −9.20048 −0.571690
\(260\) −72.7238 −4.51014
\(261\) −8.80357 −0.544927
\(262\) 7.82899 0.483677
\(263\) 29.3837 1.81188 0.905939 0.423409i \(-0.139167\pi\)
0.905939 + 0.423409i \(0.139167\pi\)
\(264\) 16.9492 1.04315
\(265\) −17.5387 −1.07739
\(266\) 33.7876 2.07165
\(267\) 7.54588 0.461800
\(268\) −22.3156 −1.36314
\(269\) −17.3531 −1.05804 −0.529019 0.848610i \(-0.677440\pi\)
−0.529019 + 0.848610i \(0.677440\pi\)
\(270\) −27.7003 −1.68578
\(271\) 15.3610 0.933116 0.466558 0.884491i \(-0.345494\pi\)
0.466558 + 0.884491i \(0.345494\pi\)
\(272\) −24.8715 −1.50806
\(273\) −6.10821 −0.369686
\(274\) 36.8863 2.22838
\(275\) 21.9318 1.32254
\(276\) 8.67340 0.522078
\(277\) 26.8801 1.61507 0.807533 0.589822i \(-0.200802\pi\)
0.807533 + 0.589822i \(0.200802\pi\)
\(278\) −47.1170 −2.82589
\(279\) 23.9833 1.43584
\(280\) 51.9617 3.10530
\(281\) −10.1136 −0.603329 −0.301664 0.953414i \(-0.597542\pi\)
−0.301664 + 0.953414i \(0.597542\pi\)
\(282\) 5.80657 0.345776
\(283\) −11.9043 −0.707637 −0.353819 0.935314i \(-0.615117\pi\)
−0.353819 + 0.935314i \(0.615117\pi\)
\(284\) 35.7016 2.11850
\(285\) −10.9577 −0.649078
\(286\) 49.4909 2.92646
\(287\) −5.61601 −0.331503
\(288\) 25.6293 1.51022
\(289\) −9.76930 −0.574665
\(290\) −27.8157 −1.63339
\(291\) −8.05812 −0.472375
\(292\) 2.18004 0.127577
\(293\) −5.53789 −0.323527 −0.161764 0.986830i \(-0.551718\pi\)
−0.161764 + 0.986830i \(0.551718\pi\)
\(294\) −3.09107 −0.180275
\(295\) 9.83889 0.572842
\(296\) −29.8403 −1.73443
\(297\) 13.2859 0.770928
\(298\) 12.6962 0.735472
\(299\) 14.7178 0.851154
\(300\) −15.1070 −0.872200
\(301\) 18.3210 1.05600
\(302\) 16.2120 0.932894
\(303\) −0.802894 −0.0461251
\(304\) 53.9170 3.09235
\(305\) 17.1898 0.984284
\(306\) −18.6277 −1.06488
\(307\) −21.6036 −1.23298 −0.616491 0.787362i \(-0.711446\pi\)
−0.616491 + 0.787362i \(0.711446\pi\)
\(308\) −42.8857 −2.44364
\(309\) 0.723427 0.0411543
\(310\) 75.7775 4.30387
\(311\) 3.07867 0.174575 0.0872877 0.996183i \(-0.472180\pi\)
0.0872877 + 0.996183i \(0.472180\pi\)
\(312\) −19.8110 −1.12158
\(313\) 20.8198 1.17680 0.588401 0.808569i \(-0.299758\pi\)
0.588401 + 0.808569i \(0.299758\pi\)
\(314\) −35.1146 −1.98163
\(315\) 19.1477 1.07885
\(316\) 41.5947 2.33988
\(317\) −18.8171 −1.05688 −0.528438 0.848972i \(-0.677222\pi\)
−0.528438 + 0.848972i \(0.677222\pi\)
\(318\) −8.22145 −0.461036
\(319\) 13.3413 0.746970
\(320\) 21.2135 1.18587
\(321\) −10.6492 −0.594379
\(322\) −18.0955 −1.00842
\(323\) −15.6748 −0.872172
\(324\) 28.9726 1.60959
\(325\) −25.6349 −1.42197
\(326\) −22.9847 −1.27301
\(327\) −8.14310 −0.450315
\(328\) −18.2146 −1.00573
\(329\) −8.53809 −0.470720
\(330\) 19.7340 1.08632
\(331\) −23.4155 −1.28703 −0.643515 0.765434i \(-0.722525\pi\)
−0.643515 + 0.765434i \(0.722525\pi\)
\(332\) 66.2382 3.63529
\(333\) −10.9960 −0.602580
\(334\) 63.0124 3.44788
\(335\) −15.0991 −0.824953
\(336\) 11.9842 0.653794
\(337\) 9.52740 0.518991 0.259495 0.965744i \(-0.416444\pi\)
0.259495 + 0.965744i \(0.416444\pi\)
\(338\) −24.0101 −1.30597
\(339\) −2.47394 −0.134366
\(340\) −41.4811 −2.24963
\(341\) −36.3453 −1.96821
\(342\) 40.3815 2.18358
\(343\) 20.1332 1.08709
\(344\) 59.4212 3.20377
\(345\) 5.86859 0.315954
\(346\) −38.7519 −2.08332
\(347\) 23.8554 1.28063 0.640313 0.768114i \(-0.278805\pi\)
0.640313 + 0.768114i \(0.278805\pi\)
\(348\) −9.18968 −0.492619
\(349\) 6.10555 0.326823 0.163411 0.986558i \(-0.447750\pi\)
0.163411 + 0.986558i \(0.447750\pi\)
\(350\) 31.5180 1.68471
\(351\) −15.5292 −0.828886
\(352\) −38.8398 −2.07017
\(353\) −13.5805 −0.722817 −0.361408 0.932408i \(-0.617704\pi\)
−0.361408 + 0.932408i \(0.617704\pi\)
\(354\) 4.61208 0.245129
\(355\) 24.1564 1.28209
\(356\) −61.9248 −3.28201
\(357\) −3.48408 −0.184397
\(358\) 11.5611 0.611021
\(359\) −20.4483 −1.07922 −0.539610 0.841915i \(-0.681428\pi\)
−0.539610 + 0.841915i \(0.681428\pi\)
\(360\) 62.1025 3.27309
\(361\) 14.9802 0.788433
\(362\) −59.4530 −3.12478
\(363\) −3.06482 −0.160861
\(364\) 50.1267 2.62735
\(365\) 1.47505 0.0772078
\(366\) 8.05789 0.421193
\(367\) 27.7405 1.44804 0.724021 0.689778i \(-0.242292\pi\)
0.724021 + 0.689778i \(0.242292\pi\)
\(368\) −28.8762 −1.50528
\(369\) −6.71203 −0.349414
\(370\) −34.7430 −1.80621
\(371\) 12.0890 0.627629
\(372\) 25.0352 1.29801
\(373\) 15.4342 0.799153 0.399577 0.916700i \(-0.369157\pi\)
0.399577 + 0.916700i \(0.369157\pi\)
\(374\) 28.2292 1.45970
\(375\) −0.822770 −0.0424877
\(376\) −27.6919 −1.42810
\(377\) −15.5939 −0.803127
\(378\) 19.0931 0.982042
\(379\) −13.4640 −0.691597 −0.345798 0.938309i \(-0.612392\pi\)
−0.345798 + 0.938309i \(0.612392\pi\)
\(380\) 89.9236 4.61298
\(381\) 2.84765 0.145890
\(382\) 59.1538 3.02657
\(383\) 24.5086 1.25233 0.626166 0.779690i \(-0.284623\pi\)
0.626166 + 0.779690i \(0.284623\pi\)
\(384\) −1.26193 −0.0643976
\(385\) −29.0173 −1.47886
\(386\) −14.1493 −0.720182
\(387\) 21.8965 1.11306
\(388\) 66.1284 3.35716
\(389\) 27.5094 1.39478 0.697391 0.716691i \(-0.254344\pi\)
0.697391 + 0.716691i \(0.254344\pi\)
\(390\) −23.0660 −1.16799
\(391\) 8.39494 0.424550
\(392\) 14.7415 0.744560
\(393\) 1.75009 0.0882803
\(394\) −22.5772 −1.13742
\(395\) 28.1437 1.41607
\(396\) −51.2553 −2.57567
\(397\) 12.2939 0.617011 0.308506 0.951223i \(-0.400171\pi\)
0.308506 + 0.951223i \(0.400171\pi\)
\(398\) 0.768020 0.0384974
\(399\) 7.55285 0.378116
\(400\) 50.2953 2.51476
\(401\) 23.5370 1.17538 0.587692 0.809085i \(-0.300037\pi\)
0.587692 + 0.809085i \(0.300037\pi\)
\(402\) −7.07787 −0.353012
\(403\) 42.4820 2.11618
\(404\) 6.58890 0.327810
\(405\) 19.6034 0.974100
\(406\) 19.1726 0.951523
\(407\) 16.6639 0.825998
\(408\) −11.3000 −0.559436
\(409\) 34.6341 1.71255 0.856273 0.516523i \(-0.172774\pi\)
0.856273 + 0.516523i \(0.172774\pi\)
\(410\) −21.2073 −1.04735
\(411\) 8.24555 0.406723
\(412\) −5.93676 −0.292483
\(413\) −6.78169 −0.333705
\(414\) −21.6270 −1.06291
\(415\) 44.8180 2.20003
\(416\) 45.3976 2.22580
\(417\) −10.5325 −0.515779
\(418\) −61.1959 −2.99319
\(419\) −17.9310 −0.875986 −0.437993 0.898978i \(-0.644311\pi\)
−0.437993 + 0.898978i \(0.644311\pi\)
\(420\) 19.9875 0.975291
\(421\) 33.4713 1.63129 0.815645 0.578553i \(-0.196383\pi\)
0.815645 + 0.578553i \(0.196383\pi\)
\(422\) −49.7723 −2.42288
\(423\) −10.2044 −0.496154
\(424\) 39.2087 1.90414
\(425\) −14.6219 −0.709268
\(426\) 11.3235 0.548628
\(427\) −11.8485 −0.573388
\(428\) 87.3917 4.22424
\(429\) 11.0632 0.534135
\(430\) 69.1841 3.33635
\(431\) −19.4577 −0.937246 −0.468623 0.883398i \(-0.655250\pi\)
−0.468623 + 0.883398i \(0.655250\pi\)
\(432\) 30.4681 1.46590
\(433\) 14.3230 0.688318 0.344159 0.938911i \(-0.388164\pi\)
0.344159 + 0.938911i \(0.388164\pi\)
\(434\) −52.2315 −2.50719
\(435\) −6.21791 −0.298126
\(436\) 66.8259 3.20038
\(437\) −18.1987 −0.870562
\(438\) 0.691446 0.0330386
\(439\) 13.2270 0.631291 0.315645 0.948877i \(-0.397779\pi\)
0.315645 + 0.948877i \(0.397779\pi\)
\(440\) −94.1128 −4.48665
\(441\) 5.43221 0.258677
\(442\) −32.9956 −1.56944
\(443\) −8.59899 −0.408550 −0.204275 0.978914i \(-0.565484\pi\)
−0.204275 + 0.978914i \(0.565484\pi\)
\(444\) −11.4783 −0.544737
\(445\) −41.8995 −1.98622
\(446\) 60.6410 2.87144
\(447\) 2.83811 0.134238
\(448\) −14.6219 −0.690822
\(449\) −28.0592 −1.32419 −0.662097 0.749418i \(-0.730333\pi\)
−0.662097 + 0.749418i \(0.730333\pi\)
\(450\) 37.6690 1.77574
\(451\) 10.1717 0.478967
\(452\) 20.3022 0.954936
\(453\) 3.62401 0.170271
\(454\) 14.9658 0.702381
\(455\) 33.9166 1.59004
\(456\) 24.4965 1.14715
\(457\) 32.9619 1.54189 0.770945 0.636901i \(-0.219784\pi\)
0.770945 + 0.636901i \(0.219784\pi\)
\(458\) −0.209629 −0.00979531
\(459\) −8.85773 −0.413443
\(460\) −48.1602 −2.24548
\(461\) −17.9855 −0.837667 −0.418834 0.908063i \(-0.637561\pi\)
−0.418834 + 0.908063i \(0.637561\pi\)
\(462\) −13.6021 −0.632829
\(463\) 33.0169 1.53443 0.767213 0.641393i \(-0.221643\pi\)
0.767213 + 0.641393i \(0.221643\pi\)
\(464\) 30.5950 1.42034
\(465\) 16.9393 0.785540
\(466\) −5.10342 −0.236411
\(467\) 22.4296 1.03792 0.518958 0.854800i \(-0.326320\pi\)
0.518958 + 0.854800i \(0.326320\pi\)
\(468\) 59.9094 2.76931
\(469\) 10.4074 0.480571
\(470\) −32.2417 −1.48720
\(471\) −7.84949 −0.361686
\(472\) −21.9953 −1.01242
\(473\) −33.1829 −1.52575
\(474\) 13.1927 0.605959
\(475\) 31.6977 1.45439
\(476\) 28.5919 1.31051
\(477\) 14.4483 0.661541
\(478\) −78.8298 −3.60559
\(479\) 7.54402 0.344695 0.172347 0.985036i \(-0.444865\pi\)
0.172347 + 0.985036i \(0.444865\pi\)
\(480\) 18.1018 0.826232
\(481\) −19.4775 −0.888096
\(482\) −3.75122 −0.170863
\(483\) −4.04507 −0.184057
\(484\) 25.1512 1.14324
\(485\) 44.7437 2.03171
\(486\) 34.9112 1.58360
\(487\) −41.5037 −1.88071 −0.940355 0.340193i \(-0.889507\pi\)
−0.940355 + 0.340193i \(0.889507\pi\)
\(488\) −38.4286 −1.73958
\(489\) −5.13799 −0.232348
\(490\) 17.1636 0.775372
\(491\) −2.05169 −0.0925913 −0.0462957 0.998928i \(-0.514742\pi\)
−0.0462957 + 0.998928i \(0.514742\pi\)
\(492\) −7.00641 −0.315874
\(493\) −8.89464 −0.400595
\(494\) 71.5284 3.21822
\(495\) −34.6803 −1.55876
\(496\) −83.3491 −3.74249
\(497\) −16.6504 −0.746871
\(498\) 21.0089 0.941431
\(499\) −17.7304 −0.793721 −0.396861 0.917879i \(-0.629900\pi\)
−0.396861 + 0.917879i \(0.629900\pi\)
\(500\) 6.75201 0.301959
\(501\) 14.0858 0.629305
\(502\) 7.79450 0.347885
\(503\) 16.2304 0.723678 0.361839 0.932241i \(-0.382149\pi\)
0.361839 + 0.932241i \(0.382149\pi\)
\(504\) −42.8056 −1.90671
\(505\) 4.45817 0.198386
\(506\) 32.7745 1.45701
\(507\) −5.36720 −0.238366
\(508\) −23.3691 −1.03684
\(509\) −16.6480 −0.737909 −0.368955 0.929447i \(-0.620284\pi\)
−0.368955 + 0.929447i \(0.620284\pi\)
\(510\) −13.1567 −0.582586
\(511\) −1.01672 −0.0449769
\(512\) 44.5374 1.96829
\(513\) 19.2020 0.847787
\(514\) −27.8472 −1.22829
\(515\) −4.01692 −0.177007
\(516\) 22.8569 1.00622
\(517\) 15.4642 0.680113
\(518\) 23.9475 1.05219
\(519\) −8.66259 −0.380246
\(520\) 110.003 4.82396
\(521\) 14.9806 0.656311 0.328156 0.944624i \(-0.393573\pi\)
0.328156 + 0.944624i \(0.393573\pi\)
\(522\) 22.9144 1.00294
\(523\) −27.7237 −1.21227 −0.606137 0.795360i \(-0.707282\pi\)
−0.606137 + 0.795360i \(0.707282\pi\)
\(524\) −14.3620 −0.627407
\(525\) 7.04552 0.307492
\(526\) −76.4814 −3.33475
\(527\) 24.2314 1.05554
\(528\) −21.7058 −0.944624
\(529\) −13.2534 −0.576233
\(530\) 45.6507 1.98294
\(531\) −8.10520 −0.351736
\(532\) −61.9820 −2.68726
\(533\) −11.8891 −0.514975
\(534\) −19.6408 −0.849940
\(535\) 59.1309 2.55645
\(536\) 33.7548 1.45799
\(537\) 2.58435 0.111523
\(538\) 45.1676 1.94731
\(539\) −8.23220 −0.354586
\(540\) 50.8151 2.18673
\(541\) 23.0589 0.991379 0.495689 0.868500i \(-0.334915\pi\)
0.495689 + 0.868500i \(0.334915\pi\)
\(542\) −39.9825 −1.71739
\(543\) −13.2901 −0.570333
\(544\) 25.8945 1.11022
\(545\) 45.2156 1.93682
\(546\) 15.8988 0.680405
\(547\) −25.6204 −1.09545 −0.547725 0.836658i \(-0.684506\pi\)
−0.547725 + 0.836658i \(0.684506\pi\)
\(548\) −67.6666 −2.89057
\(549\) −14.1608 −0.604369
\(550\) −57.0853 −2.43412
\(551\) 19.2820 0.821440
\(552\) −13.1195 −0.558404
\(553\) −19.3988 −0.824919
\(554\) −69.9648 −2.97252
\(555\) −7.76645 −0.329667
\(556\) 86.4343 3.66563
\(557\) 27.1151 1.14890 0.574452 0.818538i \(-0.305215\pi\)
0.574452 + 0.818538i \(0.305215\pi\)
\(558\) −62.4250 −2.64266
\(559\) 38.7856 1.64046
\(560\) −66.5440 −2.81200
\(561\) 6.31035 0.266423
\(562\) 26.3243 1.11042
\(563\) −40.4603 −1.70520 −0.852599 0.522566i \(-0.824975\pi\)
−0.852599 + 0.522566i \(0.824975\pi\)
\(564\) −10.6519 −0.448527
\(565\) 13.7369 0.577914
\(566\) 30.9851 1.30240
\(567\) −13.5121 −0.567455
\(568\) −54.0028 −2.26591
\(569\) 20.1464 0.844583 0.422291 0.906460i \(-0.361226\pi\)
0.422291 + 0.906460i \(0.361226\pi\)
\(570\) 28.5212 1.19462
\(571\) −27.3543 −1.14474 −0.572372 0.819994i \(-0.693977\pi\)
−0.572372 + 0.819994i \(0.693977\pi\)
\(572\) −90.7892 −3.79609
\(573\) 13.2232 0.552407
\(574\) 14.6176 0.610129
\(575\) −16.9763 −0.707960
\(576\) −17.4756 −0.728148
\(577\) 34.8432 1.45054 0.725270 0.688464i \(-0.241715\pi\)
0.725270 + 0.688464i \(0.241715\pi\)
\(578\) 25.4280 1.05767
\(579\) −3.16293 −0.131447
\(580\) 51.0269 2.11878
\(581\) −30.8919 −1.28161
\(582\) 20.9741 0.869404
\(583\) −21.8955 −0.906820
\(584\) −3.29755 −0.136454
\(585\) 40.5358 1.67595
\(586\) 14.4143 0.595450
\(587\) −17.0271 −0.702783 −0.351392 0.936229i \(-0.614291\pi\)
−0.351392 + 0.936229i \(0.614291\pi\)
\(588\) 5.67046 0.233846
\(589\) −52.5293 −2.16443
\(590\) −25.6092 −1.05431
\(591\) −5.04689 −0.207601
\(592\) 38.2145 1.57061
\(593\) −22.8666 −0.939018 −0.469509 0.882928i \(-0.655569\pi\)
−0.469509 + 0.882928i \(0.655569\pi\)
\(594\) −34.5813 −1.41889
\(595\) 19.3458 0.793100
\(596\) −23.2907 −0.954026
\(597\) 0.171683 0.00702651
\(598\) −38.3083 −1.56654
\(599\) 20.6924 0.845471 0.422735 0.906253i \(-0.361070\pi\)
0.422735 + 0.906253i \(0.361070\pi\)
\(600\) 22.8510 0.932888
\(601\) −22.5292 −0.918984 −0.459492 0.888182i \(-0.651969\pi\)
−0.459492 + 0.888182i \(0.651969\pi\)
\(602\) −47.6868 −1.94357
\(603\) 12.4385 0.506537
\(604\) −29.7402 −1.21011
\(605\) 17.0178 0.691872
\(606\) 2.08981 0.0848929
\(607\) −44.0656 −1.78857 −0.894284 0.447500i \(-0.852314\pi\)
−0.894284 + 0.447500i \(0.852314\pi\)
\(608\) −56.1345 −2.27655
\(609\) 4.28585 0.173671
\(610\) −44.7425 −1.81157
\(611\) −18.0752 −0.731243
\(612\) 34.1719 1.38132
\(613\) 17.2550 0.696922 0.348461 0.937323i \(-0.386704\pi\)
0.348461 + 0.937323i \(0.386704\pi\)
\(614\) 56.2309 2.26930
\(615\) −4.74067 −0.191162
\(616\) 64.8695 2.61367
\(617\) 30.1514 1.21385 0.606925 0.794759i \(-0.292403\pi\)
0.606925 + 0.794759i \(0.292403\pi\)
\(618\) −1.88297 −0.0757443
\(619\) −14.4811 −0.582044 −0.291022 0.956716i \(-0.593995\pi\)
−0.291022 + 0.956716i \(0.593995\pi\)
\(620\) −139.011 −5.58282
\(621\) −10.2839 −0.412681
\(622\) −8.01333 −0.321305
\(623\) 28.8802 1.15706
\(624\) 25.3707 1.01564
\(625\) −22.6199 −0.904798
\(626\) −54.1907 −2.16590
\(627\) −13.6797 −0.546315
\(628\) 64.4164 2.57049
\(629\) −11.1098 −0.442977
\(630\) −49.8386 −1.98562
\(631\) 19.6561 0.782498 0.391249 0.920285i \(-0.372043\pi\)
0.391249 + 0.920285i \(0.372043\pi\)
\(632\) −62.9167 −2.50269
\(633\) −11.1261 −0.442222
\(634\) 48.9782 1.94517
\(635\) −15.8120 −0.627479
\(636\) 15.0819 0.598038
\(637\) 9.62216 0.381244
\(638\) −34.7254 −1.37479
\(639\) −19.8998 −0.787226
\(640\) 7.00703 0.276977
\(641\) 1.05505 0.0416721 0.0208361 0.999783i \(-0.493367\pi\)
0.0208361 + 0.999783i \(0.493367\pi\)
\(642\) 27.7182 1.09395
\(643\) 31.2750 1.23336 0.616682 0.787212i \(-0.288476\pi\)
0.616682 + 0.787212i \(0.288476\pi\)
\(644\) 33.1956 1.30809
\(645\) 15.4654 0.608949
\(646\) 40.7993 1.60523
\(647\) 26.8238 1.05455 0.527275 0.849694i \(-0.323214\pi\)
0.527275 + 0.849694i \(0.323214\pi\)
\(648\) −43.8243 −1.72158
\(649\) 12.2830 0.482149
\(650\) 66.7238 2.61712
\(651\) −11.6758 −0.457611
\(652\) 42.1646 1.65129
\(653\) −5.67564 −0.222105 −0.111053 0.993815i \(-0.535422\pi\)
−0.111053 + 0.993815i \(0.535422\pi\)
\(654\) 21.1953 0.828801
\(655\) −9.71759 −0.379698
\(656\) 23.3263 0.910740
\(657\) −1.21514 −0.0474070
\(658\) 22.2234 0.866357
\(659\) −9.04844 −0.352477 −0.176239 0.984347i \(-0.556393\pi\)
−0.176239 + 0.984347i \(0.556393\pi\)
\(660\) −36.2013 −1.40913
\(661\) −3.69108 −0.143566 −0.0717831 0.997420i \(-0.522869\pi\)
−0.0717831 + 0.997420i \(0.522869\pi\)
\(662\) 60.9470 2.36877
\(663\) −7.37581 −0.286453
\(664\) −100.193 −3.88824
\(665\) −41.9382 −1.62629
\(666\) 28.6211 1.10904
\(667\) −10.3268 −0.399855
\(668\) −115.594 −4.47246
\(669\) 13.5557 0.524092
\(670\) 39.3008 1.51832
\(671\) 21.4599 0.828451
\(672\) −12.4771 −0.481316
\(673\) 0.0110551 0.000426142 0 0.000213071 1.00000i \(-0.499932\pi\)
0.000213071 1.00000i \(0.499932\pi\)
\(674\) −24.7984 −0.955199
\(675\) 17.9121 0.689438
\(676\) 44.0456 1.69406
\(677\) −8.81460 −0.338773 −0.169386 0.985550i \(-0.554179\pi\)
−0.169386 + 0.985550i \(0.554179\pi\)
\(678\) 6.43929 0.247300
\(679\) −30.8407 −1.18356
\(680\) 62.7450 2.40616
\(681\) 3.34546 0.128198
\(682\) 94.6014 3.62248
\(683\) −22.2786 −0.852467 −0.426233 0.904613i \(-0.640160\pi\)
−0.426233 + 0.904613i \(0.640160\pi\)
\(684\) −74.0784 −2.83246
\(685\) −45.7845 −1.74933
\(686\) −52.4038 −2.00079
\(687\) −0.0468603 −0.00178783
\(688\) −76.0969 −2.90117
\(689\) 25.5924 0.974994
\(690\) −15.2751 −0.581512
\(691\) 38.5630 1.46700 0.733502 0.679687i \(-0.237885\pi\)
0.733502 + 0.679687i \(0.237885\pi\)
\(692\) 71.0890 2.70240
\(693\) 23.9042 0.908046
\(694\) −62.0921 −2.35698
\(695\) 58.4831 2.21839
\(696\) 13.9004 0.526895
\(697\) −6.78147 −0.256867
\(698\) −15.8918 −0.601515
\(699\) −1.14082 −0.0431497
\(700\) −57.8186 −2.18534
\(701\) 17.1364 0.647231 0.323616 0.946189i \(-0.395102\pi\)
0.323616 + 0.946189i \(0.395102\pi\)
\(702\) 40.4201 1.52556
\(703\) 24.0840 0.908347
\(704\) 26.4832 0.998124
\(705\) −7.20729 −0.271442
\(706\) 35.3480 1.33034
\(707\) −3.07290 −0.115568
\(708\) −8.46069 −0.317972
\(709\) 22.3435 0.839128 0.419564 0.907726i \(-0.362183\pi\)
0.419564 + 0.907726i \(0.362183\pi\)
\(710\) −62.8754 −2.35967
\(711\) −23.1846 −0.869491
\(712\) 93.6683 3.51037
\(713\) 28.1330 1.05359
\(714\) 9.06854 0.339382
\(715\) −61.4297 −2.29734
\(716\) −21.2083 −0.792592
\(717\) −17.6216 −0.658090
\(718\) 53.2239 1.98630
\(719\) 10.0020 0.373011 0.186505 0.982454i \(-0.440284\pi\)
0.186505 + 0.982454i \(0.440284\pi\)
\(720\) −79.5307 −2.96394
\(721\) 2.76876 0.103114
\(722\) −38.9913 −1.45111
\(723\) −0.838546 −0.0311859
\(724\) 109.064 4.05334
\(725\) 17.9868 0.668012
\(726\) 7.97726 0.296064
\(727\) 38.9666 1.44519 0.722595 0.691271i \(-0.242949\pi\)
0.722595 + 0.691271i \(0.242949\pi\)
\(728\) −75.8223 −2.81016
\(729\) −10.3993 −0.385158
\(730\) −3.83934 −0.142100
\(731\) 22.1230 0.818250
\(732\) −14.7819 −0.546355
\(733\) 26.4891 0.978399 0.489199 0.872172i \(-0.337289\pi\)
0.489199 + 0.872172i \(0.337289\pi\)
\(734\) −72.2044 −2.66511
\(735\) 3.83674 0.141520
\(736\) 30.0638 1.10817
\(737\) −18.8499 −0.694345
\(738\) 17.4704 0.643095
\(739\) 9.04353 0.332672 0.166336 0.986069i \(-0.446806\pi\)
0.166336 + 0.986069i \(0.446806\pi\)
\(740\) 63.7348 2.34294
\(741\) 15.9894 0.587386
\(742\) −31.4658 −1.15515
\(743\) 8.83323 0.324060 0.162030 0.986786i \(-0.448196\pi\)
0.162030 + 0.986786i \(0.448196\pi\)
\(744\) −37.8686 −1.38833
\(745\) −15.7590 −0.577363
\(746\) −40.1730 −1.47084
\(747\) −36.9207 −1.35086
\(748\) −51.7855 −1.89347
\(749\) −40.7574 −1.48924
\(750\) 2.14155 0.0781983
\(751\) −8.64589 −0.315493 −0.157747 0.987480i \(-0.550423\pi\)
−0.157747 + 0.987480i \(0.550423\pi\)
\(752\) 35.4633 1.29321
\(753\) 1.74238 0.0634958
\(754\) 40.5886 1.47815
\(755\) −20.1228 −0.732344
\(756\) −35.0255 −1.27387
\(757\) 12.6187 0.458634 0.229317 0.973352i \(-0.426351\pi\)
0.229317 + 0.973352i \(0.426351\pi\)
\(758\) 35.0447 1.27288
\(759\) 7.32641 0.265932
\(760\) −136.020 −4.93395
\(761\) 19.4618 0.705488 0.352744 0.935720i \(-0.385249\pi\)
0.352744 + 0.935720i \(0.385249\pi\)
\(762\) −7.41202 −0.268509
\(763\) −31.1660 −1.12828
\(764\) −108.515 −3.92595
\(765\) 23.1213 0.835953
\(766\) −63.7923 −2.30491
\(767\) −14.3569 −0.518397
\(768\) 10.9255 0.394241
\(769\) 6.06539 0.218723 0.109362 0.994002i \(-0.465119\pi\)
0.109362 + 0.994002i \(0.465119\pi\)
\(770\) 75.5276 2.72183
\(771\) −6.22495 −0.224186
\(772\) 25.9564 0.934192
\(773\) −14.7377 −0.530079 −0.265040 0.964238i \(-0.585385\pi\)
−0.265040 + 0.964238i \(0.585385\pi\)
\(774\) −56.9934 −2.04858
\(775\) −49.0008 −1.76016
\(776\) −100.027 −3.59075
\(777\) 5.35321 0.192045
\(778\) −71.6028 −2.56709
\(779\) 14.7010 0.526718
\(780\) 42.3137 1.51507
\(781\) 30.1571 1.07911
\(782\) −21.8508 −0.781382
\(783\) 10.8961 0.389395
\(784\) −18.8786 −0.674234
\(785\) 43.5853 1.55563
\(786\) −4.55522 −0.162479
\(787\) −39.3387 −1.40227 −0.701136 0.713027i \(-0.747324\pi\)
−0.701136 + 0.713027i \(0.747324\pi\)
\(788\) 41.4170 1.47542
\(789\) −17.0966 −0.608656
\(790\) −73.2540 −2.60626
\(791\) −9.46846 −0.336660
\(792\) 77.5294 2.75489
\(793\) −25.0833 −0.890734
\(794\) −31.9991 −1.13561
\(795\) 10.2047 0.361924
\(796\) −1.40890 −0.0499373
\(797\) −12.2574 −0.434178 −0.217089 0.976152i \(-0.569656\pi\)
−0.217089 + 0.976152i \(0.569656\pi\)
\(798\) −19.6590 −0.695919
\(799\) −10.3099 −0.364740
\(800\) −52.3639 −1.85134
\(801\) 34.5165 1.21958
\(802\) −61.2634 −2.16329
\(803\) 1.84147 0.0649841
\(804\) 12.9841 0.457913
\(805\) 22.4607 0.791637
\(806\) −110.574 −3.89481
\(807\) 10.0967 0.355422
\(808\) −9.96647 −0.350619
\(809\) 14.4996 0.509780 0.254890 0.966970i \(-0.417961\pi\)
0.254890 + 0.966970i \(0.417961\pi\)
\(810\) −51.0247 −1.79283
\(811\) 34.0733 1.19647 0.598237 0.801319i \(-0.295868\pi\)
0.598237 + 0.801319i \(0.295868\pi\)
\(812\) −35.1715 −1.23428
\(813\) −8.93766 −0.313458
\(814\) −43.3736 −1.52024
\(815\) 28.5294 0.999340
\(816\) 14.4713 0.506595
\(817\) −47.9587 −1.67786
\(818\) −90.1475 −3.15193
\(819\) −27.9403 −0.976312
\(820\) 38.9040 1.35859
\(821\) −42.4020 −1.47984 −0.739920 0.672695i \(-0.765137\pi\)
−0.739920 + 0.672695i \(0.765137\pi\)
\(822\) −21.4619 −0.748571
\(823\) 28.5204 0.994160 0.497080 0.867705i \(-0.334406\pi\)
0.497080 + 0.867705i \(0.334406\pi\)
\(824\) 8.98003 0.312834
\(825\) −12.7608 −0.444275
\(826\) 17.6517 0.614182
\(827\) −51.4704 −1.78980 −0.894901 0.446266i \(-0.852754\pi\)
−0.894901 + 0.446266i \(0.852754\pi\)
\(828\) 39.6740 1.37877
\(829\) 51.5474 1.79032 0.895158 0.445748i \(-0.147062\pi\)
0.895158 + 0.445748i \(0.147062\pi\)
\(830\) −116.655 −4.04914
\(831\) −15.6399 −0.542542
\(832\) −30.9547 −1.07316
\(833\) 5.48841 0.190162
\(834\) 27.4145 0.949288
\(835\) −78.2130 −2.70667
\(836\) 112.262 3.88265
\(837\) −29.6839 −1.02603
\(838\) 46.6717 1.61225
\(839\) 21.7819 0.751995 0.375998 0.926621i \(-0.377300\pi\)
0.375998 + 0.926621i \(0.377300\pi\)
\(840\) −30.2334 −1.04315
\(841\) −18.0585 −0.622707
\(842\) −87.1207 −3.00238
\(843\) 5.88452 0.202674
\(844\) 91.3054 3.14286
\(845\) 29.8020 1.02522
\(846\) 26.5605 0.913168
\(847\) −11.7299 −0.403045
\(848\) −50.2120 −1.72429
\(849\) 6.92640 0.237713
\(850\) 38.0587 1.30540
\(851\) −12.8986 −0.442160
\(852\) −20.7726 −0.711659
\(853\) 11.5969 0.397071 0.198535 0.980094i \(-0.436381\pi\)
0.198535 + 0.980094i \(0.436381\pi\)
\(854\) 30.8398 1.05532
\(855\) −50.1228 −1.71416
\(856\) −132.190 −4.51816
\(857\) 33.3487 1.13917 0.569584 0.821933i \(-0.307104\pi\)
0.569584 + 0.821933i \(0.307104\pi\)
\(858\) −28.7958 −0.983072
\(859\) 1.56628 0.0534409 0.0267205 0.999643i \(-0.491494\pi\)
0.0267205 + 0.999643i \(0.491494\pi\)
\(860\) −126.916 −4.32779
\(861\) 3.26762 0.111360
\(862\) 50.6456 1.72500
\(863\) 44.0570 1.49972 0.749859 0.661598i \(-0.230122\pi\)
0.749859 + 0.661598i \(0.230122\pi\)
\(864\) −31.7212 −1.07918
\(865\) 48.1001 1.63545
\(866\) −37.2805 −1.26684
\(867\) 5.68417 0.193045
\(868\) 95.8167 3.25223
\(869\) 35.1350 1.19187
\(870\) 16.1843 0.548699
\(871\) 22.0326 0.746546
\(872\) −101.082 −3.42306
\(873\) −36.8596 −1.24751
\(874\) 47.3685 1.60226
\(875\) −3.14897 −0.106455
\(876\) −1.26843 −0.0428564
\(877\) 14.5725 0.492077 0.246039 0.969260i \(-0.420871\pi\)
0.246039 + 0.969260i \(0.420871\pi\)
\(878\) −34.4279 −1.16189
\(879\) 3.22217 0.108681
\(880\) 120.524 4.06287
\(881\) −29.2885 −0.986755 −0.493378 0.869815i \(-0.664238\pi\)
−0.493378 + 0.869815i \(0.664238\pi\)
\(882\) −14.1392 −0.476093
\(883\) −37.8388 −1.27338 −0.636688 0.771121i \(-0.719696\pi\)
−0.636688 + 0.771121i \(0.719696\pi\)
\(884\) 60.5292 2.03582
\(885\) −5.72466 −0.192432
\(886\) 22.3819 0.751934
\(887\) −6.93190 −0.232751 −0.116375 0.993205i \(-0.537128\pi\)
−0.116375 + 0.993205i \(0.537128\pi\)
\(888\) 17.3623 0.582640
\(889\) 10.8988 0.365533
\(890\) 109.058 3.65563
\(891\) 24.4731 0.819879
\(892\) −111.244 −3.72472
\(893\) 22.3501 0.747917
\(894\) −7.38717 −0.247064
\(895\) −14.3500 −0.479666
\(896\) −4.82976 −0.161351
\(897\) −8.56342 −0.285924
\(898\) 73.0338 2.43717
\(899\) −29.8076 −0.994139
\(900\) −69.1025 −2.30342
\(901\) 14.5977 0.486321
\(902\) −26.4754 −0.881535
\(903\) −10.6599 −0.354739
\(904\) −30.7094 −1.02138
\(905\) 73.7950 2.45303
\(906\) −9.43277 −0.313383
\(907\) 33.2360 1.10358 0.551792 0.833982i \(-0.313944\pi\)
0.551792 + 0.833982i \(0.313944\pi\)
\(908\) −27.4543 −0.911102
\(909\) −3.67261 −0.121813
\(910\) −88.2800 −2.92645
\(911\) −52.6522 −1.74445 −0.872223 0.489108i \(-0.837322\pi\)
−0.872223 + 0.489108i \(0.837322\pi\)
\(912\) −31.3711 −1.03880
\(913\) 55.9513 1.85172
\(914\) −85.7948 −2.83784
\(915\) −10.0017 −0.330646
\(916\) 0.384556 0.0127061
\(917\) 6.69808 0.221190
\(918\) 23.0554 0.760940
\(919\) 53.9502 1.77965 0.889826 0.456299i \(-0.150825\pi\)
0.889826 + 0.456299i \(0.150825\pi\)
\(920\) 72.8478 2.40172
\(921\) 12.5698 0.414190
\(922\) 46.8135 1.54172
\(923\) −35.2489 −1.16023
\(924\) 24.9526 0.820881
\(925\) 22.4663 0.738687
\(926\) −85.9381 −2.82410
\(927\) 3.30911 0.108686
\(928\) −31.8534 −1.04564
\(929\) 37.6109 1.23397 0.616987 0.786974i \(-0.288353\pi\)
0.616987 + 0.786974i \(0.288353\pi\)
\(930\) −44.0904 −1.44578
\(931\) −11.8979 −0.389937
\(932\) 9.36204 0.306664
\(933\) −1.79130 −0.0586444
\(934\) −58.3808 −1.91028
\(935\) −35.0390 −1.14590
\(936\) −90.6198 −2.96200
\(937\) 52.6193 1.71900 0.859498 0.511139i \(-0.170776\pi\)
0.859498 + 0.511139i \(0.170776\pi\)
\(938\) −27.0890 −0.884487
\(939\) −12.1138 −0.395318
\(940\) 59.1462 1.92914
\(941\) 11.0840 0.361327 0.180663 0.983545i \(-0.442176\pi\)
0.180663 + 0.983545i \(0.442176\pi\)
\(942\) 20.4311 0.665680
\(943\) −7.87338 −0.256393
\(944\) 28.1680 0.916790
\(945\) −23.6989 −0.770927
\(946\) 86.3702 2.80814
\(947\) −29.9174 −0.972184 −0.486092 0.873908i \(-0.661578\pi\)
−0.486092 + 0.873908i \(0.661578\pi\)
\(948\) −24.2015 −0.786027
\(949\) −2.15239 −0.0698696
\(950\) −82.5044 −2.67680
\(951\) 10.9486 0.355031
\(952\) −43.2485 −1.40169
\(953\) 16.0720 0.520622 0.260311 0.965525i \(-0.416175\pi\)
0.260311 + 0.965525i \(0.416175\pi\)
\(954\) −37.6067 −1.21756
\(955\) −73.4236 −2.37593
\(956\) 144.610 4.67704
\(957\) −7.76251 −0.250926
\(958\) −19.6360 −0.634409
\(959\) 31.5580 1.01906
\(960\) −12.3429 −0.398365
\(961\) 50.2040 1.61948
\(962\) 50.6969 1.63454
\(963\) −48.7116 −1.56971
\(964\) 6.88147 0.221637
\(965\) 17.5626 0.565360
\(966\) 10.5287 0.338755
\(967\) 23.9050 0.768731 0.384366 0.923181i \(-0.374420\pi\)
0.384366 + 0.923181i \(0.374420\pi\)
\(968\) −38.0441 −1.22278
\(969\) 9.12025 0.292985
\(970\) −116.461 −3.73935
\(971\) −42.8623 −1.37552 −0.687758 0.725940i \(-0.741405\pi\)
−0.687758 + 0.725940i \(0.741405\pi\)
\(972\) −64.0433 −2.05419
\(973\) −40.3109 −1.29231
\(974\) 108.028 3.46144
\(975\) 14.9154 0.477675
\(976\) 49.2131 1.57527
\(977\) 23.5289 0.752757 0.376379 0.926466i \(-0.377169\pi\)
0.376379 + 0.926466i \(0.377169\pi\)
\(978\) 13.3734 0.427635
\(979\) −52.3077 −1.67176
\(980\) −31.4860 −1.00578
\(981\) −37.2483 −1.18925
\(982\) 5.34024 0.170414
\(983\) 15.2508 0.486423 0.243212 0.969973i \(-0.421799\pi\)
0.243212 + 0.969973i \(0.421799\pi\)
\(984\) 10.5980 0.337852
\(985\) 28.0235 0.892903
\(986\) 23.1514 0.737292
\(987\) 4.96780 0.158127
\(988\) −131.216 −4.17454
\(989\) 25.6852 0.816741
\(990\) 90.2676 2.86889
\(991\) −14.9054 −0.473485 −0.236743 0.971572i \(-0.576080\pi\)
−0.236743 + 0.971572i \(0.576080\pi\)
\(992\) 86.7771 2.75518
\(993\) 13.6241 0.432346
\(994\) 43.3384 1.37461
\(995\) −0.953291 −0.0302214
\(996\) −38.5400 −1.22119
\(997\) 9.82443 0.311143 0.155571 0.987825i \(-0.450278\pi\)
0.155571 + 0.987825i \(0.450278\pi\)
\(998\) 46.1496 1.46084
\(999\) 13.6097 0.430592
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 \(a_p\))