Properties

Label 8007.2.a.e.1.1
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.80793 q^{2}\) \(+1.00000 q^{3}\) \(+5.88448 q^{4}\) \(-2.90815 q^{5}\) \(-2.80793 q^{6}\) \(-1.28847 q^{7}\) \(-10.9074 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.80793 q^{2}\) \(+1.00000 q^{3}\) \(+5.88448 q^{4}\) \(-2.90815 q^{5}\) \(-2.80793 q^{6}\) \(-1.28847 q^{7}\) \(-10.9074 q^{8}\) \(+1.00000 q^{9}\) \(+8.16589 q^{10}\) \(+2.87128 q^{11}\) \(+5.88448 q^{12}\) \(+0.133268 q^{13}\) \(+3.61794 q^{14}\) \(-2.90815 q^{15}\) \(+18.8582 q^{16}\) \(-1.00000 q^{17}\) \(-2.80793 q^{18}\) \(-3.66040 q^{19}\) \(-17.1130 q^{20}\) \(-1.28847 q^{21}\) \(-8.06235 q^{22}\) \(-6.74225 q^{23}\) \(-10.9074 q^{24}\) \(+3.45734 q^{25}\) \(-0.374207 q^{26}\) \(+1.00000 q^{27}\) \(-7.58199 q^{28}\) \(-3.28889 q^{29}\) \(+8.16589 q^{30}\) \(+8.99391 q^{31}\) \(-31.1377 q^{32}\) \(+2.87128 q^{33}\) \(+2.80793 q^{34}\) \(+3.74707 q^{35}\) \(+5.88448 q^{36}\) \(+2.72071 q^{37}\) \(+10.2781 q^{38}\) \(+0.133268 q^{39}\) \(+31.7202 q^{40}\) \(+6.71660 q^{41}\) \(+3.61794 q^{42}\) \(+5.12031 q^{43}\) \(+16.8960 q^{44}\) \(-2.90815 q^{45}\) \(+18.9318 q^{46}\) \(+3.31884 q^{47}\) \(+18.8582 q^{48}\) \(-5.33984 q^{49}\) \(-9.70797 q^{50}\) \(-1.00000 q^{51}\) \(+0.784212 q^{52}\) \(-2.37198 q^{53}\) \(-2.80793 q^{54}\) \(-8.35010 q^{55}\) \(+14.0538 q^{56}\) \(-3.66040 q^{57}\) \(+9.23497 q^{58}\) \(-1.05177 q^{59}\) \(-17.1130 q^{60}\) \(+1.13321 q^{61}\) \(-25.2543 q^{62}\) \(-1.28847 q^{63}\) \(+49.7162 q^{64}\) \(-0.387563 q^{65}\) \(-8.06235 q^{66}\) \(-5.26093 q^{67}\) \(-5.88448 q^{68}\) \(-6.74225 q^{69}\) \(-10.5215 q^{70}\) \(+14.3177 q^{71}\) \(-10.9074 q^{72}\) \(+12.5369 q^{73}\) \(-7.63956 q^{74}\) \(+3.45734 q^{75}\) \(-21.5395 q^{76}\) \(-3.69956 q^{77}\) \(-0.374207 q^{78}\) \(-5.39575 q^{79}\) \(-54.8423 q^{80}\) \(+1.00000 q^{81}\) \(-18.8598 q^{82}\) \(-9.57756 q^{83}\) \(-7.58199 q^{84}\) \(+2.90815 q^{85}\) \(-14.3775 q^{86}\) \(-3.28889 q^{87}\) \(-31.3180 q^{88}\) \(-14.0550 q^{89}\) \(+8.16589 q^{90}\) \(-0.171712 q^{91}\) \(-39.6746 q^{92}\) \(+8.99391 q^{93}\) \(-9.31907 q^{94}\) \(+10.6450 q^{95}\) \(-31.1377 q^{96}\) \(-8.78638 q^{97}\) \(+14.9939 q^{98}\) \(+2.87128 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(46q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 46q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 46q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 43q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 33q^{16} \) \(\mathstrut -\mathstrut 46q^{17} \) \(\mathstrut -\mathstrut 5q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 64q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 46q^{27} \) \(\mathstrut -\mathstrut 38q^{28} \) \(\mathstrut -\mathstrut 51q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 19q^{31} \) \(\mathstrut -\mathstrut 61q^{32} \) \(\mathstrut -\mathstrut 25q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 39q^{35} \) \(\mathstrut +\mathstrut 43q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut -\mathstrut 48q^{38} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 53q^{41} \) \(\mathstrut -\mathstrut 28q^{42} \) \(\mathstrut -\mathstrut 33q^{43} \) \(\mathstrut -\mathstrut 62q^{44} \) \(\mathstrut -\mathstrut 19q^{45} \) \(\mathstrut +\mathstrut 2q^{46} \) \(\mathstrut -\mathstrut 45q^{47} \) \(\mathstrut +\mathstrut 33q^{48} \) \(\mathstrut +\mathstrut 21q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 63q^{52} \) \(\mathstrut -\mathstrut 47q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 82q^{56} \) \(\mathstrut -\mathstrut 2q^{57} \) \(\mathstrut -\mathstrut 21q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 74q^{64} \) \(\mathstrut -\mathstrut 85q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut -\mathstrut 52q^{67} \) \(\mathstrut -\mathstrut 43q^{68} \) \(\mathstrut -\mathstrut 64q^{69} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 48q^{71} \) \(\mathstrut -\mathstrut 18q^{72} \) \(\mathstrut -\mathstrut 39q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 42q^{76} \) \(\mathstrut -\mathstrut 78q^{77} \) \(\mathstrut -\mathstrut 13q^{78} \) \(\mathstrut -\mathstrut 26q^{79} \) \(\mathstrut -\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 46q^{81} \) \(\mathstrut +\mathstrut 3q^{82} \) \(\mathstrut -\mathstrut 47q^{83} \) \(\mathstrut -\mathstrut 38q^{84} \) \(\mathstrut +\mathstrut 19q^{85} \) \(\mathstrut -\mathstrut 6q^{86} \) \(\mathstrut -\mathstrut 51q^{87} \) \(\mathstrut -\mathstrut 58q^{88} \) \(\mathstrut -\mathstrut 58q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 43q^{91} \) \(\mathstrut -\mathstrut 68q^{92} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 78q^{95} \) \(\mathstrut -\mathstrut 61q^{96} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 25q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.80793 −1.98551 −0.992754 0.120166i \(-0.961657\pi\)
−0.992754 + 0.120166i \(0.961657\pi\)
\(3\) 1.00000 0.577350
\(4\) 5.88448 2.94224
\(5\) −2.90815 −1.30056 −0.650282 0.759693i \(-0.725349\pi\)
−0.650282 + 0.759693i \(0.725349\pi\)
\(6\) −2.80793 −1.14633
\(7\) −1.28847 −0.486996 −0.243498 0.969901i \(-0.578295\pi\)
−0.243498 + 0.969901i \(0.578295\pi\)
\(8\) −10.9074 −3.85633
\(9\) 1.00000 0.333333
\(10\) 8.16589 2.58228
\(11\) 2.87128 0.865722 0.432861 0.901461i \(-0.357504\pi\)
0.432861 + 0.901461i \(0.357504\pi\)
\(12\) 5.88448 1.69870
\(13\) 0.133268 0.0369619 0.0184809 0.999829i \(-0.494117\pi\)
0.0184809 + 0.999829i \(0.494117\pi\)
\(14\) 3.61794 0.966935
\(15\) −2.90815 −0.750881
\(16\) 18.8582 4.71454
\(17\) −1.00000 −0.242536
\(18\) −2.80793 −0.661836
\(19\) −3.66040 −0.839752 −0.419876 0.907581i \(-0.637927\pi\)
−0.419876 + 0.907581i \(0.637927\pi\)
\(20\) −17.1130 −3.82657
\(21\) −1.28847 −0.281168
\(22\) −8.06235 −1.71890
\(23\) −6.74225 −1.40586 −0.702928 0.711261i \(-0.748124\pi\)
−0.702928 + 0.711261i \(0.748124\pi\)
\(24\) −10.9074 −2.22645
\(25\) 3.45734 0.691468
\(26\) −0.374207 −0.0733880
\(27\) 1.00000 0.192450
\(28\) −7.58199 −1.43286
\(29\) −3.28889 −0.610731 −0.305365 0.952235i \(-0.598779\pi\)
−0.305365 + 0.952235i \(0.598779\pi\)
\(30\) 8.16589 1.49088
\(31\) 8.99391 1.61535 0.807677 0.589625i \(-0.200725\pi\)
0.807677 + 0.589625i \(0.200725\pi\)
\(32\) −31.1377 −5.50442
\(33\) 2.87128 0.499825
\(34\) 2.80793 0.481556
\(35\) 3.74707 0.633370
\(36\) 5.88448 0.980747
\(37\) 2.72071 0.447282 0.223641 0.974672i \(-0.428206\pi\)
0.223641 + 0.974672i \(0.428206\pi\)
\(38\) 10.2781 1.66733
\(39\) 0.133268 0.0213399
\(40\) 31.7202 5.01541
\(41\) 6.71660 1.04896 0.524479 0.851424i \(-0.324260\pi\)
0.524479 + 0.851424i \(0.324260\pi\)
\(42\) 3.61794 0.558260
\(43\) 5.12031 0.780840 0.390420 0.920637i \(-0.372330\pi\)
0.390420 + 0.920637i \(0.372330\pi\)
\(44\) 16.8960 2.54716
\(45\) −2.90815 −0.433521
\(46\) 18.9318 2.79134
\(47\) 3.31884 0.484102 0.242051 0.970264i \(-0.422180\pi\)
0.242051 + 0.970264i \(0.422180\pi\)
\(48\) 18.8582 2.72194
\(49\) −5.33984 −0.762834
\(50\) −9.70797 −1.37291
\(51\) −1.00000 −0.140028
\(52\) 0.784212 0.108751
\(53\) −2.37198 −0.325816 −0.162908 0.986641i \(-0.552087\pi\)
−0.162908 + 0.986641i \(0.552087\pi\)
\(54\) −2.80793 −0.382111
\(55\) −8.35010 −1.12593
\(56\) 14.0538 1.87802
\(57\) −3.66040 −0.484831
\(58\) 9.23497 1.21261
\(59\) −1.05177 −0.136929 −0.0684647 0.997654i \(-0.521810\pi\)
−0.0684647 + 0.997654i \(0.521810\pi\)
\(60\) −17.1130 −2.20927
\(61\) 1.13321 0.145092 0.0725462 0.997365i \(-0.476888\pi\)
0.0725462 + 0.997365i \(0.476888\pi\)
\(62\) −25.2543 −3.20730
\(63\) −1.28847 −0.162332
\(64\) 49.7162 6.21453
\(65\) −0.387563 −0.0480713
\(66\) −8.06235 −0.992407
\(67\) −5.26093 −0.642725 −0.321362 0.946956i \(-0.604141\pi\)
−0.321362 + 0.946956i \(0.604141\pi\)
\(68\) −5.88448 −0.713598
\(69\) −6.74225 −0.811671
\(70\) −10.5215 −1.25756
\(71\) 14.3177 1.69919 0.849597 0.527432i \(-0.176845\pi\)
0.849597 + 0.527432i \(0.176845\pi\)
\(72\) −10.9074 −1.28544
\(73\) 12.5369 1.46733 0.733666 0.679510i \(-0.237808\pi\)
0.733666 + 0.679510i \(0.237808\pi\)
\(74\) −7.63956 −0.888081
\(75\) 3.45734 0.399219
\(76\) −21.5395 −2.47075
\(77\) −3.69956 −0.421604
\(78\) −0.374207 −0.0423706
\(79\) −5.39575 −0.607069 −0.303534 0.952820i \(-0.598167\pi\)
−0.303534 + 0.952820i \(0.598167\pi\)
\(80\) −54.8423 −6.13156
\(81\) 1.00000 0.111111
\(82\) −18.8598 −2.08271
\(83\) −9.57756 −1.05127 −0.525637 0.850709i \(-0.676173\pi\)
−0.525637 + 0.850709i \(0.676173\pi\)
\(84\) −7.58199 −0.827262
\(85\) 2.90815 0.315433
\(86\) −14.3775 −1.55036
\(87\) −3.28889 −0.352606
\(88\) −31.3180 −3.33851
\(89\) −14.0550 −1.48982 −0.744912 0.667163i \(-0.767509\pi\)
−0.744912 + 0.667163i \(0.767509\pi\)
\(90\) 8.16589 0.860760
\(91\) −0.171712 −0.0180003
\(92\) −39.6746 −4.13636
\(93\) 8.99391 0.932625
\(94\) −9.31907 −0.961189
\(95\) 10.6450 1.09215
\(96\) −31.1377 −3.17798
\(97\) −8.78638 −0.892122 −0.446061 0.895003i \(-0.647174\pi\)
−0.446061 + 0.895003i \(0.647174\pi\)
\(98\) 14.9939 1.51461
\(99\) 2.87128 0.288574
\(100\) 20.3447 2.03447
\(101\) 10.4587 1.04068 0.520340 0.853959i \(-0.325805\pi\)
0.520340 + 0.853959i \(0.325805\pi\)
\(102\) 2.80793 0.278027
\(103\) 7.12706 0.702250 0.351125 0.936329i \(-0.385799\pi\)
0.351125 + 0.936329i \(0.385799\pi\)
\(104\) −1.45360 −0.142537
\(105\) 3.74707 0.365677
\(106\) 6.66035 0.646910
\(107\) −1.75715 −0.169870 −0.0849351 0.996386i \(-0.527068\pi\)
−0.0849351 + 0.996386i \(0.527068\pi\)
\(108\) 5.88448 0.566234
\(109\) 9.86784 0.945168 0.472584 0.881286i \(-0.343321\pi\)
0.472584 + 0.881286i \(0.343321\pi\)
\(110\) 23.4465 2.23554
\(111\) 2.72071 0.258238
\(112\) −24.2982 −2.29596
\(113\) −5.14403 −0.483910 −0.241955 0.970287i \(-0.577789\pi\)
−0.241955 + 0.970287i \(0.577789\pi\)
\(114\) 10.2781 0.962636
\(115\) 19.6075 1.82841
\(116\) −19.3534 −1.79692
\(117\) 0.133268 0.0123206
\(118\) 2.95331 0.271874
\(119\) 1.28847 0.118114
\(120\) 31.7202 2.89565
\(121\) −2.75577 −0.250525
\(122\) −3.18197 −0.288082
\(123\) 6.71660 0.605616
\(124\) 52.9245 4.75276
\(125\) 4.48629 0.401266
\(126\) 3.61794 0.322312
\(127\) −13.5002 −1.19795 −0.598976 0.800767i \(-0.704425\pi\)
−0.598976 + 0.800767i \(0.704425\pi\)
\(128\) −77.3243 −6.83457
\(129\) 5.12031 0.450818
\(130\) 1.08825 0.0954459
\(131\) 6.58930 0.575710 0.287855 0.957674i \(-0.407058\pi\)
0.287855 + 0.957674i \(0.407058\pi\)
\(132\) 16.8960 1.47061
\(133\) 4.71632 0.408956
\(134\) 14.7723 1.27614
\(135\) −2.90815 −0.250294
\(136\) 10.9074 0.935298
\(137\) −3.73503 −0.319105 −0.159553 0.987189i \(-0.551005\pi\)
−0.159553 + 0.987189i \(0.551005\pi\)
\(138\) 18.9318 1.61158
\(139\) 2.67454 0.226851 0.113426 0.993546i \(-0.463818\pi\)
0.113426 + 0.993546i \(0.463818\pi\)
\(140\) 22.0496 1.86353
\(141\) 3.31884 0.279497
\(142\) −40.2030 −3.37376
\(143\) 0.382649 0.0319987
\(144\) 18.8582 1.57151
\(145\) 9.56457 0.794295
\(146\) −35.2027 −2.91340
\(147\) −5.33984 −0.440423
\(148\) 16.0100 1.31601
\(149\) 20.6313 1.69018 0.845090 0.534624i \(-0.179547\pi\)
0.845090 + 0.534624i \(0.179547\pi\)
\(150\) −9.70797 −0.792653
\(151\) 4.11025 0.334488 0.167244 0.985916i \(-0.446513\pi\)
0.167244 + 0.985916i \(0.446513\pi\)
\(152\) 39.9252 3.23836
\(153\) −1.00000 −0.0808452
\(154\) 10.3881 0.837097
\(155\) −26.1556 −2.10087
\(156\) 0.784212 0.0627872
\(157\) 1.00000 0.0798087
\(158\) 15.1509 1.20534
\(159\) −2.37198 −0.188110
\(160\) 90.5531 7.15885
\(161\) 8.68719 0.684647
\(162\) −2.80793 −0.220612
\(163\) −5.21415 −0.408404 −0.204202 0.978929i \(-0.565460\pi\)
−0.204202 + 0.978929i \(0.565460\pi\)
\(164\) 39.5237 3.08628
\(165\) −8.35010 −0.650055
\(166\) 26.8931 2.08731
\(167\) −1.38489 −0.107166 −0.0535831 0.998563i \(-0.517064\pi\)
−0.0535831 + 0.998563i \(0.517064\pi\)
\(168\) 14.0538 1.08428
\(169\) −12.9822 −0.998634
\(170\) −8.16589 −0.626295
\(171\) −3.66040 −0.279917
\(172\) 30.1304 2.29742
\(173\) 11.1036 0.844195 0.422097 0.906551i \(-0.361294\pi\)
0.422097 + 0.906551i \(0.361294\pi\)
\(174\) 9.23497 0.700101
\(175\) −4.45468 −0.336742
\(176\) 54.1470 4.08148
\(177\) −1.05177 −0.0790562
\(178\) 39.4654 2.95806
\(179\) −7.57997 −0.566553 −0.283277 0.959038i \(-0.591421\pi\)
−0.283277 + 0.959038i \(0.591421\pi\)
\(180\) −17.1130 −1.27552
\(181\) −18.0235 −1.33968 −0.669840 0.742506i \(-0.733637\pi\)
−0.669840 + 0.742506i \(0.733637\pi\)
\(182\) 0.482155 0.0357397
\(183\) 1.13321 0.0837692
\(184\) 73.5401 5.42145
\(185\) −7.91223 −0.581719
\(186\) −25.2543 −1.85173
\(187\) −2.87128 −0.209969
\(188\) 19.5296 1.42435
\(189\) −1.28847 −0.0937225
\(190\) −29.8904 −2.16848
\(191\) −8.52767 −0.617041 −0.308520 0.951218i \(-0.599834\pi\)
−0.308520 + 0.951218i \(0.599834\pi\)
\(192\) 49.7162 3.58796
\(193\) 13.6048 0.979292 0.489646 0.871921i \(-0.337126\pi\)
0.489646 + 0.871921i \(0.337126\pi\)
\(194\) 24.6716 1.77131
\(195\) −0.387563 −0.0277540
\(196\) −31.4222 −2.24444
\(197\) −2.40419 −0.171291 −0.0856456 0.996326i \(-0.527295\pi\)
−0.0856456 + 0.996326i \(0.527295\pi\)
\(198\) −8.06235 −0.572966
\(199\) −19.2211 −1.36255 −0.681275 0.732028i \(-0.738574\pi\)
−0.681275 + 0.732028i \(0.738574\pi\)
\(200\) −37.7104 −2.66653
\(201\) −5.26093 −0.371077
\(202\) −29.3674 −2.06628
\(203\) 4.23764 0.297424
\(204\) −5.88448 −0.411996
\(205\) −19.5329 −1.36424
\(206\) −20.0123 −1.39432
\(207\) −6.74225 −0.468618
\(208\) 2.51319 0.174258
\(209\) −10.5100 −0.726993
\(210\) −10.5215 −0.726053
\(211\) 22.2081 1.52887 0.764435 0.644701i \(-0.223018\pi\)
0.764435 + 0.644701i \(0.223018\pi\)
\(212\) −13.9579 −0.958629
\(213\) 14.3177 0.981030
\(214\) 4.93396 0.337279
\(215\) −14.8906 −1.01553
\(216\) −10.9074 −0.742152
\(217\) −11.5884 −0.786672
\(218\) −27.7082 −1.87664
\(219\) 12.5369 0.847164
\(220\) −49.1360 −3.31275
\(221\) −0.133268 −0.00896457
\(222\) −7.63956 −0.512734
\(223\) 0.0941128 0.00630226 0.00315113 0.999995i \(-0.498997\pi\)
0.00315113 + 0.999995i \(0.498997\pi\)
\(224\) 40.1200 2.68063
\(225\) 3.45734 0.230489
\(226\) 14.4441 0.960807
\(227\) −14.0971 −0.935661 −0.467830 0.883818i \(-0.654964\pi\)
−0.467830 + 0.883818i \(0.654964\pi\)
\(228\) −21.5395 −1.42649
\(229\) −5.50497 −0.363779 −0.181889 0.983319i \(-0.558221\pi\)
−0.181889 + 0.983319i \(0.558221\pi\)
\(230\) −55.0564 −3.63031
\(231\) −3.69956 −0.243413
\(232\) 35.8730 2.35518
\(233\) 16.5264 1.08268 0.541341 0.840803i \(-0.317917\pi\)
0.541341 + 0.840803i \(0.317917\pi\)
\(234\) −0.374207 −0.0244627
\(235\) −9.65168 −0.629606
\(236\) −6.18914 −0.402879
\(237\) −5.39575 −0.350491
\(238\) −3.61794 −0.234516
\(239\) −5.72835 −0.370536 −0.185268 0.982688i \(-0.559315\pi\)
−0.185268 + 0.982688i \(0.559315\pi\)
\(240\) −54.8423 −3.54006
\(241\) 1.50515 0.0969555 0.0484777 0.998824i \(-0.484563\pi\)
0.0484777 + 0.998824i \(0.484563\pi\)
\(242\) 7.73802 0.497418
\(243\) 1.00000 0.0641500
\(244\) 6.66834 0.426897
\(245\) 15.5291 0.992115
\(246\) −18.8598 −1.20245
\(247\) −0.487813 −0.0310388
\(248\) −98.0998 −6.22934
\(249\) −9.57756 −0.606953
\(250\) −12.5972 −0.796716
\(251\) −23.3651 −1.47479 −0.737395 0.675462i \(-0.763944\pi\)
−0.737395 + 0.675462i \(0.763944\pi\)
\(252\) −7.58199 −0.477620
\(253\) −19.3589 −1.21708
\(254\) 37.9077 2.37854
\(255\) 2.90815 0.182115
\(256\) 117.689 7.35556
\(257\) 1.70344 0.106257 0.0531287 0.998588i \(-0.483081\pi\)
0.0531287 + 0.998588i \(0.483081\pi\)
\(258\) −14.3775 −0.895102
\(259\) −3.50555 −0.217825
\(260\) −2.28061 −0.141437
\(261\) −3.28889 −0.203577
\(262\) −18.5023 −1.14308
\(263\) 9.94962 0.613520 0.306760 0.951787i \(-0.400755\pi\)
0.306760 + 0.951787i \(0.400755\pi\)
\(264\) −31.3180 −1.92749
\(265\) 6.89807 0.423745
\(266\) −13.2431 −0.811986
\(267\) −14.0550 −0.860150
\(268\) −30.9578 −1.89105
\(269\) −17.1490 −1.04559 −0.522797 0.852457i \(-0.675111\pi\)
−0.522797 + 0.852457i \(0.675111\pi\)
\(270\) 8.16589 0.496960
\(271\) 21.8207 1.32551 0.662757 0.748835i \(-0.269386\pi\)
0.662757 + 0.748835i \(0.269386\pi\)
\(272\) −18.8582 −1.14344
\(273\) −0.171712 −0.0103925
\(274\) 10.4877 0.633585
\(275\) 9.92698 0.598619
\(276\) −39.6746 −2.38813
\(277\) −3.05926 −0.183813 −0.0919065 0.995768i \(-0.529296\pi\)
−0.0919065 + 0.995768i \(0.529296\pi\)
\(278\) −7.50992 −0.450415
\(279\) 8.99391 0.538451
\(280\) −40.8706 −2.44249
\(281\) 9.29164 0.554293 0.277146 0.960828i \(-0.410611\pi\)
0.277146 + 0.960828i \(0.410611\pi\)
\(282\) −9.31907 −0.554943
\(283\) 2.06289 0.122626 0.0613129 0.998119i \(-0.480471\pi\)
0.0613129 + 0.998119i \(0.480471\pi\)
\(284\) 84.2520 4.99944
\(285\) 10.6450 0.630554
\(286\) −1.07445 −0.0635337
\(287\) −8.65415 −0.510838
\(288\) −31.1377 −1.83481
\(289\) 1.00000 0.0588235
\(290\) −26.8567 −1.57708
\(291\) −8.78638 −0.515067
\(292\) 73.7731 4.31724
\(293\) −19.8767 −1.16121 −0.580603 0.814187i \(-0.697183\pi\)
−0.580603 + 0.814187i \(0.697183\pi\)
\(294\) 14.9939 0.874463
\(295\) 3.05872 0.178085
\(296\) −29.6757 −1.72487
\(297\) 2.87128 0.166608
\(298\) −57.9312 −3.35587
\(299\) −0.898525 −0.0519630
\(300\) 20.3447 1.17460
\(301\) −6.59737 −0.380266
\(302\) −11.5413 −0.664128
\(303\) 10.4587 0.600837
\(304\) −69.0283 −3.95904
\(305\) −3.29554 −0.188702
\(306\) 2.80793 0.160519
\(307\) 23.8024 1.35848 0.679238 0.733918i \(-0.262311\pi\)
0.679238 + 0.733918i \(0.262311\pi\)
\(308\) −21.7700 −1.24046
\(309\) 7.12706 0.405444
\(310\) 73.4433 4.17130
\(311\) 17.9061 1.01536 0.507680 0.861545i \(-0.330503\pi\)
0.507680 + 0.861545i \(0.330503\pi\)
\(312\) −1.45360 −0.0822939
\(313\) −1.01797 −0.0575393 −0.0287697 0.999586i \(-0.509159\pi\)
−0.0287697 + 0.999586i \(0.509159\pi\)
\(314\) −2.80793 −0.158461
\(315\) 3.74707 0.211123
\(316\) −31.7512 −1.78614
\(317\) 12.3144 0.691645 0.345822 0.938300i \(-0.387600\pi\)
0.345822 + 0.938300i \(0.387600\pi\)
\(318\) 6.66035 0.373494
\(319\) −9.44330 −0.528723
\(320\) −144.582 −8.08239
\(321\) −1.75715 −0.0980746
\(322\) −24.3930 −1.35937
\(323\) 3.66040 0.203670
\(324\) 5.88448 0.326916
\(325\) 0.460752 0.0255579
\(326\) 14.6410 0.810889
\(327\) 9.86784 0.545693
\(328\) −73.2604 −4.04513
\(329\) −4.27623 −0.235756
\(330\) 23.4465 1.29069
\(331\) −8.45256 −0.464595 −0.232297 0.972645i \(-0.574624\pi\)
−0.232297 + 0.972645i \(0.574624\pi\)
\(332\) −56.3590 −3.09310
\(333\) 2.72071 0.149094
\(334\) 3.88868 0.212779
\(335\) 15.2996 0.835905
\(336\) −24.2982 −1.32558
\(337\) −11.6009 −0.631941 −0.315971 0.948769i \(-0.602330\pi\)
−0.315971 + 0.948769i \(0.602330\pi\)
\(338\) 36.4532 1.98280
\(339\) −5.14403 −0.279385
\(340\) 17.1130 0.928080
\(341\) 25.8240 1.39845
\(342\) 10.2781 0.555778
\(343\) 15.8995 0.858494
\(344\) −55.8490 −3.01118
\(345\) 19.6075 1.05563
\(346\) −31.1783 −1.67616
\(347\) −31.9027 −1.71262 −0.856312 0.516459i \(-0.827250\pi\)
−0.856312 + 0.516459i \(0.827250\pi\)
\(348\) −19.3534 −1.03745
\(349\) −26.8329 −1.43633 −0.718165 0.695872i \(-0.755018\pi\)
−0.718165 + 0.695872i \(0.755018\pi\)
\(350\) 12.5084 0.668605
\(351\) 0.133268 0.00711331
\(352\) −89.4049 −4.76530
\(353\) −8.87924 −0.472594 −0.236297 0.971681i \(-0.575934\pi\)
−0.236297 + 0.971681i \(0.575934\pi\)
\(354\) 2.95331 0.156967
\(355\) −41.6379 −2.20991
\(356\) −82.7062 −4.38342
\(357\) 1.28847 0.0681931
\(358\) 21.2840 1.12490
\(359\) 14.5187 0.766268 0.383134 0.923693i \(-0.374845\pi\)
0.383134 + 0.923693i \(0.374845\pi\)
\(360\) 31.7202 1.67180
\(361\) −5.60150 −0.294816
\(362\) 50.6089 2.65994
\(363\) −2.75577 −0.144640
\(364\) −1.01043 −0.0529612
\(365\) −36.4592 −1.90836
\(366\) −3.18197 −0.166324
\(367\) 3.60734 0.188302 0.0941509 0.995558i \(-0.469986\pi\)
0.0941509 + 0.995558i \(0.469986\pi\)
\(368\) −127.146 −6.62796
\(369\) 6.71660 0.349652
\(370\) 22.2170 1.15501
\(371\) 3.05622 0.158671
\(372\) 52.9245 2.74401
\(373\) −8.52599 −0.441459 −0.220730 0.975335i \(-0.570844\pi\)
−0.220730 + 0.975335i \(0.570844\pi\)
\(374\) 8.06235 0.416894
\(375\) 4.48629 0.231671
\(376\) −36.1997 −1.86686
\(377\) −0.438303 −0.0225737
\(378\) 3.61794 0.186087
\(379\) 33.2349 1.70716 0.853580 0.520961i \(-0.174426\pi\)
0.853580 + 0.520961i \(0.174426\pi\)
\(380\) 62.6402 3.21337
\(381\) −13.5002 −0.691637
\(382\) 23.9451 1.22514
\(383\) −31.5693 −1.61312 −0.806558 0.591155i \(-0.798672\pi\)
−0.806558 + 0.591155i \(0.798672\pi\)
\(384\) −77.3243 −3.94594
\(385\) 10.7589 0.548323
\(386\) −38.2012 −1.94439
\(387\) 5.12031 0.260280
\(388\) −51.7033 −2.62484
\(389\) −17.2392 −0.874063 −0.437031 0.899446i \(-0.643970\pi\)
−0.437031 + 0.899446i \(0.643970\pi\)
\(390\) 1.08825 0.0551057
\(391\) 6.74225 0.340970
\(392\) 58.2436 2.94174
\(393\) 6.58930 0.332386
\(394\) 6.75079 0.340100
\(395\) 15.6916 0.789532
\(396\) 16.8960 0.849055
\(397\) −16.4911 −0.827662 −0.413831 0.910354i \(-0.635810\pi\)
−0.413831 + 0.910354i \(0.635810\pi\)
\(398\) 53.9716 2.70535
\(399\) 4.71632 0.236111
\(400\) 65.1990 3.25995
\(401\) 6.24554 0.311888 0.155944 0.987766i \(-0.450158\pi\)
0.155944 + 0.987766i \(0.450158\pi\)
\(402\) 14.7723 0.736777
\(403\) 1.19860 0.0597065
\(404\) 61.5441 3.06193
\(405\) −2.90815 −0.144507
\(406\) −11.8990 −0.590537
\(407\) 7.81190 0.387222
\(408\) 10.9074 0.539995
\(409\) −4.86304 −0.240462 −0.120231 0.992746i \(-0.538363\pi\)
−0.120231 + 0.992746i \(0.538363\pi\)
\(410\) 54.8470 2.70870
\(411\) −3.73503 −0.184235
\(412\) 41.9390 2.06619
\(413\) 1.35518 0.0666841
\(414\) 18.9318 0.930446
\(415\) 27.8530 1.36725
\(416\) −4.14965 −0.203453
\(417\) 2.67454 0.130973
\(418\) 29.5114 1.44345
\(419\) −29.2476 −1.42884 −0.714421 0.699717i \(-0.753310\pi\)
−0.714421 + 0.699717i \(0.753310\pi\)
\(420\) 22.0496 1.07591
\(421\) −20.5578 −1.00192 −0.500962 0.865469i \(-0.667021\pi\)
−0.500962 + 0.865469i \(0.667021\pi\)
\(422\) −62.3588 −3.03558
\(423\) 3.31884 0.161367
\(424\) 25.8720 1.25646
\(425\) −3.45734 −0.167706
\(426\) −40.2030 −1.94784
\(427\) −1.46011 −0.0706595
\(428\) −10.3399 −0.499799
\(429\) 0.382649 0.0184745
\(430\) 41.8119 2.01635
\(431\) 35.8182 1.72530 0.862652 0.505798i \(-0.168802\pi\)
0.862652 + 0.505798i \(0.168802\pi\)
\(432\) 18.8582 0.907313
\(433\) 4.07089 0.195634 0.0978172 0.995204i \(-0.468814\pi\)
0.0978172 + 0.995204i \(0.468814\pi\)
\(434\) 32.5394 1.56194
\(435\) 9.56457 0.458586
\(436\) 58.0671 2.78091
\(437\) 24.6793 1.18057
\(438\) −35.2027 −1.68205
\(439\) 14.1330 0.674531 0.337266 0.941409i \(-0.390498\pi\)
0.337266 + 0.941409i \(0.390498\pi\)
\(440\) 91.0776 4.34195
\(441\) −5.33984 −0.254278
\(442\) 0.374207 0.0177992
\(443\) −0.407127 −0.0193432 −0.00967160 0.999953i \(-0.503079\pi\)
−0.00967160 + 0.999953i \(0.503079\pi\)
\(444\) 16.0100 0.759799
\(445\) 40.8740 1.93761
\(446\) −0.264262 −0.0125132
\(447\) 20.6313 0.975826
\(448\) −64.0579 −3.02645
\(449\) −5.41251 −0.255432 −0.127716 0.991811i \(-0.540765\pi\)
−0.127716 + 0.991811i \(0.540765\pi\)
\(450\) −9.70797 −0.457638
\(451\) 19.2852 0.908106
\(452\) −30.2700 −1.42378
\(453\) 4.11025 0.193117
\(454\) 39.5838 1.85776
\(455\) 0.499364 0.0234105
\(456\) 39.9252 1.86967
\(457\) −13.7435 −0.642893 −0.321446 0.946928i \(-0.604169\pi\)
−0.321446 + 0.946928i \(0.604169\pi\)
\(458\) 15.4576 0.722285
\(459\) −1.00000 −0.0466760
\(460\) 115.380 5.37961
\(461\) 15.6747 0.730045 0.365023 0.930999i \(-0.381061\pi\)
0.365023 + 0.930999i \(0.381061\pi\)
\(462\) 10.3881 0.483298
\(463\) −6.47091 −0.300729 −0.150364 0.988631i \(-0.548045\pi\)
−0.150364 + 0.988631i \(0.548045\pi\)
\(464\) −62.0223 −2.87931
\(465\) −26.1556 −1.21294
\(466\) −46.4051 −2.14967
\(467\) 22.9284 1.06100 0.530499 0.847685i \(-0.322004\pi\)
0.530499 + 0.847685i \(0.322004\pi\)
\(468\) 0.784212 0.0362502
\(469\) 6.77856 0.313005
\(470\) 27.1013 1.25009
\(471\) 1.00000 0.0460776
\(472\) 11.4721 0.528045
\(473\) 14.7018 0.675990
\(474\) 15.1509 0.695903
\(475\) −12.6552 −0.580662
\(476\) 7.58199 0.347520
\(477\) −2.37198 −0.108605
\(478\) 16.0848 0.735702
\(479\) −30.0813 −1.37445 −0.687224 0.726445i \(-0.741171\pi\)
−0.687224 + 0.726445i \(0.741171\pi\)
\(480\) 90.5531 4.13316
\(481\) 0.362583 0.0165324
\(482\) −4.22637 −0.192506
\(483\) 8.68719 0.395281
\(484\) −16.2163 −0.737104
\(485\) 25.5521 1.16026
\(486\) −2.80793 −0.127370
\(487\) −27.2449 −1.23459 −0.617293 0.786733i \(-0.711771\pi\)
−0.617293 + 0.786733i \(0.711771\pi\)
\(488\) −12.3603 −0.559525
\(489\) −5.21415 −0.235792
\(490\) −43.6045 −1.96985
\(491\) −10.8703 −0.490571 −0.245286 0.969451i \(-0.578882\pi\)
−0.245286 + 0.969451i \(0.578882\pi\)
\(492\) 39.5237 1.78187
\(493\) 3.28889 0.148124
\(494\) 1.36975 0.0616278
\(495\) −8.35010 −0.375309
\(496\) 169.609 7.61565
\(497\) −18.4479 −0.827502
\(498\) 26.8931 1.20511
\(499\) 41.3409 1.85067 0.925336 0.379149i \(-0.123783\pi\)
0.925336 + 0.379149i \(0.123783\pi\)
\(500\) 26.3995 1.18062
\(501\) −1.38489 −0.0618724
\(502\) 65.6075 2.92821
\(503\) −19.2099 −0.856529 −0.428264 0.903653i \(-0.640875\pi\)
−0.428264 + 0.903653i \(0.640875\pi\)
\(504\) 14.0538 0.626007
\(505\) −30.4155 −1.35347
\(506\) 54.3583 2.41652
\(507\) −12.9822 −0.576562
\(508\) −79.4418 −3.52466
\(509\) 24.7924 1.09890 0.549451 0.835526i \(-0.314837\pi\)
0.549451 + 0.835526i \(0.314837\pi\)
\(510\) −8.16589 −0.361592
\(511\) −16.1534 −0.714585
\(512\) −175.814 −7.76996
\(513\) −3.66040 −0.161610
\(514\) −4.78313 −0.210975
\(515\) −20.7266 −0.913321
\(516\) 30.1304 1.32641
\(517\) 9.52930 0.419098
\(518\) 9.84336 0.432492
\(519\) 11.1036 0.487396
\(520\) 4.22729 0.185379
\(521\) −29.1578 −1.27743 −0.638713 0.769445i \(-0.720533\pi\)
−0.638713 + 0.769445i \(0.720533\pi\)
\(522\) 9.23497 0.404203
\(523\) −8.95983 −0.391786 −0.195893 0.980625i \(-0.562761\pi\)
−0.195893 + 0.980625i \(0.562761\pi\)
\(524\) 38.7746 1.69388
\(525\) −4.45468 −0.194418
\(526\) −27.9379 −1.21815
\(527\) −8.99391 −0.391781
\(528\) 54.1470 2.35644
\(529\) 22.4579 0.976430
\(530\) −19.3693 −0.841348
\(531\) −1.05177 −0.0456431
\(532\) 27.7531 1.20325
\(533\) 0.895107 0.0387714
\(534\) 39.4654 1.70783
\(535\) 5.11006 0.220927
\(536\) 57.3828 2.47856
\(537\) −7.57997 −0.327100
\(538\) 48.1532 2.07603
\(539\) −15.3322 −0.660403
\(540\) −17.1130 −0.736424
\(541\) −36.5427 −1.57109 −0.785546 0.618804i \(-0.787618\pi\)
−0.785546 + 0.618804i \(0.787618\pi\)
\(542\) −61.2711 −2.63182
\(543\) −18.0235 −0.773464
\(544\) 31.1377 1.33502
\(545\) −28.6972 −1.22925
\(546\) 0.482155 0.0206343
\(547\) −27.0369 −1.15601 −0.578006 0.816032i \(-0.696169\pi\)
−0.578006 + 0.816032i \(0.696169\pi\)
\(548\) −21.9787 −0.938884
\(549\) 1.13321 0.0483642
\(550\) −27.8743 −1.18856
\(551\) 12.0386 0.512863
\(552\) 73.5401 3.13007
\(553\) 6.95226 0.295640
\(554\) 8.59019 0.364962
\(555\) −7.91223 −0.335855
\(556\) 15.7383 0.667451
\(557\) 32.1479 1.36215 0.681076 0.732213i \(-0.261512\pi\)
0.681076 + 0.732213i \(0.261512\pi\)
\(558\) −25.2543 −1.06910
\(559\) 0.682372 0.0288613
\(560\) 70.6628 2.98605
\(561\) −2.87128 −0.121225
\(562\) −26.0903 −1.10055
\(563\) −30.9982 −1.30642 −0.653209 0.757177i \(-0.726578\pi\)
−0.653209 + 0.757177i \(0.726578\pi\)
\(564\) 19.5296 0.822346
\(565\) 14.9596 0.629356
\(566\) −5.79244 −0.243475
\(567\) −1.28847 −0.0541107
\(568\) −156.168 −6.55266
\(569\) 44.3789 1.86046 0.930229 0.366978i \(-0.119608\pi\)
0.930229 + 0.366978i \(0.119608\pi\)
\(570\) −29.8904 −1.25197
\(571\) −38.8995 −1.62789 −0.813947 0.580939i \(-0.802685\pi\)
−0.813947 + 0.580939i \(0.802685\pi\)
\(572\) 2.25169 0.0941479
\(573\) −8.52767 −0.356249
\(574\) 24.3003 1.01427
\(575\) −23.3102 −0.972104
\(576\) 49.7162 2.07151
\(577\) 17.9961 0.749186 0.374593 0.927189i \(-0.377782\pi\)
0.374593 + 0.927189i \(0.377782\pi\)
\(578\) −2.80793 −0.116795
\(579\) 13.6048 0.565395
\(580\) 56.2826 2.33701
\(581\) 12.3404 0.511967
\(582\) 24.6716 1.02267
\(583\) −6.81060 −0.282066
\(584\) −136.744 −5.65852
\(585\) −0.387563 −0.0160238
\(586\) 55.8123 2.30559
\(587\) 29.2595 1.20767 0.603835 0.797109i \(-0.293639\pi\)
0.603835 + 0.797109i \(0.293639\pi\)
\(588\) −31.4222 −1.29583
\(589\) −32.9213 −1.35650
\(590\) −8.58867 −0.353590
\(591\) −2.40419 −0.0988950
\(592\) 51.3075 2.10873
\(593\) 26.7778 1.09963 0.549817 0.835285i \(-0.314698\pi\)
0.549817 + 0.835285i \(0.314698\pi\)
\(594\) −8.06235 −0.330802
\(595\) −3.74707 −0.153615
\(596\) 121.404 4.97292
\(597\) −19.2211 −0.786668
\(598\) 2.52300 0.103173
\(599\) −5.39440 −0.220409 −0.110205 0.993909i \(-0.535151\pi\)
−0.110205 + 0.993909i \(0.535151\pi\)
\(600\) −37.7104 −1.53952
\(601\) 1.00618 0.0410430 0.0205215 0.999789i \(-0.493467\pi\)
0.0205215 + 0.999789i \(0.493467\pi\)
\(602\) 18.5250 0.755021
\(603\) −5.26093 −0.214242
\(604\) 24.1867 0.984143
\(605\) 8.01420 0.325823
\(606\) −29.3674 −1.19297
\(607\) −24.7351 −1.00397 −0.501984 0.864877i \(-0.667396\pi\)
−0.501984 + 0.864877i \(0.667396\pi\)
\(608\) 113.976 4.62235
\(609\) 4.23764 0.171718
\(610\) 9.25365 0.374669
\(611\) 0.442294 0.0178933
\(612\) −5.88448 −0.237866
\(613\) 0.521629 0.0210684 0.0105342 0.999945i \(-0.496647\pi\)
0.0105342 + 0.999945i \(0.496647\pi\)
\(614\) −66.8356 −2.69726
\(615\) −19.5329 −0.787642
\(616\) 40.3524 1.62584
\(617\) −39.4737 −1.58915 −0.794575 0.607165i \(-0.792306\pi\)
−0.794575 + 0.607165i \(0.792306\pi\)
\(618\) −20.0123 −0.805012
\(619\) 8.44707 0.339516 0.169758 0.985486i \(-0.445701\pi\)
0.169758 + 0.985486i \(0.445701\pi\)
\(620\) −153.912 −6.18127
\(621\) −6.74225 −0.270557
\(622\) −50.2791 −2.01601
\(623\) 18.1094 0.725539
\(624\) 2.51319 0.100608
\(625\) −30.3335 −1.21334
\(626\) 2.85840 0.114245
\(627\) −10.5100 −0.419729
\(628\) 5.88448 0.234816
\(629\) −2.72071 −0.108482
\(630\) −10.5215 −0.419187
\(631\) −30.4099 −1.21060 −0.605300 0.795998i \(-0.706947\pi\)
−0.605300 + 0.795998i \(0.706947\pi\)
\(632\) 58.8533 2.34106
\(633\) 22.2081 0.882693
\(634\) −34.5779 −1.37327
\(635\) 39.2607 1.55801
\(636\) −13.9579 −0.553465
\(637\) −0.711629 −0.0281958
\(638\) 26.5161 1.04978
\(639\) 14.3177 0.566398
\(640\) 224.871 8.88880
\(641\) −49.1630 −1.94182 −0.970912 0.239437i \(-0.923037\pi\)
−0.970912 + 0.239437i \(0.923037\pi\)
\(642\) 4.93396 0.194728
\(643\) −12.5553 −0.495131 −0.247566 0.968871i \(-0.579631\pi\)
−0.247566 + 0.968871i \(0.579631\pi\)
\(644\) 51.1196 2.01439
\(645\) −14.8906 −0.586318
\(646\) −10.2781 −0.404388
\(647\) −41.7319 −1.64065 −0.820325 0.571897i \(-0.806208\pi\)
−0.820325 + 0.571897i \(0.806208\pi\)
\(648\) −10.9074 −0.428481
\(649\) −3.01993 −0.118543
\(650\) −1.29376 −0.0507455
\(651\) −11.5884 −0.454185
\(652\) −30.6826 −1.20162
\(653\) −0.473896 −0.0185450 −0.00927249 0.999957i \(-0.502952\pi\)
−0.00927249 + 0.999957i \(0.502952\pi\)
\(654\) −27.7082 −1.08348
\(655\) −19.1627 −0.748748
\(656\) 126.663 4.94535
\(657\) 12.5369 0.489111
\(658\) 12.0074 0.468095
\(659\) 43.7787 1.70538 0.852688 0.522420i \(-0.174971\pi\)
0.852688 + 0.522420i \(0.174971\pi\)
\(660\) −49.1360 −1.91262
\(661\) −33.8576 −1.31691 −0.658455 0.752620i \(-0.728790\pi\)
−0.658455 + 0.752620i \(0.728790\pi\)
\(662\) 23.7342 0.922456
\(663\) −0.133268 −0.00517569
\(664\) 104.466 4.05406
\(665\) −13.7158 −0.531874
\(666\) −7.63956 −0.296027
\(667\) 22.1745 0.858599
\(668\) −8.14937 −0.315309
\(669\) 0.0941128 0.00363861
\(670\) −42.9602 −1.65970
\(671\) 3.25375 0.125610
\(672\) 40.1200 1.54766
\(673\) −4.74172 −0.182780 −0.0913899 0.995815i \(-0.529131\pi\)
−0.0913899 + 0.995815i \(0.529131\pi\)
\(674\) 32.5745 1.25472
\(675\) 3.45734 0.133073
\(676\) −76.3937 −2.93822
\(677\) −21.6484 −0.832014 −0.416007 0.909361i \(-0.636571\pi\)
−0.416007 + 0.909361i \(0.636571\pi\)
\(678\) 14.4441 0.554722
\(679\) 11.3210 0.434460
\(680\) −31.7202 −1.21642
\(681\) −14.0971 −0.540204
\(682\) −72.5120 −2.77663
\(683\) 1.35646 0.0519035 0.0259517 0.999663i \(-0.491738\pi\)
0.0259517 + 0.999663i \(0.491738\pi\)
\(684\) −21.5395 −0.823584
\(685\) 10.8620 0.415017
\(686\) −44.6448 −1.70455
\(687\) −5.50497 −0.210028
\(688\) 96.5595 3.68130
\(689\) −0.316108 −0.0120428
\(690\) −55.0564 −2.09596
\(691\) −28.9862 −1.10269 −0.551343 0.834278i \(-0.685885\pi\)
−0.551343 + 0.834278i \(0.685885\pi\)
\(692\) 65.3392 2.48382
\(693\) −3.69956 −0.140535
\(694\) 89.5805 3.40043
\(695\) −7.77796 −0.295035
\(696\) 35.8730 1.35976
\(697\) −6.71660 −0.254409
\(698\) 75.3449 2.85185
\(699\) 16.5264 0.625087
\(700\) −26.2135 −0.990777
\(701\) 51.6003 1.94891 0.974457 0.224572i \(-0.0720984\pi\)
0.974457 + 0.224572i \(0.0720984\pi\)
\(702\) −0.374207 −0.0141235
\(703\) −9.95887 −0.375606
\(704\) 142.749 5.38005
\(705\) −9.65168 −0.363503
\(706\) 24.9323 0.938339
\(707\) −13.4758 −0.506808
\(708\) −6.18914 −0.232602
\(709\) −2.83202 −0.106359 −0.0531793 0.998585i \(-0.516935\pi\)
−0.0531793 + 0.998585i \(0.516935\pi\)
\(710\) 116.916 4.38780
\(711\) −5.39575 −0.202356
\(712\) 153.303 5.74526
\(713\) −60.6392 −2.27095
\(714\) −3.61794 −0.135398
\(715\) −1.11280 −0.0416164
\(716\) −44.6042 −1.66694
\(717\) −5.72835 −0.213929
\(718\) −40.7675 −1.52143
\(719\) −33.9380 −1.26568 −0.632838 0.774284i \(-0.718110\pi\)
−0.632838 + 0.774284i \(0.718110\pi\)
\(720\) −54.8423 −2.04385
\(721\) −9.18301 −0.341993
\(722\) 15.7286 0.585359
\(723\) 1.50515 0.0559773
\(724\) −106.059 −3.94166
\(725\) −11.3708 −0.422301
\(726\) 7.73802 0.287185
\(727\) 28.5940 1.06049 0.530247 0.847843i \(-0.322099\pi\)
0.530247 + 0.847843i \(0.322099\pi\)
\(728\) 1.87292 0.0694151
\(729\) 1.00000 0.0370370
\(730\) 102.375 3.78906
\(731\) −5.12031 −0.189381
\(732\) 6.66834 0.246469
\(733\) −26.2415 −0.969251 −0.484625 0.874722i \(-0.661044\pi\)
−0.484625 + 0.874722i \(0.661044\pi\)
\(734\) −10.1292 −0.373875
\(735\) 15.5291 0.572798
\(736\) 209.938 7.73842
\(737\) −15.1056 −0.556421
\(738\) −18.8598 −0.694237
\(739\) −40.4398 −1.48760 −0.743801 0.668401i \(-0.766979\pi\)
−0.743801 + 0.668401i \(0.766979\pi\)
\(740\) −46.5594 −1.71156
\(741\) −0.487813 −0.0179203
\(742\) −8.58167 −0.315043
\(743\) −2.74985 −0.100882 −0.0504412 0.998727i \(-0.516063\pi\)
−0.0504412 + 0.998727i \(0.516063\pi\)
\(744\) −98.0998 −3.59651
\(745\) −59.9989 −2.19819
\(746\) 23.9404 0.876520
\(747\) −9.57756 −0.350425
\(748\) −16.8960 −0.617778
\(749\) 2.26404 0.0827262
\(750\) −12.5972 −0.459984
\(751\) −15.4487 −0.563730 −0.281865 0.959454i \(-0.590953\pi\)
−0.281865 + 0.959454i \(0.590953\pi\)
\(752\) 62.5871 2.28232
\(753\) −23.3651 −0.851470
\(754\) 1.23072 0.0448203
\(755\) −11.9532 −0.435023
\(756\) −7.58199 −0.275754
\(757\) −26.1707 −0.951190 −0.475595 0.879664i \(-0.657767\pi\)
−0.475595 + 0.879664i \(0.657767\pi\)
\(758\) −93.3213 −3.38958
\(759\) −19.3589 −0.702682
\(760\) −116.109 −4.21170
\(761\) 33.1131 1.20035 0.600175 0.799869i \(-0.295098\pi\)
0.600175 + 0.799869i \(0.295098\pi\)
\(762\) 37.9077 1.37325
\(763\) −12.7144 −0.460293
\(764\) −50.1809 −1.81548
\(765\) 2.90815 0.105144
\(766\) 88.6445 3.20285
\(767\) −0.140168 −0.00506116
\(768\) 117.689 4.24674
\(769\) −29.4567 −1.06224 −0.531118 0.847298i \(-0.678228\pi\)
−0.531118 + 0.847298i \(0.678228\pi\)
\(770\) −30.2102 −1.08870
\(771\) 1.70344 0.0613478
\(772\) 80.0570 2.88131
\(773\) 44.1402 1.58761 0.793806 0.608171i \(-0.208097\pi\)
0.793806 + 0.608171i \(0.208097\pi\)
\(774\) −14.3775 −0.516788
\(775\) 31.0950 1.11697
\(776\) 95.8362 3.44032
\(777\) −3.50555 −0.125761
\(778\) 48.4065 1.73546
\(779\) −24.5854 −0.880864
\(780\) −2.28061 −0.0816588
\(781\) 41.1100 1.47103
\(782\) −18.9318 −0.676999
\(783\) −3.28889 −0.117535
\(784\) −100.700 −3.59641
\(785\) −2.90815 −0.103796
\(786\) −18.5023 −0.659956
\(787\) −39.6166 −1.41218 −0.706090 0.708123i \(-0.749542\pi\)
−0.706090 + 0.708123i \(0.749542\pi\)
\(788\) −14.1474 −0.503980
\(789\) 9.94962 0.354216
\(790\) −44.0611 −1.56762
\(791\) 6.62794 0.235662
\(792\) −31.3180 −1.11284
\(793\) 0.151020 0.00536289
\(794\) 46.3058 1.64333
\(795\) 6.89807 0.244649
\(796\) −113.106 −4.00895
\(797\) 22.3187 0.790570 0.395285 0.918559i \(-0.370646\pi\)
0.395285 + 0.918559i \(0.370646\pi\)
\(798\) −13.2431 −0.468800
\(799\) −3.31884 −0.117412
\(800\) −107.654 −3.80613
\(801\) −14.0550 −0.496608
\(802\) −17.5371 −0.619255
\(803\) 35.9969 1.27030
\(804\) −30.9578 −1.09180
\(805\) −25.2637 −0.890427
\(806\) −3.36558 −0.118548
\(807\) −17.1490 −0.603674
\(808\) −114.077 −4.01321
\(809\) −16.5912 −0.583315 −0.291658 0.956523i \(-0.594207\pi\)
−0.291658 + 0.956523i \(0.594207\pi\)
\(810\) 8.16589 0.286920
\(811\) −49.7074 −1.74546 −0.872731 0.488201i \(-0.837653\pi\)
−0.872731 + 0.488201i \(0.837653\pi\)
\(812\) 24.9363 0.875092
\(813\) 21.8207 0.765286
\(814\) −21.9353 −0.768832
\(815\) 15.1635 0.531156
\(816\) −18.8582 −0.660167
\(817\) −18.7424 −0.655712
\(818\) 13.6551 0.477439
\(819\) −0.171712 −0.00600010
\(820\) −114.941 −4.01391
\(821\) 15.1023 0.527072 0.263536 0.964650i \(-0.415111\pi\)
0.263536 + 0.964650i \(0.415111\pi\)
\(822\) 10.4877 0.365801
\(823\) −1.21422 −0.0423250 −0.0211625 0.999776i \(-0.506737\pi\)
−0.0211625 + 0.999776i \(0.506737\pi\)
\(824\) −77.7374 −2.70811
\(825\) 9.92698 0.345613
\(826\) −3.80526 −0.132402
\(827\) −0.423889 −0.0147401 −0.00737004 0.999973i \(-0.502346\pi\)
−0.00737004 + 0.999973i \(0.502346\pi\)
\(828\) −39.6746 −1.37879
\(829\) 5.23791 0.181920 0.0909601 0.995855i \(-0.471006\pi\)
0.0909601 + 0.995855i \(0.471006\pi\)
\(830\) −78.2093 −2.71468
\(831\) −3.05926 −0.106125
\(832\) 6.62557 0.229700
\(833\) 5.33984 0.185015
\(834\) −7.50992 −0.260047
\(835\) 4.02747 0.139376
\(836\) −61.8459 −2.13899
\(837\) 8.99391 0.310875
\(838\) 82.1254 2.83697
\(839\) 28.1603 0.972201 0.486100 0.873903i \(-0.338419\pi\)
0.486100 + 0.873903i \(0.338419\pi\)
\(840\) −40.8706 −1.41017
\(841\) −18.1832 −0.627008
\(842\) 57.7248 1.98933
\(843\) 9.29164 0.320021
\(844\) 130.683 4.49830
\(845\) 37.7543 1.29879
\(846\) −9.31907 −0.320396
\(847\) 3.55073 0.122005
\(848\) −44.7311 −1.53607
\(849\) 2.06289 0.0707981
\(850\) 9.70797 0.332981
\(851\) −18.3437 −0.628813
\(852\) 84.2520 2.88643
\(853\) 27.7941 0.951652 0.475826 0.879540i \(-0.342149\pi\)
0.475826 + 0.879540i \(0.342149\pi\)
\(854\) 4.09988 0.140295
\(855\) 10.6450 0.364051
\(856\) 19.1659 0.655076
\(857\) −7.29383 −0.249153 −0.124576 0.992210i \(-0.539757\pi\)
−0.124576 + 0.992210i \(0.539757\pi\)
\(858\) −1.07445 −0.0366812
\(859\) −46.1510 −1.57465 −0.787326 0.616537i \(-0.788535\pi\)
−0.787326 + 0.616537i \(0.788535\pi\)
\(860\) −87.6236 −2.98794
\(861\) −8.65415 −0.294933
\(862\) −100.575 −3.42560
\(863\) −14.3470 −0.488378 −0.244189 0.969728i \(-0.578522\pi\)
−0.244189 + 0.969728i \(0.578522\pi\)
\(864\) −31.1377 −1.05933
\(865\) −32.2911 −1.09793
\(866\) −11.4308 −0.388434
\(867\) 1.00000 0.0339618
\(868\) −68.1917 −2.31458
\(869\) −15.4927 −0.525553
\(870\) −26.8567 −0.910526
\(871\) −0.701113 −0.0237563
\(872\) −107.632 −3.64488
\(873\) −8.78638 −0.297374
\(874\) −69.2978 −2.34403
\(875\) −5.78045 −0.195415
\(876\) 73.7731 2.49256
\(877\) 49.4979 1.67143 0.835713 0.549166i \(-0.185054\pi\)
0.835713 + 0.549166i \(0.185054\pi\)
\(878\) −39.6845 −1.33929
\(879\) −19.8767 −0.670423
\(880\) −157.468 −5.30823
\(881\) 29.5729 0.996335 0.498168 0.867081i \(-0.334006\pi\)
0.498168 + 0.867081i \(0.334006\pi\)
\(882\) 14.9939 0.504871
\(883\) −6.27119 −0.211042 −0.105521 0.994417i \(-0.533651\pi\)
−0.105521 + 0.994417i \(0.533651\pi\)
\(884\) −0.784212 −0.0263759
\(885\) 3.05872 0.102818
\(886\) 1.14319 0.0384061
\(887\) 9.12356 0.306339 0.153170 0.988200i \(-0.451052\pi\)
0.153170 + 0.988200i \(0.451052\pi\)
\(888\) −29.6757 −0.995852
\(889\) 17.3947 0.583398
\(890\) −114.771 −3.84714
\(891\) 2.87128 0.0961914
\(892\) 0.553805 0.0185428
\(893\) −12.1483 −0.406526
\(894\) −57.9312 −1.93751
\(895\) 22.0437 0.736839
\(896\) 99.6302 3.32841
\(897\) −0.898525 −0.0300009
\(898\) 15.1980 0.507162
\(899\) −29.5799 −0.986546
\(900\) 20.3447 0.678155
\(901\) 2.37198 0.0790220
\(902\) −54.1516 −1.80305
\(903\) −6.59737 −0.219547
\(904\) 56.1078 1.86612
\(905\) 52.4152 1.74234
\(906\) −11.5413 −0.383434
\(907\) 13.6771 0.454141 0.227071 0.973878i \(-0.427085\pi\)
0.227071 + 0.973878i \(0.427085\pi\)
\(908\) −82.9544 −2.75294
\(909\) 10.4587 0.346894
\(910\) −1.40218 −0.0464818
\(911\) 41.0779 1.36097 0.680486 0.732761i \(-0.261769\pi\)
0.680486 + 0.732761i \(0.261769\pi\)
\(912\) −69.0283 −2.28576
\(913\) −27.4998 −0.910111
\(914\) 38.5907 1.27647
\(915\) −3.29554 −0.108947
\(916\) −32.3939 −1.07032
\(917\) −8.49013 −0.280369
\(918\) 2.80793 0.0926756
\(919\) −54.4953 −1.79763 −0.898816 0.438325i \(-0.855572\pi\)
−0.898816 + 0.438325i \(0.855572\pi\)
\(920\) −213.866 −7.05094
\(921\) 23.8024 0.784316
\(922\) −44.0136 −1.44951
\(923\) 1.90808 0.0628054
\(924\) −21.7700 −0.716180
\(925\) 9.40641 0.309281
\(926\) 18.1699 0.597099
\(927\) 7.12706 0.234083
\(928\) 102.408 3.36172
\(929\) 10.8939 0.357418 0.178709 0.983902i \(-0.442808\pi\)
0.178709 + 0.983902i \(0.442808\pi\)
\(930\) 73.4433 2.40830
\(931\) 19.5459 0.640592
\(932\) 97.2494 3.18551
\(933\) 17.9061 0.586219
\(934\) −64.3813 −2.10662
\(935\) 8.35010 0.273078
\(936\) −1.45360 −0.0475124
\(937\) −35.1768 −1.14917 −0.574587 0.818443i \(-0.694837\pi\)
−0.574587 + 0.818443i \(0.694837\pi\)
\(938\) −19.0337 −0.621473
\(939\) −1.01797 −0.0332203
\(940\) −56.7951 −1.85245
\(941\) −5.99388 −0.195395 −0.0976974 0.995216i \(-0.531148\pi\)
−0.0976974 + 0.995216i \(0.531148\pi\)
\(942\) −2.80793 −0.0914874
\(943\) −45.2850 −1.47468
\(944\) −19.8345 −0.645559
\(945\) 3.74707 0.121892
\(946\) −41.2817 −1.34218
\(947\) −23.6295 −0.767856 −0.383928 0.923363i \(-0.625429\pi\)
−0.383928 + 0.923363i \(0.625429\pi\)
\(948\) −31.7512 −1.03123
\(949\) 1.67076 0.0542353
\(950\) 35.5350 1.15291
\(951\) 12.3144 0.399321
\(952\) −14.0538 −0.455487
\(953\) −45.1915 −1.46390 −0.731949 0.681360i \(-0.761389\pi\)
−0.731949 + 0.681360i \(0.761389\pi\)
\(954\) 6.66035 0.215637
\(955\) 24.7998 0.802501
\(956\) −33.7083 −1.09021
\(957\) −9.44330 −0.305259
\(958\) 84.4662 2.72898
\(959\) 4.81248 0.155403
\(960\) −144.582 −4.66637
\(961\) 49.8904 1.60937
\(962\) −1.01811 −0.0328251
\(963\) −1.75715 −0.0566234
\(964\) 8.85705 0.285266
\(965\) −39.5647 −1.27363
\(966\) −24.3930 −0.784833
\(967\) −44.5026 −1.43111 −0.715554 0.698558i \(-0.753826\pi\)
−0.715554 + 0.698558i \(0.753826\pi\)
\(968\) 30.0582 0.966106
\(969\) 3.66040 0.117589
\(970\) −71.7486 −2.30371
\(971\) 42.2630 1.35629 0.678143 0.734930i \(-0.262785\pi\)
0.678143 + 0.734930i \(0.262785\pi\)
\(972\) 5.88448 0.188745
\(973\) −3.44607 −0.110476
\(974\) 76.5019 2.45128
\(975\) 0.460752 0.0147559
\(976\) 21.3702 0.684044
\(977\) 30.4814 0.975187 0.487593 0.873071i \(-0.337875\pi\)
0.487593 + 0.873071i \(0.337875\pi\)
\(978\) 14.6410 0.468167
\(979\) −40.3557 −1.28977
\(980\) 91.3805 2.91904
\(981\) 9.86784 0.315056
\(982\) 30.5231 0.974033
\(983\) −42.9806 −1.37087 −0.685434 0.728134i \(-0.740388\pi\)
−0.685434 + 0.728134i \(0.740388\pi\)
\(984\) −73.2604 −2.33546
\(985\) 6.99174 0.222775
\(986\) −9.23497 −0.294101
\(987\) −4.27623 −0.136114
\(988\) −2.87053 −0.0913236
\(989\) −34.5224 −1.09775
\(990\) 23.4465 0.745179
\(991\) 3.13287 0.0995189 0.0497594 0.998761i \(-0.484155\pi\)
0.0497594 + 0.998761i \(0.484155\pi\)
\(992\) −280.050 −8.89158
\(993\) −8.45256 −0.268234
\(994\) 51.8005 1.64301
\(995\) 55.8979 1.77208
\(996\) −56.3590 −1.78580
\(997\) 45.9326 1.45470 0.727349 0.686267i \(-0.240752\pi\)
0.727349 + 0.686267i \(0.240752\pi\)
\(998\) −116.082 −3.67452
\(999\) 2.72071 0.0860794
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 \(a_p\))