Properties

Label 8007.2.a.j.1.8
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 0
Dimension 64
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: \(0\)
Dimension: \(64\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.37098 q^{2}\) \(-1.00000 q^{3}\) \(+3.62156 q^{4}\) \(-2.47104 q^{5}\) \(+2.37098 q^{6}\) \(+5.22837 q^{7}\) \(-3.84468 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.37098 q^{2}\) \(-1.00000 q^{3}\) \(+3.62156 q^{4}\) \(-2.47104 q^{5}\) \(+2.37098 q^{6}\) \(+5.22837 q^{7}\) \(-3.84468 q^{8}\) \(+1.00000 q^{9}\) \(+5.85879 q^{10}\) \(-2.69830 q^{11}\) \(-3.62156 q^{12}\) \(-4.61025 q^{13}\) \(-12.3964 q^{14}\) \(+2.47104 q^{15}\) \(+1.87256 q^{16}\) \(+1.00000 q^{17}\) \(-2.37098 q^{18}\) \(+3.89560 q^{19}\) \(-8.94902 q^{20}\) \(-5.22837 q^{21}\) \(+6.39763 q^{22}\) \(-1.31247 q^{23}\) \(+3.84468 q^{24}\) \(+1.10604 q^{25}\) \(+10.9308 q^{26}\) \(-1.00000 q^{27}\) \(+18.9348 q^{28}\) \(-6.14894 q^{29}\) \(-5.85879 q^{30}\) \(-6.63171 q^{31}\) \(+3.24955 q^{32}\) \(+2.69830 q^{33}\) \(-2.37098 q^{34}\) \(-12.9195 q^{35}\) \(+3.62156 q^{36}\) \(-3.63240 q^{37}\) \(-9.23639 q^{38}\) \(+4.61025 q^{39}\) \(+9.50037 q^{40}\) \(-7.09471 q^{41}\) \(+12.3964 q^{42}\) \(+4.62347 q^{43}\) \(-9.77206 q^{44}\) \(-2.47104 q^{45}\) \(+3.11185 q^{46}\) \(-10.0238 q^{47}\) \(-1.87256 q^{48}\) \(+20.3358 q^{49}\) \(-2.62241 q^{50}\) \(-1.00000 q^{51}\) \(-16.6963 q^{52}\) \(-6.19366 q^{53}\) \(+2.37098 q^{54}\) \(+6.66762 q^{55}\) \(-20.1014 q^{56}\) \(-3.89560 q^{57}\) \(+14.5790 q^{58}\) \(+2.92971 q^{59}\) \(+8.94902 q^{60}\) \(-6.46956 q^{61}\) \(+15.7237 q^{62}\) \(+5.22837 q^{63}\) \(-11.4498 q^{64}\) \(+11.3921 q^{65}\) \(-6.39763 q^{66}\) \(-11.2487 q^{67}\) \(+3.62156 q^{68}\) \(+1.31247 q^{69}\) \(+30.6319 q^{70}\) \(+4.39922 q^{71}\) \(-3.84468 q^{72}\) \(+0.488239 q^{73}\) \(+8.61235 q^{74}\) \(-1.10604 q^{75}\) \(+14.1081 q^{76}\) \(-14.1077 q^{77}\) \(-10.9308 q^{78}\) \(-2.57608 q^{79}\) \(-4.62718 q^{80}\) \(+1.00000 q^{81}\) \(+16.8214 q^{82}\) \(-2.95749 q^{83}\) \(-18.9348 q^{84}\) \(-2.47104 q^{85}\) \(-10.9622 q^{86}\) \(+6.14894 q^{87}\) \(+10.3741 q^{88}\) \(+11.7140 q^{89}\) \(+5.85879 q^{90}\) \(-24.1041 q^{91}\) \(-4.75319 q^{92}\) \(+6.63171 q^{93}\) \(+23.7663 q^{94}\) \(-9.62618 q^{95}\) \(-3.24955 q^{96}\) \(-3.40745 q^{97}\) \(-48.2159 q^{98}\) \(-2.69830 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 64q^{3} \) \(\mathstrut +\mathstrut 77q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 64q^{9} \) \(\mathstrut +\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut -\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 103q^{16} \) \(\mathstrut +\mathstrut 64q^{17} \) \(\mathstrut +\mathstrut 5q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut -\mathstrut 24q^{20} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut +\mathstrut 20q^{23} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 141q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 64q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 31q^{32} \) \(\mathstrut +\mathstrut 7q^{33} \) \(\mathstrut +\mathstrut 5q^{34} \) \(\mathstrut -\mathstrut 3q^{35} \) \(\mathstrut +\mathstrut 77q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut +\mathstrut 28q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 14q^{42} \) \(\mathstrut +\mathstrut 59q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 11q^{47} \) \(\mathstrut -\mathstrut 103q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 20q^{50} \) \(\mathstrut -\mathstrut 64q^{51} \) \(\mathstrut +\mathstrut 65q^{52} \) \(\mathstrut +\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 5q^{54} \) \(\mathstrut +\mathstrut 35q^{55} \) \(\mathstrut -\mathstrut 34q^{56} \) \(\mathstrut -\mathstrut 26q^{57} \) \(\mathstrut -\mathstrut 27q^{58} \) \(\mathstrut -\mathstrut 65q^{59} \) \(\mathstrut +\mathstrut 24q^{60} \) \(\mathstrut +\mathstrut 15q^{61} \) \(\mathstrut +\mathstrut 18q^{62} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 152q^{64} \) \(\mathstrut +\mathstrut 49q^{65} \) \(\mathstrut -\mathstrut 25q^{66} \) \(\mathstrut +\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 28q^{70} \) \(\mathstrut -\mathstrut 18q^{71} \) \(\mathstrut +\mathstrut 18q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut -\mathstrut 76q^{74} \) \(\mathstrut -\mathstrut 141q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut +\mathstrut 80q^{77} \) \(\mathstrut -\mathstrut 9q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 144q^{80} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 27q^{82} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 5q^{87} \) \(\mathstrut +\mathstrut 108q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut +\mathstrut 12q^{90} \) \(\mathstrut +\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 60q^{94} \) \(\mathstrut +\mathstrut 42q^{95} \) \(\mathstrut -\mathstrut 31q^{96} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 7q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.37098 −1.67654 −0.838269 0.545257i \(-0.816432\pi\)
−0.838269 + 0.545257i \(0.816432\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.62156 1.81078
\(5\) −2.47104 −1.10508 −0.552542 0.833485i \(-0.686342\pi\)
−0.552542 + 0.833485i \(0.686342\pi\)
\(6\) 2.37098 0.967950
\(7\) 5.22837 1.97614 0.988069 0.154013i \(-0.0492197\pi\)
0.988069 + 0.154013i \(0.0492197\pi\)
\(8\) −3.84468 −1.35930
\(9\) 1.00000 0.333333
\(10\) 5.85879 1.85271
\(11\) −2.69830 −0.813569 −0.406784 0.913524i \(-0.633350\pi\)
−0.406784 + 0.913524i \(0.633350\pi\)
\(12\) −3.62156 −1.04545
\(13\) −4.61025 −1.27865 −0.639326 0.768936i \(-0.720787\pi\)
−0.639326 + 0.768936i \(0.720787\pi\)
\(14\) −12.3964 −3.31307
\(15\) 2.47104 0.638020
\(16\) 1.87256 0.468141
\(17\) 1.00000 0.242536
\(18\) −2.37098 −0.558846
\(19\) 3.89560 0.893711 0.446856 0.894606i \(-0.352544\pi\)
0.446856 + 0.894606i \(0.352544\pi\)
\(20\) −8.94902 −2.00106
\(21\) −5.22837 −1.14092
\(22\) 6.39763 1.36398
\(23\) −1.31247 −0.273669 −0.136835 0.990594i \(-0.543693\pi\)
−0.136835 + 0.990594i \(0.543693\pi\)
\(24\) 3.84468 0.784793
\(25\) 1.10604 0.221209
\(26\) 10.9308 2.14371
\(27\) −1.00000 −0.192450
\(28\) 18.9348 3.57835
\(29\) −6.14894 −1.14183 −0.570914 0.821010i \(-0.693411\pi\)
−0.570914 + 0.821010i \(0.693411\pi\)
\(30\) −5.85879 −1.06966
\(31\) −6.63171 −1.19109 −0.595545 0.803322i \(-0.703064\pi\)
−0.595545 + 0.803322i \(0.703064\pi\)
\(32\) 3.24955 0.574445
\(33\) 2.69830 0.469714
\(34\) −2.37098 −0.406620
\(35\) −12.9195 −2.18380
\(36\) 3.62156 0.603593
\(37\) −3.63240 −0.597162 −0.298581 0.954384i \(-0.596513\pi\)
−0.298581 + 0.954384i \(0.596513\pi\)
\(38\) −9.23639 −1.49834
\(39\) 4.61025 0.738230
\(40\) 9.50037 1.50214
\(41\) −7.09471 −1.10801 −0.554004 0.832514i \(-0.686901\pi\)
−0.554004 + 0.832514i \(0.686901\pi\)
\(42\) 12.3964 1.91280
\(43\) 4.62347 0.705072 0.352536 0.935798i \(-0.385319\pi\)
0.352536 + 0.935798i \(0.385319\pi\)
\(44\) −9.77206 −1.47319
\(45\) −2.47104 −0.368361
\(46\) 3.11185 0.458817
\(47\) −10.0238 −1.46212 −0.731062 0.682311i \(-0.760975\pi\)
−0.731062 + 0.682311i \(0.760975\pi\)
\(48\) −1.87256 −0.270281
\(49\) 20.3358 2.90512
\(50\) −2.62241 −0.370865
\(51\) −1.00000 −0.140028
\(52\) −16.6963 −2.31536
\(53\) −6.19366 −0.850764 −0.425382 0.905014i \(-0.639860\pi\)
−0.425382 + 0.905014i \(0.639860\pi\)
\(54\) 2.37098 0.322650
\(55\) 6.66762 0.899061
\(56\) −20.1014 −2.68617
\(57\) −3.89560 −0.515984
\(58\) 14.5790 1.91432
\(59\) 2.92971 0.381415 0.190708 0.981647i \(-0.438922\pi\)
0.190708 + 0.981647i \(0.438922\pi\)
\(60\) 8.94902 1.15531
\(61\) −6.46956 −0.828342 −0.414171 0.910199i \(-0.635929\pi\)
−0.414171 + 0.910199i \(0.635929\pi\)
\(62\) 15.7237 1.99691
\(63\) 5.22837 0.658713
\(64\) −11.4498 −1.43122
\(65\) 11.3921 1.41302
\(66\) −6.39763 −0.787494
\(67\) −11.2487 −1.37424 −0.687121 0.726543i \(-0.741126\pi\)
−0.687121 + 0.726543i \(0.741126\pi\)
\(68\) 3.62156 0.439178
\(69\) 1.31247 0.158003
\(70\) 30.6319 3.66122
\(71\) 4.39922 0.522092 0.261046 0.965326i \(-0.415933\pi\)
0.261046 + 0.965326i \(0.415933\pi\)
\(72\) −3.84468 −0.453100
\(73\) 0.488239 0.0571441 0.0285720 0.999592i \(-0.490904\pi\)
0.0285720 + 0.999592i \(0.490904\pi\)
\(74\) 8.61235 1.00117
\(75\) −1.10604 −0.127715
\(76\) 14.1081 1.61831
\(77\) −14.1077 −1.60772
\(78\) −10.9308 −1.23767
\(79\) −2.57608 −0.289832 −0.144916 0.989444i \(-0.546291\pi\)
−0.144916 + 0.989444i \(0.546291\pi\)
\(80\) −4.62718 −0.517335
\(81\) 1.00000 0.111111
\(82\) 16.8214 1.85762
\(83\) −2.95749 −0.324627 −0.162313 0.986739i \(-0.551896\pi\)
−0.162313 + 0.986739i \(0.551896\pi\)
\(84\) −18.9348 −2.06596
\(85\) −2.47104 −0.268022
\(86\) −10.9622 −1.18208
\(87\) 6.14894 0.659235
\(88\) 10.3741 1.10589
\(89\) 11.7140 1.24168 0.620841 0.783937i \(-0.286791\pi\)
0.620841 + 0.783937i \(0.286791\pi\)
\(90\) 5.85879 0.617571
\(91\) −24.1041 −2.52679
\(92\) −4.75319 −0.495555
\(93\) 6.63171 0.687677
\(94\) 23.7663 2.45131
\(95\) −9.62618 −0.987625
\(96\) −3.24955 −0.331656
\(97\) −3.40745 −0.345974 −0.172987 0.984924i \(-0.555342\pi\)
−0.172987 + 0.984924i \(0.555342\pi\)
\(98\) −48.2159 −4.87054
\(99\) −2.69830 −0.271190
\(100\) 4.00560 0.400560
\(101\) 12.9375 1.28733 0.643663 0.765309i \(-0.277414\pi\)
0.643663 + 0.765309i \(0.277414\pi\)
\(102\) 2.37098 0.234762
\(103\) 15.3394 1.51144 0.755719 0.654896i \(-0.227287\pi\)
0.755719 + 0.654896i \(0.227287\pi\)
\(104\) 17.7249 1.73807
\(105\) 12.9195 1.26082
\(106\) 14.6851 1.42634
\(107\) 10.4852 1.01364 0.506820 0.862052i \(-0.330821\pi\)
0.506820 + 0.862052i \(0.330821\pi\)
\(108\) −3.62156 −0.348485
\(109\) −0.790168 −0.0756843 −0.0378422 0.999284i \(-0.512048\pi\)
−0.0378422 + 0.999284i \(0.512048\pi\)
\(110\) −15.8088 −1.50731
\(111\) 3.63240 0.344772
\(112\) 9.79045 0.925111
\(113\) −14.4514 −1.35947 −0.679735 0.733457i \(-0.737905\pi\)
−0.679735 + 0.733457i \(0.737905\pi\)
\(114\) 9.23639 0.865067
\(115\) 3.24317 0.302427
\(116\) −22.2687 −2.06760
\(117\) −4.61025 −0.426217
\(118\) −6.94629 −0.639457
\(119\) 5.22837 0.479284
\(120\) −9.50037 −0.867261
\(121\) −3.71916 −0.338106
\(122\) 15.3392 1.38875
\(123\) 7.09471 0.639708
\(124\) −24.0171 −2.15680
\(125\) 9.62213 0.860629
\(126\) −12.3964 −1.10436
\(127\) 7.69943 0.683214 0.341607 0.939843i \(-0.389029\pi\)
0.341607 + 0.939843i \(0.389029\pi\)
\(128\) 20.6481 1.82505
\(129\) −4.62347 −0.407074
\(130\) −27.0105 −2.36898
\(131\) −6.33756 −0.553715 −0.276858 0.960911i \(-0.589293\pi\)
−0.276858 + 0.960911i \(0.589293\pi\)
\(132\) 9.77206 0.850549
\(133\) 20.3676 1.76610
\(134\) 26.6704 2.30397
\(135\) 2.47104 0.212673
\(136\) −3.84468 −0.329679
\(137\) 21.4514 1.83272 0.916360 0.400356i \(-0.131113\pi\)
0.916360 + 0.400356i \(0.131113\pi\)
\(138\) −3.11185 −0.264898
\(139\) 20.5715 1.74485 0.872426 0.488746i \(-0.162546\pi\)
0.872426 + 0.488746i \(0.162546\pi\)
\(140\) −46.7888 −3.95437
\(141\) 10.0238 0.844157
\(142\) −10.4305 −0.875307
\(143\) 12.4398 1.04027
\(144\) 1.87256 0.156047
\(145\) 15.1943 1.26182
\(146\) −1.15761 −0.0958042
\(147\) −20.3358 −1.67727
\(148\) −13.1549 −1.08133
\(149\) −6.85932 −0.561937 −0.280968 0.959717i \(-0.590656\pi\)
−0.280968 + 0.959717i \(0.590656\pi\)
\(150\) 2.62241 0.214119
\(151\) 10.7211 0.872471 0.436236 0.899832i \(-0.356311\pi\)
0.436236 + 0.899832i \(0.356311\pi\)
\(152\) −14.9773 −1.21482
\(153\) 1.00000 0.0808452
\(154\) 33.4492 2.69541
\(155\) 16.3872 1.31625
\(156\) 16.6963 1.33677
\(157\) −1.00000 −0.0798087
\(158\) 6.10784 0.485914
\(159\) 6.19366 0.491189
\(160\) −8.02978 −0.634810
\(161\) −6.86209 −0.540808
\(162\) −2.37098 −0.186282
\(163\) 11.9402 0.935229 0.467615 0.883932i \(-0.345114\pi\)
0.467615 + 0.883932i \(0.345114\pi\)
\(164\) −25.6939 −2.00636
\(165\) −6.66762 −0.519073
\(166\) 7.01216 0.544249
\(167\) −11.3402 −0.877528 −0.438764 0.898602i \(-0.644584\pi\)
−0.438764 + 0.898602i \(0.644584\pi\)
\(168\) 20.1014 1.55086
\(169\) 8.25437 0.634951
\(170\) 5.85879 0.449349
\(171\) 3.89560 0.297904
\(172\) 16.7442 1.27673
\(173\) −22.8280 −1.73558 −0.867791 0.496929i \(-0.834461\pi\)
−0.867791 + 0.496929i \(0.834461\pi\)
\(174\) −14.5790 −1.10523
\(175\) 5.78280 0.437139
\(176\) −5.05274 −0.380865
\(177\) −2.92971 −0.220210
\(178\) −27.7737 −2.08173
\(179\) 22.2811 1.66537 0.832684 0.553748i \(-0.186803\pi\)
0.832684 + 0.553748i \(0.186803\pi\)
\(180\) −8.94902 −0.667020
\(181\) −8.52326 −0.633529 −0.316764 0.948504i \(-0.602596\pi\)
−0.316764 + 0.948504i \(0.602596\pi\)
\(182\) 57.1503 4.23626
\(183\) 6.46956 0.478244
\(184\) 5.04604 0.371999
\(185\) 8.97580 0.659914
\(186\) −15.7237 −1.15292
\(187\) −2.69830 −0.197319
\(188\) −36.3018 −2.64758
\(189\) −5.22837 −0.380308
\(190\) 22.8235 1.65579
\(191\) −16.8920 −1.22226 −0.611129 0.791531i \(-0.709285\pi\)
−0.611129 + 0.791531i \(0.709285\pi\)
\(192\) 11.4498 0.826315
\(193\) 18.4292 1.32657 0.663283 0.748369i \(-0.269163\pi\)
0.663283 + 0.748369i \(0.269163\pi\)
\(194\) 8.07901 0.580039
\(195\) −11.3921 −0.815806
\(196\) 73.6474 5.26053
\(197\) −5.02015 −0.357671 −0.178835 0.983879i \(-0.557233\pi\)
−0.178835 + 0.983879i \(0.557233\pi\)
\(198\) 6.39763 0.454660
\(199\) −2.23856 −0.158687 −0.0793436 0.996847i \(-0.525282\pi\)
−0.0793436 + 0.996847i \(0.525282\pi\)
\(200\) −4.25239 −0.300689
\(201\) 11.2487 0.793419
\(202\) −30.6745 −2.15825
\(203\) −32.1489 −2.25641
\(204\) −3.62156 −0.253560
\(205\) 17.5313 1.22444
\(206\) −36.3695 −2.53398
\(207\) −1.31247 −0.0912231
\(208\) −8.63298 −0.598589
\(209\) −10.5115 −0.727096
\(210\) −30.6319 −2.11380
\(211\) 14.7607 1.01617 0.508083 0.861308i \(-0.330354\pi\)
0.508083 + 0.861308i \(0.330354\pi\)
\(212\) −22.4307 −1.54055
\(213\) −4.39922 −0.301430
\(214\) −24.8601 −1.69940
\(215\) −11.4248 −0.779163
\(216\) 3.84468 0.261598
\(217\) −34.6730 −2.35376
\(218\) 1.87347 0.126888
\(219\) −0.488239 −0.0329921
\(220\) 24.1472 1.62800
\(221\) −4.61025 −0.310119
\(222\) −8.61235 −0.578023
\(223\) −6.47232 −0.433418 −0.216709 0.976236i \(-0.569532\pi\)
−0.216709 + 0.976236i \(0.569532\pi\)
\(224\) 16.9899 1.13518
\(225\) 1.10604 0.0737362
\(226\) 34.2640 2.27920
\(227\) −10.3529 −0.687148 −0.343574 0.939126i \(-0.611638\pi\)
−0.343574 + 0.939126i \(0.611638\pi\)
\(228\) −14.1081 −0.934334
\(229\) −28.5081 −1.88387 −0.941933 0.335800i \(-0.890993\pi\)
−0.941933 + 0.335800i \(0.890993\pi\)
\(230\) −7.68950 −0.507031
\(231\) 14.1077 0.928220
\(232\) 23.6407 1.55209
\(233\) 2.47644 0.162237 0.0811184 0.996704i \(-0.474151\pi\)
0.0811184 + 0.996704i \(0.474151\pi\)
\(234\) 10.9308 0.714569
\(235\) 24.7693 1.61577
\(236\) 10.6101 0.690659
\(237\) 2.57608 0.167334
\(238\) −12.3964 −0.803537
\(239\) 21.5273 1.39249 0.696243 0.717807i \(-0.254854\pi\)
0.696243 + 0.717807i \(0.254854\pi\)
\(240\) 4.62718 0.298683
\(241\) −15.8335 −1.01992 −0.509961 0.860197i \(-0.670340\pi\)
−0.509961 + 0.860197i \(0.670340\pi\)
\(242\) 8.81806 0.566847
\(243\) −1.00000 −0.0641500
\(244\) −23.4299 −1.49994
\(245\) −50.2507 −3.21040
\(246\) −16.8214 −1.07250
\(247\) −17.9597 −1.14275
\(248\) 25.4968 1.61905
\(249\) 2.95749 0.187423
\(250\) −22.8139 −1.44288
\(251\) 17.3138 1.09284 0.546420 0.837512i \(-0.315990\pi\)
0.546420 + 0.837512i \(0.315990\pi\)
\(252\) 18.9348 1.19278
\(253\) 3.54145 0.222649
\(254\) −18.2552 −1.14543
\(255\) 2.47104 0.154743
\(256\) −26.0567 −1.62854
\(257\) 0.945145 0.0589565 0.0294783 0.999565i \(-0.490615\pi\)
0.0294783 + 0.999565i \(0.490615\pi\)
\(258\) 10.9622 0.682474
\(259\) −18.9915 −1.18008
\(260\) 41.2572 2.55866
\(261\) −6.14894 −0.380610
\(262\) 15.0262 0.928324
\(263\) 20.0507 1.23638 0.618190 0.786029i \(-0.287866\pi\)
0.618190 + 0.786029i \(0.287866\pi\)
\(264\) −10.3741 −0.638483
\(265\) 15.3048 0.940165
\(266\) −48.2913 −2.96093
\(267\) −11.7140 −0.716885
\(268\) −40.7377 −2.48845
\(269\) −25.0222 −1.52563 −0.762816 0.646615i \(-0.776184\pi\)
−0.762816 + 0.646615i \(0.776184\pi\)
\(270\) −5.85879 −0.356555
\(271\) −12.0829 −0.733986 −0.366993 0.930224i \(-0.619613\pi\)
−0.366993 + 0.930224i \(0.619613\pi\)
\(272\) 1.87256 0.113541
\(273\) 24.1041 1.45884
\(274\) −50.8610 −3.07262
\(275\) −2.98444 −0.179968
\(276\) 4.75319 0.286109
\(277\) −11.9900 −0.720411 −0.360206 0.932873i \(-0.617294\pi\)
−0.360206 + 0.932873i \(0.617294\pi\)
\(278\) −48.7747 −2.92531
\(279\) −6.63171 −0.397030
\(280\) 49.6714 2.96844
\(281\) −3.78720 −0.225925 −0.112963 0.993599i \(-0.536034\pi\)
−0.112963 + 0.993599i \(0.536034\pi\)
\(282\) −23.7663 −1.41526
\(283\) −19.6833 −1.17005 −0.585025 0.811015i \(-0.698915\pi\)
−0.585025 + 0.811015i \(0.698915\pi\)
\(284\) 15.9320 0.945393
\(285\) 9.62618 0.570206
\(286\) −29.4946 −1.74405
\(287\) −37.0938 −2.18958
\(288\) 3.24955 0.191482
\(289\) 1.00000 0.0588235
\(290\) −36.0253 −2.11548
\(291\) 3.40745 0.199748
\(292\) 1.76819 0.103475
\(293\) −5.42312 −0.316822 −0.158411 0.987373i \(-0.550637\pi\)
−0.158411 + 0.987373i \(0.550637\pi\)
\(294\) 48.2159 2.81201
\(295\) −7.23943 −0.421496
\(296\) 13.9654 0.811724
\(297\) 2.69830 0.156571
\(298\) 16.2633 0.942109
\(299\) 6.05082 0.349928
\(300\) −4.00560 −0.231263
\(301\) 24.1732 1.39332
\(302\) −25.4196 −1.46273
\(303\) −12.9375 −0.743238
\(304\) 7.29475 0.418383
\(305\) 15.9865 0.915387
\(306\) −2.37098 −0.135540
\(307\) 11.6524 0.665039 0.332520 0.943096i \(-0.392101\pi\)
0.332520 + 0.943096i \(0.392101\pi\)
\(308\) −51.0919 −2.91123
\(309\) −15.3394 −0.872630
\(310\) −38.8538 −2.20675
\(311\) 6.91745 0.392252 0.196126 0.980579i \(-0.437164\pi\)
0.196126 + 0.980579i \(0.437164\pi\)
\(312\) −17.7249 −1.00348
\(313\) 7.62009 0.430713 0.215357 0.976535i \(-0.430909\pi\)
0.215357 + 0.976535i \(0.430909\pi\)
\(314\) 2.37098 0.133802
\(315\) −12.9195 −0.727932
\(316\) −9.32942 −0.524821
\(317\) −17.2337 −0.967940 −0.483970 0.875085i \(-0.660806\pi\)
−0.483970 + 0.875085i \(0.660806\pi\)
\(318\) −14.6851 −0.823497
\(319\) 16.5917 0.928956
\(320\) 28.2928 1.58162
\(321\) −10.4852 −0.585225
\(322\) 16.2699 0.906685
\(323\) 3.89560 0.216757
\(324\) 3.62156 0.201198
\(325\) −5.09913 −0.282849
\(326\) −28.3100 −1.56795
\(327\) 0.790168 0.0436964
\(328\) 27.2769 1.50612
\(329\) −52.4082 −2.88936
\(330\) 15.8088 0.870246
\(331\) −3.41851 −0.187898 −0.0939492 0.995577i \(-0.529949\pi\)
−0.0939492 + 0.995577i \(0.529949\pi\)
\(332\) −10.7107 −0.587828
\(333\) −3.63240 −0.199054
\(334\) 26.8873 1.47121
\(335\) 27.7959 1.51865
\(336\) −9.79045 −0.534113
\(337\) 8.67559 0.472589 0.236295 0.971681i \(-0.424067\pi\)
0.236295 + 0.971681i \(0.424067\pi\)
\(338\) −19.5710 −1.06452
\(339\) 14.4514 0.784891
\(340\) −8.94902 −0.485329
\(341\) 17.8944 0.969035
\(342\) −9.23639 −0.499447
\(343\) 69.7247 3.76478
\(344\) −17.7758 −0.958405
\(345\) −3.24317 −0.174606
\(346\) 54.1249 2.90977
\(347\) 36.6289 1.96634 0.983172 0.182684i \(-0.0584784\pi\)
0.983172 + 0.182684i \(0.0584784\pi\)
\(348\) 22.2687 1.19373
\(349\) 0.392277 0.0209981 0.0104991 0.999945i \(-0.496658\pi\)
0.0104991 + 0.999945i \(0.496658\pi\)
\(350\) −13.7109 −0.732879
\(351\) 4.61025 0.246077
\(352\) −8.76828 −0.467351
\(353\) 10.1166 0.538453 0.269227 0.963077i \(-0.413232\pi\)
0.269227 + 0.963077i \(0.413232\pi\)
\(354\) 6.94629 0.369191
\(355\) −10.8707 −0.576955
\(356\) 42.4229 2.24841
\(357\) −5.22837 −0.276715
\(358\) −52.8281 −2.79205
\(359\) 13.6110 0.718362 0.359181 0.933268i \(-0.383056\pi\)
0.359181 + 0.933268i \(0.383056\pi\)
\(360\) 9.50037 0.500714
\(361\) −3.82432 −0.201280
\(362\) 20.2085 1.06214
\(363\) 3.71916 0.195205
\(364\) −87.2943 −4.57546
\(365\) −1.20646 −0.0631490
\(366\) −15.3392 −0.801794
\(367\) −5.45469 −0.284732 −0.142366 0.989814i \(-0.545471\pi\)
−0.142366 + 0.989814i \(0.545471\pi\)
\(368\) −2.45769 −0.128116
\(369\) −7.09471 −0.369336
\(370\) −21.2815 −1.10637
\(371\) −32.3827 −1.68123
\(372\) 24.0171 1.24523
\(373\) 20.4238 1.05751 0.528753 0.848776i \(-0.322660\pi\)
0.528753 + 0.848776i \(0.322660\pi\)
\(374\) 6.39763 0.330814
\(375\) −9.62213 −0.496885
\(376\) 38.5384 1.98747
\(377\) 28.3481 1.46000
\(378\) 12.3964 0.637600
\(379\) −2.81061 −0.144371 −0.0721857 0.997391i \(-0.522997\pi\)
−0.0721857 + 0.997391i \(0.522997\pi\)
\(380\) −34.8618 −1.78837
\(381\) −7.69943 −0.394454
\(382\) 40.0505 2.04916
\(383\) −3.61760 −0.184851 −0.0924253 0.995720i \(-0.529462\pi\)
−0.0924253 + 0.995720i \(0.529462\pi\)
\(384\) −20.6481 −1.05369
\(385\) 34.8608 1.77667
\(386\) −43.6954 −2.22404
\(387\) 4.62347 0.235024
\(388\) −12.3403 −0.626483
\(389\) −33.0758 −1.67701 −0.838504 0.544896i \(-0.816569\pi\)
−0.838504 + 0.544896i \(0.816569\pi\)
\(390\) 27.0105 1.36773
\(391\) −1.31247 −0.0663746
\(392\) −78.1849 −3.94893
\(393\) 6.33756 0.319688
\(394\) 11.9027 0.599649
\(395\) 6.36560 0.320288
\(396\) −9.77206 −0.491064
\(397\) −12.0119 −0.602858 −0.301429 0.953489i \(-0.597464\pi\)
−0.301429 + 0.953489i \(0.597464\pi\)
\(398\) 5.30758 0.266045
\(399\) −20.3676 −1.01966
\(400\) 2.07114 0.103557
\(401\) 4.09414 0.204451 0.102226 0.994761i \(-0.467404\pi\)
0.102226 + 0.994761i \(0.467404\pi\)
\(402\) −26.6704 −1.33020
\(403\) 30.5738 1.52299
\(404\) 46.8538 2.33106
\(405\) −2.47104 −0.122787
\(406\) 76.2245 3.78296
\(407\) 9.80131 0.485833
\(408\) 3.84468 0.190340
\(409\) −28.8685 −1.42746 −0.713728 0.700423i \(-0.752995\pi\)
−0.713728 + 0.700423i \(0.752995\pi\)
\(410\) −41.5664 −2.05282
\(411\) −21.4514 −1.05812
\(412\) 55.5526 2.73688
\(413\) 15.3176 0.753729
\(414\) 3.11185 0.152939
\(415\) 7.30809 0.358740
\(416\) −14.9812 −0.734516
\(417\) −20.5715 −1.00739
\(418\) 24.9226 1.21900
\(419\) −3.10891 −0.151880 −0.0759402 0.997112i \(-0.524196\pi\)
−0.0759402 + 0.997112i \(0.524196\pi\)
\(420\) 46.7888 2.28306
\(421\) −13.0424 −0.635647 −0.317824 0.948150i \(-0.602952\pi\)
−0.317824 + 0.948150i \(0.602952\pi\)
\(422\) −34.9973 −1.70364
\(423\) −10.0238 −0.487375
\(424\) 23.8127 1.15644
\(425\) 1.10604 0.0536510
\(426\) 10.4305 0.505358
\(427\) −33.8253 −1.63692
\(428\) 37.9726 1.83548
\(429\) −12.4398 −0.600601
\(430\) 27.0879 1.30630
\(431\) 23.4130 1.12777 0.563883 0.825855i \(-0.309307\pi\)
0.563883 + 0.825855i \(0.309307\pi\)
\(432\) −1.87256 −0.0900938
\(433\) 39.3613 1.89158 0.945792 0.324772i \(-0.105288\pi\)
0.945792 + 0.324772i \(0.105288\pi\)
\(434\) 82.2092 3.94617
\(435\) −15.1943 −0.728510
\(436\) −2.86164 −0.137048
\(437\) −5.11286 −0.244581
\(438\) 1.15761 0.0553126
\(439\) −1.79667 −0.0857506 −0.0428753 0.999080i \(-0.513652\pi\)
−0.0428753 + 0.999080i \(0.513652\pi\)
\(440\) −25.6349 −1.22210
\(441\) 20.3358 0.968373
\(442\) 10.9308 0.519926
\(443\) −1.79144 −0.0851138 −0.0425569 0.999094i \(-0.513550\pi\)
−0.0425569 + 0.999094i \(0.513550\pi\)
\(444\) 13.1549 0.624306
\(445\) −28.9458 −1.37216
\(446\) 15.3458 0.726642
\(447\) 6.85932 0.324434
\(448\) −59.8636 −2.82829
\(449\) 12.7484 0.601632 0.300816 0.953682i \(-0.402741\pi\)
0.300816 + 0.953682i \(0.402741\pi\)
\(450\) −2.62241 −0.123622
\(451\) 19.1437 0.901440
\(452\) −52.3365 −2.46170
\(453\) −10.7211 −0.503722
\(454\) 24.5466 1.15203
\(455\) 59.5621 2.79232
\(456\) 14.9773 0.701378
\(457\) −15.1845 −0.710300 −0.355150 0.934809i \(-0.615570\pi\)
−0.355150 + 0.934809i \(0.615570\pi\)
\(458\) 67.5921 3.15837
\(459\) −1.00000 −0.0466760
\(460\) 11.7453 0.547629
\(461\) 10.2843 0.478987 0.239493 0.970898i \(-0.423019\pi\)
0.239493 + 0.970898i \(0.423019\pi\)
\(462\) −33.4492 −1.55620
\(463\) −28.9102 −1.34357 −0.671786 0.740745i \(-0.734473\pi\)
−0.671786 + 0.740745i \(0.734473\pi\)
\(464\) −11.5143 −0.534537
\(465\) −16.3872 −0.759940
\(466\) −5.87159 −0.271996
\(467\) 31.6556 1.46485 0.732424 0.680849i \(-0.238389\pi\)
0.732424 + 0.680849i \(0.238389\pi\)
\(468\) −16.6963 −0.771785
\(469\) −58.8121 −2.71569
\(470\) −58.7275 −2.70890
\(471\) 1.00000 0.0460776
\(472\) −11.2638 −0.518458
\(473\) −12.4755 −0.573625
\(474\) −6.10784 −0.280542
\(475\) 4.30870 0.197697
\(476\) 18.9348 0.867877
\(477\) −6.19366 −0.283588
\(478\) −51.0408 −2.33455
\(479\) 17.1393 0.783115 0.391558 0.920154i \(-0.371936\pi\)
0.391558 + 0.920154i \(0.371936\pi\)
\(480\) 8.02978 0.366508
\(481\) 16.7462 0.763563
\(482\) 37.5408 1.70994
\(483\) 6.86209 0.312236
\(484\) −13.4692 −0.612234
\(485\) 8.41995 0.382330
\(486\) 2.37098 0.107550
\(487\) 40.0408 1.81442 0.907210 0.420678i \(-0.138208\pi\)
0.907210 + 0.420678i \(0.138208\pi\)
\(488\) 24.8734 1.12597
\(489\) −11.9402 −0.539955
\(490\) 119.144 5.38236
\(491\) 16.8237 0.759244 0.379622 0.925142i \(-0.376054\pi\)
0.379622 + 0.925142i \(0.376054\pi\)
\(492\) 25.6939 1.15837
\(493\) −6.14894 −0.276934
\(494\) 42.5820 1.91586
\(495\) 6.66762 0.299687
\(496\) −12.4183 −0.557598
\(497\) 23.0008 1.03173
\(498\) −7.01216 −0.314223
\(499\) −18.0131 −0.806376 −0.403188 0.915117i \(-0.632098\pi\)
−0.403188 + 0.915117i \(0.632098\pi\)
\(500\) 34.8471 1.55841
\(501\) 11.3402 0.506641
\(502\) −41.0508 −1.83219
\(503\) 27.5885 1.23011 0.615055 0.788485i \(-0.289134\pi\)
0.615055 + 0.788485i \(0.289134\pi\)
\(504\) −20.1014 −0.895389
\(505\) −31.9690 −1.42260
\(506\) −8.39671 −0.373279
\(507\) −8.25437 −0.366589
\(508\) 27.8839 1.23715
\(509\) 16.1843 0.717354 0.358677 0.933462i \(-0.383228\pi\)
0.358677 + 0.933462i \(0.383228\pi\)
\(510\) −5.85879 −0.259432
\(511\) 2.55269 0.112925
\(512\) 20.4838 0.905266
\(513\) −3.89560 −0.171995
\(514\) −2.24092 −0.0988428
\(515\) −37.9044 −1.67027
\(516\) −16.7442 −0.737120
\(517\) 27.0473 1.18954
\(518\) 45.0285 1.97844
\(519\) 22.8280 1.00204
\(520\) −43.7990 −1.92072
\(521\) −1.87747 −0.0822534 −0.0411267 0.999154i \(-0.513095\pi\)
−0.0411267 + 0.999154i \(0.513095\pi\)
\(522\) 14.5790 0.638106
\(523\) −5.56844 −0.243491 −0.121746 0.992561i \(-0.538849\pi\)
−0.121746 + 0.992561i \(0.538849\pi\)
\(524\) −22.9518 −1.00266
\(525\) −5.78280 −0.252382
\(526\) −47.5399 −2.07284
\(527\) −6.63171 −0.288882
\(528\) 5.05274 0.219892
\(529\) −21.2774 −0.925105
\(530\) −36.2874 −1.57622
\(531\) 2.92971 0.127138
\(532\) 73.7625 3.19801
\(533\) 32.7084 1.41676
\(534\) 27.7737 1.20188
\(535\) −25.9093 −1.12016
\(536\) 43.2475 1.86801
\(537\) −22.2811 −0.961501
\(538\) 59.3273 2.55778
\(539\) −54.8723 −2.36352
\(540\) 8.94902 0.385104
\(541\) 14.1546 0.608556 0.304278 0.952583i \(-0.401585\pi\)
0.304278 + 0.952583i \(0.401585\pi\)
\(542\) 28.6484 1.23055
\(543\) 8.52326 0.365768
\(544\) 3.24955 0.139323
\(545\) 1.95254 0.0836375
\(546\) −57.1503 −2.44581
\(547\) −37.4452 −1.60104 −0.800521 0.599305i \(-0.795444\pi\)
−0.800521 + 0.599305i \(0.795444\pi\)
\(548\) 77.6876 3.31865
\(549\) −6.46956 −0.276114
\(550\) 7.07605 0.301724
\(551\) −23.9538 −1.02047
\(552\) −5.04604 −0.214774
\(553\) −13.4687 −0.572747
\(554\) 28.4282 1.20780
\(555\) −8.97580 −0.381002
\(556\) 74.5009 3.15954
\(557\) −2.38070 −0.100873 −0.0504367 0.998727i \(-0.516061\pi\)
−0.0504367 + 0.998727i \(0.516061\pi\)
\(558\) 15.7237 0.665636
\(559\) −21.3153 −0.901542
\(560\) −24.1926 −1.02232
\(561\) 2.69830 0.113922
\(562\) 8.97937 0.378772
\(563\) 39.6280 1.67012 0.835060 0.550159i \(-0.185433\pi\)
0.835060 + 0.550159i \(0.185433\pi\)
\(564\) 36.3018 1.52858
\(565\) 35.7099 1.50233
\(566\) 46.6687 1.96163
\(567\) 5.22837 0.219571
\(568\) −16.9136 −0.709680
\(569\) 12.5126 0.524556 0.262278 0.964992i \(-0.415526\pi\)
0.262278 + 0.964992i \(0.415526\pi\)
\(570\) −22.8235 −0.955971
\(571\) −41.6648 −1.74362 −0.871809 0.489846i \(-0.837053\pi\)
−0.871809 + 0.489846i \(0.837053\pi\)
\(572\) 45.0516 1.88370
\(573\) 16.8920 0.705672
\(574\) 87.9486 3.67091
\(575\) −1.45165 −0.0605380
\(576\) −11.4498 −0.477073
\(577\) 24.6149 1.02473 0.512366 0.858767i \(-0.328769\pi\)
0.512366 + 0.858767i \(0.328769\pi\)
\(578\) −2.37098 −0.0986199
\(579\) −18.4292 −0.765893
\(580\) 55.0269 2.28487
\(581\) −15.4629 −0.641508
\(582\) −8.07901 −0.334886
\(583\) 16.7124 0.692155
\(584\) −1.87713 −0.0776760
\(585\) 11.3921 0.471006
\(586\) 12.8581 0.531164
\(587\) 27.3401 1.12845 0.564223 0.825622i \(-0.309176\pi\)
0.564223 + 0.825622i \(0.309176\pi\)
\(588\) −73.6474 −3.03717
\(589\) −25.8345 −1.06449
\(590\) 17.1646 0.706654
\(591\) 5.02015 0.206501
\(592\) −6.80190 −0.279556
\(593\) 34.9444 1.43499 0.717497 0.696562i \(-0.245288\pi\)
0.717497 + 0.696562i \(0.245288\pi\)
\(594\) −6.39763 −0.262498
\(595\) −12.9195 −0.529648
\(596\) −24.8414 −1.01754
\(597\) 2.23856 0.0916181
\(598\) −14.3464 −0.586667
\(599\) −15.9735 −0.652658 −0.326329 0.945256i \(-0.605812\pi\)
−0.326329 + 0.945256i \(0.605812\pi\)
\(600\) 4.25239 0.173603
\(601\) −17.4472 −0.711686 −0.355843 0.934546i \(-0.615806\pi\)
−0.355843 + 0.934546i \(0.615806\pi\)
\(602\) −57.3142 −2.33595
\(603\) −11.2487 −0.458081
\(604\) 38.8271 1.57985
\(605\) 9.19020 0.373635
\(606\) 30.6745 1.24607
\(607\) 43.8396 1.77939 0.889697 0.456551i \(-0.150915\pi\)
0.889697 + 0.456551i \(0.150915\pi\)
\(608\) 12.6589 0.513388
\(609\) 32.1489 1.30274
\(610\) −37.9038 −1.53468
\(611\) 46.2122 1.86955
\(612\) 3.62156 0.146393
\(613\) 18.4040 0.743332 0.371666 0.928367i \(-0.378787\pi\)
0.371666 + 0.928367i \(0.378787\pi\)
\(614\) −27.6277 −1.11496
\(615\) −17.5313 −0.706931
\(616\) 54.2397 2.18538
\(617\) −20.7757 −0.836399 −0.418200 0.908355i \(-0.637339\pi\)
−0.418200 + 0.908355i \(0.637339\pi\)
\(618\) 36.3695 1.46300
\(619\) 22.0025 0.884354 0.442177 0.896928i \(-0.354206\pi\)
0.442177 + 0.896928i \(0.354206\pi\)
\(620\) 59.3473 2.38345
\(621\) 1.31247 0.0526677
\(622\) −16.4011 −0.657626
\(623\) 61.2451 2.45373
\(624\) 8.63298 0.345596
\(625\) −29.3069 −1.17228
\(626\) −18.0671 −0.722107
\(627\) 10.5115 0.419789
\(628\) −3.62156 −0.144516
\(629\) −3.63240 −0.144833
\(630\) 30.6319 1.22041
\(631\) −12.4476 −0.495532 −0.247766 0.968820i \(-0.579696\pi\)
−0.247766 + 0.968820i \(0.579696\pi\)
\(632\) 9.90422 0.393969
\(633\) −14.7607 −0.586683
\(634\) 40.8608 1.62279
\(635\) −19.0256 −0.755008
\(636\) 22.4307 0.889435
\(637\) −93.7532 −3.71464
\(638\) −39.3386 −1.55743
\(639\) 4.39922 0.174031
\(640\) −51.0222 −2.01683
\(641\) 35.9584 1.42027 0.710135 0.704065i \(-0.248634\pi\)
0.710135 + 0.704065i \(0.248634\pi\)
\(642\) 24.8601 0.981152
\(643\) 27.8508 1.09833 0.549163 0.835715i \(-0.314947\pi\)
0.549163 + 0.835715i \(0.314947\pi\)
\(644\) −24.8514 −0.979284
\(645\) 11.4248 0.449850
\(646\) −9.23639 −0.363401
\(647\) −39.8037 −1.56484 −0.782422 0.622748i \(-0.786016\pi\)
−0.782422 + 0.622748i \(0.786016\pi\)
\(648\) −3.84468 −0.151033
\(649\) −7.90524 −0.310308
\(650\) 12.0899 0.474207
\(651\) 34.6730 1.35894
\(652\) 43.2422 1.69349
\(653\) −8.51179 −0.333092 −0.166546 0.986034i \(-0.553261\pi\)
−0.166546 + 0.986034i \(0.553261\pi\)
\(654\) −1.87347 −0.0732586
\(655\) 15.6604 0.611901
\(656\) −13.2853 −0.518704
\(657\) 0.488239 0.0190480
\(658\) 124.259 4.84412
\(659\) −11.1397 −0.433943 −0.216971 0.976178i \(-0.569618\pi\)
−0.216971 + 0.976178i \(0.569618\pi\)
\(660\) −24.1472 −0.939927
\(661\) −19.7188 −0.766974 −0.383487 0.923546i \(-0.625277\pi\)
−0.383487 + 0.923546i \(0.625277\pi\)
\(662\) 8.10523 0.315019
\(663\) 4.61025 0.179047
\(664\) 11.3706 0.441266
\(665\) −50.3292 −1.95168
\(666\) 8.61235 0.333722
\(667\) 8.07030 0.312483
\(668\) −41.0690 −1.58901
\(669\) 6.47232 0.250234
\(670\) −65.9036 −2.54608
\(671\) 17.4568 0.673914
\(672\) −16.9899 −0.655398
\(673\) −14.4367 −0.556494 −0.278247 0.960510i \(-0.589753\pi\)
−0.278247 + 0.960510i \(0.589753\pi\)
\(674\) −20.5697 −0.792314
\(675\) −1.10604 −0.0425716
\(676\) 29.8937 1.14976
\(677\) −41.6253 −1.59979 −0.799894 0.600141i \(-0.795111\pi\)
−0.799894 + 0.600141i \(0.795111\pi\)
\(678\) −34.2640 −1.31590
\(679\) −17.8154 −0.683693
\(680\) 9.50037 0.364323
\(681\) 10.3529 0.396725
\(682\) −42.4272 −1.62462
\(683\) −35.9057 −1.37389 −0.686947 0.726708i \(-0.741049\pi\)
−0.686947 + 0.726708i \(0.741049\pi\)
\(684\) 14.1081 0.539438
\(685\) −53.0074 −2.02531
\(686\) −165.316 −6.31180
\(687\) 28.5081 1.08765
\(688\) 8.65774 0.330073
\(689\) 28.5543 1.08783
\(690\) 7.68950 0.292734
\(691\) −28.0004 −1.06519 −0.532593 0.846372i \(-0.678782\pi\)
−0.532593 + 0.846372i \(0.678782\pi\)
\(692\) −82.6730 −3.14276
\(693\) −14.1077 −0.535908
\(694\) −86.8465 −3.29665
\(695\) −50.8330 −1.92821
\(696\) −23.6407 −0.896099
\(697\) −7.09471 −0.268731
\(698\) −0.930082 −0.0352041
\(699\) −2.47644 −0.0936674
\(700\) 20.9427 0.791561
\(701\) 20.1014 0.759218 0.379609 0.925147i \(-0.376059\pi\)
0.379609 + 0.925147i \(0.376059\pi\)
\(702\) −10.9308 −0.412557
\(703\) −14.1504 −0.533691
\(704\) 30.8949 1.16440
\(705\) −24.7693 −0.932864
\(706\) −23.9863 −0.902737
\(707\) 67.6418 2.54393
\(708\) −10.6101 −0.398752
\(709\) 9.96787 0.374351 0.187176 0.982326i \(-0.440067\pi\)
0.187176 + 0.982326i \(0.440067\pi\)
\(710\) 25.7741 0.967286
\(711\) −2.57608 −0.0966106
\(712\) −45.0366 −1.68782
\(713\) 8.70394 0.325965
\(714\) 12.3964 0.463923
\(715\) −30.7394 −1.14959
\(716\) 80.6923 3.01561
\(717\) −21.5273 −0.803952
\(718\) −32.2715 −1.20436
\(719\) 16.6736 0.621821 0.310911 0.950439i \(-0.399366\pi\)
0.310911 + 0.950439i \(0.399366\pi\)
\(720\) −4.62718 −0.172445
\(721\) 80.2002 2.98681
\(722\) 9.06740 0.337454
\(723\) 15.8335 0.588852
\(724\) −30.8675 −1.14718
\(725\) −6.80099 −0.252582
\(726\) −8.81806 −0.327269
\(727\) 19.3536 0.717785 0.358893 0.933379i \(-0.383154\pi\)
0.358893 + 0.933379i \(0.383154\pi\)
\(728\) 92.6725 3.43467
\(729\) 1.00000 0.0370370
\(730\) 2.86049 0.105872
\(731\) 4.62347 0.171005
\(732\) 23.4299 0.865994
\(733\) 37.6818 1.39181 0.695904 0.718135i \(-0.255004\pi\)
0.695904 + 0.718135i \(0.255004\pi\)
\(734\) 12.9330 0.477365
\(735\) 50.2507 1.85352
\(736\) −4.26495 −0.157208
\(737\) 30.3523 1.11804
\(738\) 16.8214 0.619205
\(739\) −35.0246 −1.28840 −0.644201 0.764856i \(-0.722810\pi\)
−0.644201 + 0.764856i \(0.722810\pi\)
\(740\) 32.5064 1.19496
\(741\) 17.9597 0.659765
\(742\) 76.7789 2.81864
\(743\) 10.7145 0.393076 0.196538 0.980496i \(-0.437030\pi\)
0.196538 + 0.980496i \(0.437030\pi\)
\(744\) −25.4968 −0.934760
\(745\) 16.9496 0.620987
\(746\) −48.4245 −1.77295
\(747\) −2.95749 −0.108209
\(748\) −9.77206 −0.357302
\(749\) 54.8203 2.00309
\(750\) 22.8139 0.833046
\(751\) 8.76531 0.319851 0.159925 0.987129i \(-0.448875\pi\)
0.159925 + 0.987129i \(0.448875\pi\)
\(752\) −18.7702 −0.684480
\(753\) −17.3138 −0.630951
\(754\) −67.2129 −2.44775
\(755\) −26.4923 −0.964153
\(756\) −18.9348 −0.688653
\(757\) 7.09252 0.257782 0.128891 0.991659i \(-0.458858\pi\)
0.128891 + 0.991659i \(0.458858\pi\)
\(758\) 6.66391 0.242044
\(759\) −3.54145 −0.128546
\(760\) 37.0096 1.34248
\(761\) 19.7331 0.715326 0.357663 0.933851i \(-0.383574\pi\)
0.357663 + 0.933851i \(0.383574\pi\)
\(762\) 18.2552 0.661316
\(763\) −4.13129 −0.149563
\(764\) −61.1752 −2.21324
\(765\) −2.47104 −0.0893407
\(766\) 8.57726 0.309909
\(767\) −13.5067 −0.487698
\(768\) 26.0567 0.940240
\(769\) 45.2567 1.63200 0.815999 0.578053i \(-0.196187\pi\)
0.815999 + 0.578053i \(0.196187\pi\)
\(770\) −82.6543 −2.97865
\(771\) −0.945145 −0.0340386
\(772\) 66.7426 2.40212
\(773\) −52.8290 −1.90013 −0.950063 0.312058i \(-0.898982\pi\)
−0.950063 + 0.312058i \(0.898982\pi\)
\(774\) −10.9622 −0.394027
\(775\) −7.33496 −0.263480
\(776\) 13.1006 0.470283
\(777\) 18.9915 0.681317
\(778\) 78.4220 2.81157
\(779\) −27.6381 −0.990239
\(780\) −41.2572 −1.47724
\(781\) −11.8704 −0.424758
\(782\) 3.11185 0.111279
\(783\) 6.14894 0.219745
\(784\) 38.0802 1.36001
\(785\) 2.47104 0.0881952
\(786\) −15.0262 −0.535968
\(787\) 52.4223 1.86865 0.934327 0.356417i \(-0.116002\pi\)
0.934327 + 0.356417i \(0.116002\pi\)
\(788\) −18.1808 −0.647663
\(789\) −20.0507 −0.713824
\(790\) −15.0927 −0.536975
\(791\) −75.5571 −2.68650
\(792\) 10.3741 0.368628
\(793\) 29.8263 1.05916
\(794\) 28.4799 1.01071
\(795\) −15.3048 −0.542805
\(796\) −8.10707 −0.287347
\(797\) −45.7120 −1.61920 −0.809601 0.586980i \(-0.800317\pi\)
−0.809601 + 0.586980i \(0.800317\pi\)
\(798\) 48.2913 1.70949
\(799\) −10.0238 −0.354617
\(800\) 3.59415 0.127072
\(801\) 11.7140 0.413894
\(802\) −9.70713 −0.342771
\(803\) −1.31742 −0.0464907
\(804\) 40.7377 1.43671
\(805\) 16.9565 0.597638
\(806\) −72.4900 −2.55335
\(807\) 25.0222 0.880825
\(808\) −49.7405 −1.74986
\(809\) −14.0152 −0.492749 −0.246375 0.969175i \(-0.579239\pi\)
−0.246375 + 0.969175i \(0.579239\pi\)
\(810\) 5.85879 0.205857
\(811\) −14.6650 −0.514957 −0.257478 0.966284i \(-0.582892\pi\)
−0.257478 + 0.966284i \(0.582892\pi\)
\(812\) −116.429 −4.08586
\(813\) 12.0829 0.423767
\(814\) −23.2387 −0.814517
\(815\) −29.5047 −1.03351
\(816\) −1.87256 −0.0655528
\(817\) 18.0112 0.630131
\(818\) 68.4467 2.39318
\(819\) −24.1041 −0.842264
\(820\) 63.4907 2.21719
\(821\) 10.7239 0.374267 0.187134 0.982334i \(-0.440080\pi\)
0.187134 + 0.982334i \(0.440080\pi\)
\(822\) 50.8610 1.77398
\(823\) 47.2063 1.64551 0.822754 0.568397i \(-0.192436\pi\)
0.822754 + 0.568397i \(0.192436\pi\)
\(824\) −58.9753 −2.05450
\(825\) 2.98444 0.103905
\(826\) −36.3177 −1.26366
\(827\) −12.1829 −0.423639 −0.211820 0.977309i \(-0.567939\pi\)
−0.211820 + 0.977309i \(0.567939\pi\)
\(828\) −4.75319 −0.165185
\(829\) 8.53163 0.296316 0.148158 0.988964i \(-0.452666\pi\)
0.148158 + 0.988964i \(0.452666\pi\)
\(830\) −17.3273 −0.601441
\(831\) 11.9900 0.415930
\(832\) 52.7862 1.83003
\(833\) 20.3358 0.704595
\(834\) 48.7747 1.68893
\(835\) 28.0220 0.969741
\(836\) −38.0680 −1.31661
\(837\) 6.63171 0.229226
\(838\) 7.37118 0.254633
\(839\) 4.13492 0.142753 0.0713766 0.997449i \(-0.477261\pi\)
0.0713766 + 0.997449i \(0.477261\pi\)
\(840\) −49.6714 −1.71383
\(841\) 8.80941 0.303773
\(842\) 30.9233 1.06569
\(843\) 3.78720 0.130438
\(844\) 53.4566 1.84005
\(845\) −20.3969 −0.701674
\(846\) 23.7663 0.817102
\(847\) −19.4451 −0.668143
\(848\) −11.5980 −0.398278
\(849\) 19.6833 0.675529
\(850\) −2.62241 −0.0899479
\(851\) 4.76742 0.163425
\(852\) −15.9320 −0.545823
\(853\) 29.1229 0.997147 0.498574 0.866847i \(-0.333857\pi\)
0.498574 + 0.866847i \(0.333857\pi\)
\(854\) 80.1991 2.74436
\(855\) −9.62618 −0.329208
\(856\) −40.3122 −1.37784
\(857\) −21.2480 −0.725818 −0.362909 0.931825i \(-0.618216\pi\)
−0.362909 + 0.931825i \(0.618216\pi\)
\(858\) 29.4946 1.00693
\(859\) 42.9267 1.46464 0.732321 0.680960i \(-0.238437\pi\)
0.732321 + 0.680960i \(0.238437\pi\)
\(860\) −41.3755 −1.41089
\(861\) 37.0938 1.26415
\(862\) −55.5119 −1.89074
\(863\) 42.7711 1.45594 0.727972 0.685606i \(-0.240463\pi\)
0.727972 + 0.685606i \(0.240463\pi\)
\(864\) −3.24955 −0.110552
\(865\) 56.4090 1.91796
\(866\) −93.3250 −3.17131
\(867\) −1.00000 −0.0339618
\(868\) −125.570 −4.26214
\(869\) 6.95105 0.235798
\(870\) 36.0253 1.22137
\(871\) 51.8591 1.75718
\(872\) 3.03794 0.102878
\(873\) −3.40745 −0.115325
\(874\) 12.1225 0.410050
\(875\) 50.3080 1.70072
\(876\) −1.76819 −0.0597415
\(877\) 3.09226 0.104418 0.0522091 0.998636i \(-0.483374\pi\)
0.0522091 + 0.998636i \(0.483374\pi\)
\(878\) 4.25988 0.143764
\(879\) 5.42312 0.182917
\(880\) 12.4855 0.420887
\(881\) 22.0756 0.743746 0.371873 0.928284i \(-0.378716\pi\)
0.371873 + 0.928284i \(0.378716\pi\)
\(882\) −48.2159 −1.62351
\(883\) 0.933810 0.0314252 0.0157126 0.999877i \(-0.494998\pi\)
0.0157126 + 0.999877i \(0.494998\pi\)
\(884\) −16.6963 −0.561556
\(885\) 7.23943 0.243351
\(886\) 4.24747 0.142696
\(887\) 57.1959 1.92045 0.960226 0.279224i \(-0.0900773\pi\)
0.960226 + 0.279224i \(0.0900773\pi\)
\(888\) −13.9654 −0.468649
\(889\) 40.2555 1.35012
\(890\) 68.6299 2.30048
\(891\) −2.69830 −0.0903966
\(892\) −23.4399 −0.784825
\(893\) −39.0487 −1.30672
\(894\) −16.2633 −0.543927
\(895\) −55.0575 −1.84037
\(896\) 107.956 3.60655
\(897\) −6.05082 −0.202031
\(898\) −30.2261 −1.00866
\(899\) 40.7780 1.36002
\(900\) 4.00560 0.133520
\(901\) −6.19366 −0.206341
\(902\) −45.3893 −1.51130
\(903\) −24.1732 −0.804434
\(904\) 55.5610 1.84793
\(905\) 21.0613 0.700102
\(906\) 25.4196 0.844508
\(907\) 47.0996 1.56392 0.781958 0.623331i \(-0.214221\pi\)
0.781958 + 0.623331i \(0.214221\pi\)
\(908\) −37.4938 −1.24427
\(909\) 12.9375 0.429109
\(910\) −141.221 −4.68142
\(911\) −13.6451 −0.452083 −0.226041 0.974118i \(-0.572578\pi\)
−0.226041 + 0.974118i \(0.572578\pi\)
\(912\) −7.29475 −0.241553
\(913\) 7.98021 0.264106
\(914\) 36.0021 1.19085
\(915\) −15.9865 −0.528499
\(916\) −103.244 −3.41127
\(917\) −33.1351 −1.09422
\(918\) 2.37098 0.0782541
\(919\) 10.4768 0.345599 0.172799 0.984957i \(-0.444719\pi\)
0.172799 + 0.984957i \(0.444719\pi\)
\(920\) −12.4690 −0.411090
\(921\) −11.6524 −0.383961
\(922\) −24.3839 −0.803040
\(923\) −20.2815 −0.667574
\(924\) 51.0919 1.68080
\(925\) −4.01759 −0.132097
\(926\) 68.5457 2.25255
\(927\) 15.3394 0.503813
\(928\) −19.9813 −0.655918
\(929\) 36.3078 1.19122 0.595610 0.803274i \(-0.296911\pi\)
0.595610 + 0.803274i \(0.296911\pi\)
\(930\) 38.8538 1.27407
\(931\) 79.2202 2.59634
\(932\) 8.96856 0.293775
\(933\) −6.91745 −0.226467
\(934\) −75.0549 −2.45587
\(935\) 6.66762 0.218054
\(936\) 17.7249 0.579358
\(937\) −23.8356 −0.778675 −0.389337 0.921095i \(-0.627296\pi\)
−0.389337 + 0.921095i \(0.627296\pi\)
\(938\) 139.443 4.55296
\(939\) −7.62009 −0.248672
\(940\) 89.7033 2.92580
\(941\) −55.4565 −1.80783 −0.903915 0.427711i \(-0.859320\pi\)
−0.903915 + 0.427711i \(0.859320\pi\)
\(942\) −2.37098 −0.0772508
\(943\) 9.31161 0.303228
\(944\) 5.48606 0.178556
\(945\) 12.9195 0.420272
\(946\) 29.5792 0.961704
\(947\) 0.627943 0.0204054 0.0102027 0.999948i \(-0.496752\pi\)
0.0102027 + 0.999948i \(0.496752\pi\)
\(948\) 9.32942 0.303006
\(949\) −2.25090 −0.0730674
\(950\) −10.2158 −0.331446
\(951\) 17.2337 0.558840
\(952\) −20.1014 −0.651491
\(953\) 25.4306 0.823777 0.411888 0.911234i \(-0.364869\pi\)
0.411888 + 0.911234i \(0.364869\pi\)
\(954\) 14.6851 0.475446
\(955\) 41.7407 1.35070
\(956\) 77.9623 2.52148
\(957\) −16.5917 −0.536333
\(958\) −40.6370 −1.31292
\(959\) 112.156 3.62171
\(960\) −28.2928 −0.913147
\(961\) 12.9796 0.418697
\(962\) −39.7051 −1.28014
\(963\) 10.4852 0.337880
\(964\) −57.3418 −1.84685
\(965\) −45.5394 −1.46597
\(966\) −16.2699 −0.523475
\(967\) −19.8242 −0.637504 −0.318752 0.947838i \(-0.603264\pi\)
−0.318752 + 0.947838i \(0.603264\pi\)
\(968\) 14.2990 0.459587
\(969\) −3.89560 −0.125145
\(970\) −19.9636 −0.640991
\(971\) 37.3772 1.19949 0.599746 0.800191i \(-0.295268\pi\)
0.599746 + 0.800191i \(0.295268\pi\)
\(972\) −3.62156 −0.116162
\(973\) 107.555 3.44807
\(974\) −94.9359 −3.04194
\(975\) 5.09913 0.163303
\(976\) −12.1147 −0.387781
\(977\) −0.783683 −0.0250723 −0.0125361 0.999921i \(-0.503990\pi\)
−0.0125361 + 0.999921i \(0.503990\pi\)
\(978\) 28.3100 0.905255
\(979\) −31.6079 −1.01019
\(980\) −181.986 −5.81332
\(981\) −0.790168 −0.0252281
\(982\) −39.8887 −1.27290
\(983\) 1.62564 0.0518500 0.0259250 0.999664i \(-0.491747\pi\)
0.0259250 + 0.999664i \(0.491747\pi\)
\(984\) −27.2769 −0.869556
\(985\) 12.4050 0.395256
\(986\) 14.5790 0.464291
\(987\) 52.4082 1.66817
\(988\) −65.0419 −2.06926
\(989\) −6.06817 −0.192957
\(990\) −15.8088 −0.502437
\(991\) −4.02362 −0.127815 −0.0639073 0.997956i \(-0.520356\pi\)
−0.0639073 + 0.997956i \(0.520356\pi\)
\(992\) −21.5501 −0.684216
\(993\) 3.41851 0.108483
\(994\) −54.5344 −1.72973
\(995\) 5.53157 0.175363
\(996\) 10.7107 0.339382
\(997\) 33.7232 1.06802 0.534012 0.845477i \(-0.320684\pi\)
0.534012 + 0.845477i \(0.320684\pi\)
\(998\) 42.7087 1.35192
\(999\) 3.63240 0.114924
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 \(a_p\))