Properties

Label 8034.2.a.o.1.7
Level 8034
Weight 2
Character 8034.1
Self dual Yes
Analytic conductor 64.152
Analytic rank 1
Dimension 7
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(0.194986\)
Character \(\chi\) = 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.32958 q^{5}\) \(+1.00000 q^{6}\) \(-1.38443 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.32958 q^{5}\) \(+1.00000 q^{6}\) \(-1.38443 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(-3.32958 q^{10}\) \(-2.60808 q^{11}\) \(-1.00000 q^{12}\) \(+1.00000 q^{13}\) \(+1.38443 q^{14}\) \(-3.32958 q^{15}\) \(+1.00000 q^{16}\) \(-1.65277 q^{17}\) \(-1.00000 q^{18}\) \(-2.38443 q^{19}\) \(+3.32958 q^{20}\) \(+1.38443 q^{21}\) \(+2.60808 q^{22}\) \(+0.437417 q^{23}\) \(+1.00000 q^{24}\) \(+6.08609 q^{25}\) \(-1.00000 q^{26}\) \(-1.00000 q^{27}\) \(-1.38443 q^{28}\) \(+1.38942 q^{29}\) \(+3.32958 q^{30}\) \(-5.09491 q^{31}\) \(-1.00000 q^{32}\) \(+2.60808 q^{33}\) \(+1.65277 q^{34}\) \(-4.60958 q^{35}\) \(+1.00000 q^{36}\) \(+6.25229 q^{37}\) \(+2.38443 q^{38}\) \(-1.00000 q^{39}\) \(-3.32958 q^{40}\) \(+2.88017 q^{41}\) \(-1.38443 q^{42}\) \(+0.927277 q^{43}\) \(-2.60808 q^{44}\) \(+3.32958 q^{45}\) \(-0.437417 q^{46}\) \(-10.7983 q^{47}\) \(-1.00000 q^{48}\) \(-5.08334 q^{49}\) \(-6.08609 q^{50}\) \(+1.65277 q^{51}\) \(+1.00000 q^{52}\) \(+8.01315 q^{53}\) \(+1.00000 q^{54}\) \(-8.68380 q^{55}\) \(+1.38443 q^{56}\) \(+2.38443 q^{57}\) \(-1.38942 q^{58}\) \(+3.33907 q^{59}\) \(-3.32958 q^{60}\) \(-1.16385 q^{61}\) \(+5.09491 q^{62}\) \(-1.38443 q^{63}\) \(+1.00000 q^{64}\) \(+3.32958 q^{65}\) \(-2.60808 q^{66}\) \(+8.02334 q^{67}\) \(-1.65277 q^{68}\) \(-0.437417 q^{69}\) \(+4.60958 q^{70}\) \(+5.77612 q^{71}\) \(-1.00000 q^{72}\) \(-5.91373 q^{73}\) \(-6.25229 q^{74}\) \(-6.08609 q^{75}\) \(-2.38443 q^{76}\) \(+3.61071 q^{77}\) \(+1.00000 q^{78}\) \(+5.61371 q^{79}\) \(+3.32958 q^{80}\) \(+1.00000 q^{81}\) \(-2.88017 q^{82}\) \(-7.43809 q^{83}\) \(+1.38443 q^{84}\) \(-5.50301 q^{85}\) \(-0.927277 q^{86}\) \(-1.38942 q^{87}\) \(+2.60808 q^{88}\) \(+17.2269 q^{89}\) \(-3.32958 q^{90}\) \(-1.38443 q^{91}\) \(+0.437417 q^{92}\) \(+5.09491 q^{93}\) \(+10.7983 q^{94}\) \(-7.93916 q^{95}\) \(+1.00000 q^{96}\) \(-1.80223 q^{97}\) \(+5.08334 q^{98}\) \(-2.60808 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(7q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 7q^{16} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 7q^{18} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 15q^{25} \) \(\mathstrut -\mathstrut 7q^{26} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 7q^{32} \) \(\mathstrut -\mathstrut 3q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 7q^{36} \) \(\mathstrut +\mathstrut 17q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut -\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 7q^{54} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 5q^{58} \) \(\mathstrut -\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 16q^{62} \) \(\mathstrut -\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 7q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut q^{67} \) \(\mathstrut +\mathstrut 3q^{68} \) \(\mathstrut -\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 10q^{70} \) \(\mathstrut +\mathstrut 15q^{71} \) \(\mathstrut -\mathstrut 7q^{72} \) \(\mathstrut +\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 10q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 7q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 22q^{86} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut 9q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 16q^{93} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut +\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 3.32958 1.48903 0.744516 0.667604i \(-0.232680\pi\)
0.744516 + 0.667604i \(0.232680\pi\)
\(6\) 1.00000 0.408248
\(7\) −1.38443 −0.523267 −0.261634 0.965167i \(-0.584261\pi\)
−0.261634 + 0.965167i \(0.584261\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −3.32958 −1.05290
\(11\) −2.60808 −0.786365 −0.393183 0.919460i \(-0.628626\pi\)
−0.393183 + 0.919460i \(0.628626\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) 1.38443 0.370006
\(15\) −3.32958 −0.859693
\(16\) 1.00000 0.250000
\(17\) −1.65277 −0.400854 −0.200427 0.979709i \(-0.564233\pi\)
−0.200427 + 0.979709i \(0.564233\pi\)
\(18\) −1.00000 −0.235702
\(19\) −2.38443 −0.547027 −0.273513 0.961868i \(-0.588186\pi\)
−0.273513 + 0.961868i \(0.588186\pi\)
\(20\) 3.32958 0.744516
\(21\) 1.38443 0.302108
\(22\) 2.60808 0.556044
\(23\) 0.437417 0.0912077 0.0456038 0.998960i \(-0.485479\pi\)
0.0456038 + 0.998960i \(0.485479\pi\)
\(24\) 1.00000 0.204124
\(25\) 6.08609 1.21722
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) −1.38443 −0.261634
\(29\) 1.38942 0.258009 0.129004 0.991644i \(-0.458822\pi\)
0.129004 + 0.991644i \(0.458822\pi\)
\(30\) 3.32958 0.607895
\(31\) −5.09491 −0.915072 −0.457536 0.889191i \(-0.651268\pi\)
−0.457536 + 0.889191i \(0.651268\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.60808 0.454008
\(34\) 1.65277 0.283447
\(35\) −4.60958 −0.779162
\(36\) 1.00000 0.166667
\(37\) 6.25229 1.02787 0.513935 0.857829i \(-0.328187\pi\)
0.513935 + 0.857829i \(0.328187\pi\)
\(38\) 2.38443 0.386806
\(39\) −1.00000 −0.160128
\(40\) −3.32958 −0.526452
\(41\) 2.88017 0.449807 0.224904 0.974381i \(-0.427793\pi\)
0.224904 + 0.974381i \(0.427793\pi\)
\(42\) −1.38443 −0.213623
\(43\) 0.927277 0.141408 0.0707042 0.997497i \(-0.477475\pi\)
0.0707042 + 0.997497i \(0.477475\pi\)
\(44\) −2.60808 −0.393183
\(45\) 3.32958 0.496344
\(46\) −0.437417 −0.0644936
\(47\) −10.7983 −1.57509 −0.787545 0.616258i \(-0.788648\pi\)
−0.787545 + 0.616258i \(0.788648\pi\)
\(48\) −1.00000 −0.144338
\(49\) −5.08334 −0.726192
\(50\) −6.08609 −0.860702
\(51\) 1.65277 0.231433
\(52\) 1.00000 0.138675
\(53\) 8.01315 1.10069 0.550345 0.834937i \(-0.314496\pi\)
0.550345 + 0.834937i \(0.314496\pi\)
\(54\) 1.00000 0.136083
\(55\) −8.68380 −1.17092
\(56\) 1.38443 0.185003
\(57\) 2.38443 0.315826
\(58\) −1.38942 −0.182440
\(59\) 3.33907 0.434709 0.217355 0.976093i \(-0.430257\pi\)
0.217355 + 0.976093i \(0.430257\pi\)
\(60\) −3.32958 −0.429847
\(61\) −1.16385 −0.149016 −0.0745081 0.997220i \(-0.523739\pi\)
−0.0745081 + 0.997220i \(0.523739\pi\)
\(62\) 5.09491 0.647054
\(63\) −1.38443 −0.174422
\(64\) 1.00000 0.125000
\(65\) 3.32958 0.412983
\(66\) −2.60808 −0.321032
\(67\) 8.02334 0.980207 0.490104 0.871664i \(-0.336959\pi\)
0.490104 + 0.871664i \(0.336959\pi\)
\(68\) −1.65277 −0.200427
\(69\) −0.437417 −0.0526588
\(70\) 4.60958 0.550950
\(71\) 5.77612 0.685499 0.342750 0.939427i \(-0.388642\pi\)
0.342750 + 0.939427i \(0.388642\pi\)
\(72\) −1.00000 −0.117851
\(73\) −5.91373 −0.692150 −0.346075 0.938207i \(-0.612486\pi\)
−0.346075 + 0.938207i \(0.612486\pi\)
\(74\) −6.25229 −0.726814
\(75\) −6.08609 −0.702761
\(76\) −2.38443 −0.273513
\(77\) 3.61071 0.411479
\(78\) 1.00000 0.113228
\(79\) 5.61371 0.631592 0.315796 0.948827i \(-0.397728\pi\)
0.315796 + 0.948827i \(0.397728\pi\)
\(80\) 3.32958 0.372258
\(81\) 1.00000 0.111111
\(82\) −2.88017 −0.318062
\(83\) −7.43809 −0.816437 −0.408218 0.912884i \(-0.633850\pi\)
−0.408218 + 0.912884i \(0.633850\pi\)
\(84\) 1.38443 0.151054
\(85\) −5.50301 −0.596885
\(86\) −0.927277 −0.0999909
\(87\) −1.38942 −0.148961
\(88\) 2.60808 0.278022
\(89\) 17.2269 1.82605 0.913023 0.407908i \(-0.133741\pi\)
0.913023 + 0.407908i \(0.133741\pi\)
\(90\) −3.32958 −0.350968
\(91\) −1.38443 −0.145128
\(92\) 0.437417 0.0456038
\(93\) 5.09491 0.528317
\(94\) 10.7983 1.11376
\(95\) −7.93916 −0.814541
\(96\) 1.00000 0.102062
\(97\) −1.80223 −0.182989 −0.0914945 0.995806i \(-0.529164\pi\)
−0.0914945 + 0.995806i \(0.529164\pi\)
\(98\) 5.08334 0.513495
\(99\) −2.60808 −0.262122
\(100\) 6.08609 0.608609
\(101\) −2.58210 −0.256929 −0.128464 0.991714i \(-0.541005\pi\)
−0.128464 + 0.991714i \(0.541005\pi\)
\(102\) −1.65277 −0.163648
\(103\) 1.00000 0.0985329
\(104\) −1.00000 −0.0980581
\(105\) 4.60958 0.449849
\(106\) −8.01315 −0.778306
\(107\) −12.0189 −1.16191 −0.580957 0.813934i \(-0.697322\pi\)
−0.580957 + 0.813934i \(0.697322\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −9.77876 −0.936636 −0.468318 0.883560i \(-0.655140\pi\)
−0.468318 + 0.883560i \(0.655140\pi\)
\(110\) 8.68380 0.827968
\(111\) −6.25229 −0.593441
\(112\) −1.38443 −0.130817
\(113\) −14.8934 −1.40105 −0.700527 0.713626i \(-0.747051\pi\)
−0.700527 + 0.713626i \(0.747051\pi\)
\(114\) −2.38443 −0.223323
\(115\) 1.45641 0.135811
\(116\) 1.38942 0.129004
\(117\) 1.00000 0.0924500
\(118\) −3.33907 −0.307386
\(119\) 2.28815 0.209754
\(120\) 3.32958 0.303947
\(121\) −4.19793 −0.381630
\(122\) 1.16385 0.105370
\(123\) −2.88017 −0.259696
\(124\) −5.09491 −0.457536
\(125\) 3.61621 0.323443
\(126\) 1.38443 0.123335
\(127\) 6.22507 0.552385 0.276193 0.961102i \(-0.410927\pi\)
0.276193 + 0.961102i \(0.410927\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.927277 −0.0816422
\(130\) −3.32958 −0.292023
\(131\) −9.84125 −0.859834 −0.429917 0.902868i \(-0.641457\pi\)
−0.429917 + 0.902868i \(0.641457\pi\)
\(132\) 2.60808 0.227004
\(133\) 3.30109 0.286241
\(134\) −8.02334 −0.693111
\(135\) −3.32958 −0.286564
\(136\) 1.65277 0.141723
\(137\) −10.1134 −0.864043 −0.432022 0.901863i \(-0.642200\pi\)
−0.432022 + 0.901863i \(0.642200\pi\)
\(138\) 0.437417 0.0372354
\(139\) −22.7082 −1.92608 −0.963041 0.269356i \(-0.913189\pi\)
−0.963041 + 0.269356i \(0.913189\pi\)
\(140\) −4.60958 −0.389581
\(141\) 10.7983 0.909378
\(142\) −5.77612 −0.484721
\(143\) −2.60808 −0.218098
\(144\) 1.00000 0.0833333
\(145\) 4.62618 0.384183
\(146\) 5.91373 0.489424
\(147\) 5.08334 0.419267
\(148\) 6.25229 0.513935
\(149\) −5.39722 −0.442158 −0.221079 0.975256i \(-0.570958\pi\)
−0.221079 + 0.975256i \(0.570958\pi\)
\(150\) 6.08609 0.496927
\(151\) −2.23675 −0.182024 −0.0910122 0.995850i \(-0.529010\pi\)
−0.0910122 + 0.995850i \(0.529010\pi\)
\(152\) 2.38443 0.193403
\(153\) −1.65277 −0.133618
\(154\) −3.61071 −0.290960
\(155\) −16.9639 −1.36257
\(156\) −1.00000 −0.0800641
\(157\) 16.1805 1.29134 0.645671 0.763616i \(-0.276578\pi\)
0.645671 + 0.763616i \(0.276578\pi\)
\(158\) −5.61371 −0.446603
\(159\) −8.01315 −0.635484
\(160\) −3.32958 −0.263226
\(161\) −0.605575 −0.0477260
\(162\) −1.00000 −0.0785674
\(163\) −11.0400 −0.864722 −0.432361 0.901701i \(-0.642319\pi\)
−0.432361 + 0.901701i \(0.642319\pi\)
\(164\) 2.88017 0.224904
\(165\) 8.68380 0.676033
\(166\) 7.43809 0.577308
\(167\) −16.6481 −1.28827 −0.644134 0.764913i \(-0.722782\pi\)
−0.644134 + 0.764913i \(0.722782\pi\)
\(168\) −1.38443 −0.106811
\(169\) 1.00000 0.0769231
\(170\) 5.50301 0.422062
\(171\) −2.38443 −0.182342
\(172\) 0.927277 0.0707042
\(173\) −11.4486 −0.870424 −0.435212 0.900328i \(-0.643327\pi\)
−0.435212 + 0.900328i \(0.643327\pi\)
\(174\) 1.38942 0.105332
\(175\) −8.42579 −0.636930
\(176\) −2.60808 −0.196591
\(177\) −3.33907 −0.250980
\(178\) −17.2269 −1.29121
\(179\) −10.1335 −0.757413 −0.378706 0.925517i \(-0.623631\pi\)
−0.378706 + 0.925517i \(0.623631\pi\)
\(180\) 3.32958 0.248172
\(181\) −20.8197 −1.54751 −0.773757 0.633483i \(-0.781625\pi\)
−0.773757 + 0.633483i \(0.781625\pi\)
\(182\) 1.38443 0.102621
\(183\) 1.16385 0.0860345
\(184\) −0.437417 −0.0322468
\(185\) 20.8175 1.53053
\(186\) −5.09491 −0.373577
\(187\) 4.31054 0.315218
\(188\) −10.7983 −0.787545
\(189\) 1.38443 0.100703
\(190\) 7.93916 0.575967
\(191\) −5.92513 −0.428727 −0.214364 0.976754i \(-0.568768\pi\)
−0.214364 + 0.976754i \(0.568768\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 20.0653 1.44433 0.722167 0.691718i \(-0.243146\pi\)
0.722167 + 0.691718i \(0.243146\pi\)
\(194\) 1.80223 0.129393
\(195\) −3.32958 −0.238436
\(196\) −5.08334 −0.363096
\(197\) 11.0734 0.788948 0.394474 0.918907i \(-0.370927\pi\)
0.394474 + 0.918907i \(0.370927\pi\)
\(198\) 2.60808 0.185348
\(199\) −7.37014 −0.522455 −0.261228 0.965277i \(-0.584127\pi\)
−0.261228 + 0.965277i \(0.584127\pi\)
\(200\) −6.08609 −0.430351
\(201\) −8.02334 −0.565923
\(202\) 2.58210 0.181676
\(203\) −1.92356 −0.135007
\(204\) 1.65277 0.115717
\(205\) 9.58975 0.669777
\(206\) −1.00000 −0.0696733
\(207\) 0.437417 0.0304026
\(208\) 1.00000 0.0693375
\(209\) 6.21879 0.430163
\(210\) −4.60958 −0.318091
\(211\) 4.63742 0.319253 0.159627 0.987177i \(-0.448971\pi\)
0.159627 + 0.987177i \(0.448971\pi\)
\(212\) 8.01315 0.550345
\(213\) −5.77612 −0.395773
\(214\) 12.0189 0.821598
\(215\) 3.08744 0.210562
\(216\) 1.00000 0.0680414
\(217\) 7.05356 0.478827
\(218\) 9.77876 0.662301
\(219\) 5.91373 0.399613
\(220\) −8.68380 −0.585462
\(221\) −1.65277 −0.111177
\(222\) 6.25229 0.419626
\(223\) 2.11474 0.141613 0.0708067 0.997490i \(-0.477443\pi\)
0.0708067 + 0.997490i \(0.477443\pi\)
\(224\) 1.38443 0.0925014
\(225\) 6.08609 0.405739
\(226\) 14.8934 0.990694
\(227\) 6.63719 0.440526 0.220263 0.975441i \(-0.429308\pi\)
0.220263 + 0.975441i \(0.429308\pi\)
\(228\) 2.38443 0.157913
\(229\) −13.0876 −0.864856 −0.432428 0.901668i \(-0.642343\pi\)
−0.432428 + 0.901668i \(0.642343\pi\)
\(230\) −1.45641 −0.0960330
\(231\) −3.61071 −0.237567
\(232\) −1.38942 −0.0912199
\(233\) −5.29335 −0.346779 −0.173389 0.984853i \(-0.555472\pi\)
−0.173389 + 0.984853i \(0.555472\pi\)
\(234\) −1.00000 −0.0653720
\(235\) −35.9537 −2.34536
\(236\) 3.33907 0.217355
\(237\) −5.61371 −0.364650
\(238\) −2.28815 −0.148318
\(239\) −14.4156 −0.932465 −0.466232 0.884662i \(-0.654389\pi\)
−0.466232 + 0.884662i \(0.654389\pi\)
\(240\) −3.32958 −0.214923
\(241\) 13.6057 0.876417 0.438209 0.898873i \(-0.355613\pi\)
0.438209 + 0.898873i \(0.355613\pi\)
\(242\) 4.19793 0.269853
\(243\) −1.00000 −0.0641500
\(244\) −1.16385 −0.0745081
\(245\) −16.9254 −1.08132
\(246\) 2.88017 0.183633
\(247\) −2.38443 −0.151718
\(248\) 5.09491 0.323527
\(249\) 7.43809 0.471370
\(250\) −3.61621 −0.228709
\(251\) 27.1248 1.71210 0.856052 0.516890i \(-0.172910\pi\)
0.856052 + 0.516890i \(0.172910\pi\)
\(252\) −1.38443 −0.0872112
\(253\) −1.14082 −0.0717225
\(254\) −6.22507 −0.390595
\(255\) 5.50301 0.344612
\(256\) 1.00000 0.0625000
\(257\) 24.8096 1.54758 0.773791 0.633441i \(-0.218358\pi\)
0.773791 + 0.633441i \(0.218358\pi\)
\(258\) 0.927277 0.0577298
\(259\) −8.65588 −0.537850
\(260\) 3.32958 0.206492
\(261\) 1.38942 0.0860029
\(262\) 9.84125 0.607994
\(263\) 17.4130 1.07373 0.536865 0.843668i \(-0.319608\pi\)
0.536865 + 0.843668i \(0.319608\pi\)
\(264\) −2.60808 −0.160516
\(265\) 26.6804 1.63896
\(266\) −3.30109 −0.202403
\(267\) −17.2269 −1.05427
\(268\) 8.02334 0.490104
\(269\) −4.80067 −0.292702 −0.146351 0.989233i \(-0.546753\pi\)
−0.146351 + 0.989233i \(0.546753\pi\)
\(270\) 3.32958 0.202632
\(271\) 17.6247 1.07063 0.535313 0.844654i \(-0.320194\pi\)
0.535313 + 0.844654i \(0.320194\pi\)
\(272\) −1.65277 −0.100214
\(273\) 1.38443 0.0837898
\(274\) 10.1134 0.610971
\(275\) −15.8730 −0.957177
\(276\) −0.437417 −0.0263294
\(277\) −20.2994 −1.21967 −0.609836 0.792527i \(-0.708765\pi\)
−0.609836 + 0.792527i \(0.708765\pi\)
\(278\) 22.7082 1.36195
\(279\) −5.09491 −0.305024
\(280\) 4.60958 0.275475
\(281\) −3.46316 −0.206595 −0.103297 0.994651i \(-0.532939\pi\)
−0.103297 + 0.994651i \(0.532939\pi\)
\(282\) −10.7983 −0.643028
\(283\) −16.2956 −0.968671 −0.484335 0.874882i \(-0.660939\pi\)
−0.484335 + 0.874882i \(0.660939\pi\)
\(284\) 5.77612 0.342750
\(285\) 7.93916 0.470275
\(286\) 2.60808 0.154219
\(287\) −3.98741 −0.235369
\(288\) −1.00000 −0.0589256
\(289\) −14.2684 −0.839316
\(290\) −4.62618 −0.271659
\(291\) 1.80223 0.105649
\(292\) −5.91373 −0.346075
\(293\) 16.2465 0.949132 0.474566 0.880220i \(-0.342605\pi\)
0.474566 + 0.880220i \(0.342605\pi\)
\(294\) −5.08334 −0.296466
\(295\) 11.1177 0.647296
\(296\) −6.25229 −0.363407
\(297\) 2.60808 0.151336
\(298\) 5.39722 0.312653
\(299\) 0.437417 0.0252965
\(300\) −6.08609 −0.351380
\(301\) −1.28375 −0.0739944
\(302\) 2.23675 0.128711
\(303\) 2.58210 0.148338
\(304\) −2.38443 −0.136757
\(305\) −3.87514 −0.221890
\(306\) 1.65277 0.0944823
\(307\) 22.2353 1.26903 0.634517 0.772909i \(-0.281199\pi\)
0.634517 + 0.772909i \(0.281199\pi\)
\(308\) 3.61071 0.205739
\(309\) −1.00000 −0.0568880
\(310\) 16.9639 0.963484
\(311\) 16.5685 0.939515 0.469758 0.882795i \(-0.344341\pi\)
0.469758 + 0.882795i \(0.344341\pi\)
\(312\) 1.00000 0.0566139
\(313\) −31.5663 −1.78423 −0.892116 0.451807i \(-0.850780\pi\)
−0.892116 + 0.451807i \(0.850780\pi\)
\(314\) −16.1805 −0.913117
\(315\) −4.60958 −0.259721
\(316\) 5.61371 0.315796
\(317\) −21.3357 −1.19833 −0.599165 0.800625i \(-0.704501\pi\)
−0.599165 + 0.800625i \(0.704501\pi\)
\(318\) 8.01315 0.449355
\(319\) −3.62371 −0.202889
\(320\) 3.32958 0.186129
\(321\) 12.0189 0.670832
\(322\) 0.605575 0.0337474
\(323\) 3.94091 0.219278
\(324\) 1.00000 0.0555556
\(325\) 6.08609 0.337595
\(326\) 11.0400 0.611451
\(327\) 9.77876 0.540767
\(328\) −2.88017 −0.159031
\(329\) 14.9495 0.824192
\(330\) −8.68380 −0.478027
\(331\) −27.7441 −1.52495 −0.762476 0.647017i \(-0.776016\pi\)
−0.762476 + 0.647017i \(0.776016\pi\)
\(332\) −7.43809 −0.408218
\(333\) 6.25229 0.342623
\(334\) 16.6481 0.910943
\(335\) 26.7143 1.45956
\(336\) 1.38443 0.0755271
\(337\) −20.7986 −1.13297 −0.566487 0.824071i \(-0.691698\pi\)
−0.566487 + 0.824071i \(0.691698\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 14.8934 0.808898
\(340\) −5.50301 −0.298443
\(341\) 13.2879 0.719581
\(342\) 2.38443 0.128935
\(343\) 16.7286 0.903259
\(344\) −0.927277 −0.0499955
\(345\) −1.45641 −0.0784106
\(346\) 11.4486 0.615482
\(347\) −25.8264 −1.38644 −0.693218 0.720728i \(-0.743808\pi\)
−0.693218 + 0.720728i \(0.743808\pi\)
\(348\) −1.38942 −0.0744807
\(349\) 2.17223 0.116277 0.0581383 0.998309i \(-0.481484\pi\)
0.0581383 + 0.998309i \(0.481484\pi\)
\(350\) 8.42579 0.450377
\(351\) −1.00000 −0.0533761
\(352\) 2.60808 0.139011
\(353\) 16.9804 0.903773 0.451887 0.892075i \(-0.350751\pi\)
0.451887 + 0.892075i \(0.350751\pi\)
\(354\) 3.33907 0.177469
\(355\) 19.2320 1.02073
\(356\) 17.2269 0.913023
\(357\) −2.28815 −0.121101
\(358\) 10.1335 0.535572
\(359\) 16.9652 0.895390 0.447695 0.894186i \(-0.352245\pi\)
0.447695 + 0.894186i \(0.352245\pi\)
\(360\) −3.32958 −0.175484
\(361\) −13.3145 −0.700762
\(362\) 20.8197 1.09426
\(363\) 4.19793 0.220334
\(364\) −1.38443 −0.0725641
\(365\) −19.6902 −1.03063
\(366\) −1.16385 −0.0608356
\(367\) −13.2181 −0.689980 −0.344990 0.938606i \(-0.612118\pi\)
−0.344990 + 0.938606i \(0.612118\pi\)
\(368\) 0.437417 0.0228019
\(369\) 2.88017 0.149936
\(370\) −20.8175 −1.08225
\(371\) −11.0937 −0.575955
\(372\) 5.09491 0.264159
\(373\) −4.80685 −0.248889 −0.124445 0.992227i \(-0.539715\pi\)
−0.124445 + 0.992227i \(0.539715\pi\)
\(374\) −4.31054 −0.222893
\(375\) −3.61621 −0.186740
\(376\) 10.7983 0.556878
\(377\) 1.38942 0.0715587
\(378\) −1.38443 −0.0712076
\(379\) −31.6430 −1.62539 −0.812695 0.582689i \(-0.802001\pi\)
−0.812695 + 0.582689i \(0.802001\pi\)
\(380\) −7.93916 −0.407270
\(381\) −6.22507 −0.318920
\(382\) 5.92513 0.303156
\(383\) −0.530233 −0.0270937 −0.0135468 0.999908i \(-0.504312\pi\)
−0.0135468 + 0.999908i \(0.504312\pi\)
\(384\) 1.00000 0.0510310
\(385\) 12.0221 0.612705
\(386\) −20.0653 −1.02130
\(387\) 0.927277 0.0471362
\(388\) −1.80223 −0.0914945
\(389\) 19.6701 0.997315 0.498658 0.866799i \(-0.333827\pi\)
0.498658 + 0.866799i \(0.333827\pi\)
\(390\) 3.32958 0.168600
\(391\) −0.722947 −0.0365610
\(392\) 5.08334 0.256747
\(393\) 9.84125 0.496425
\(394\) −11.0734 −0.557871
\(395\) 18.6913 0.940461
\(396\) −2.60808 −0.131061
\(397\) 8.59657 0.431450 0.215725 0.976454i \(-0.430789\pi\)
0.215725 + 0.976454i \(0.430789\pi\)
\(398\) 7.37014 0.369432
\(399\) −3.30109 −0.165261
\(400\) 6.08609 0.304304
\(401\) −22.9750 −1.14732 −0.573659 0.819094i \(-0.694477\pi\)
−0.573659 + 0.819094i \(0.694477\pi\)
\(402\) 8.02334 0.400168
\(403\) −5.09491 −0.253795
\(404\) −2.58210 −0.128464
\(405\) 3.32958 0.165448
\(406\) 1.92356 0.0954647
\(407\) −16.3065 −0.808281
\(408\) −1.65277 −0.0818241
\(409\) −20.0669 −0.992245 −0.496122 0.868253i \(-0.665243\pi\)
−0.496122 + 0.868253i \(0.665243\pi\)
\(410\) −9.58975 −0.473604
\(411\) 10.1134 0.498856
\(412\) 1.00000 0.0492665
\(413\) −4.62272 −0.227469
\(414\) −0.437417 −0.0214979
\(415\) −24.7657 −1.21570
\(416\) −1.00000 −0.0490290
\(417\) 22.7082 1.11202
\(418\) −6.21879 −0.304171
\(419\) 16.5765 0.809813 0.404907 0.914358i \(-0.367304\pi\)
0.404907 + 0.914358i \(0.367304\pi\)
\(420\) 4.60958 0.224925
\(421\) −31.7963 −1.54966 −0.774829 0.632171i \(-0.782164\pi\)
−0.774829 + 0.632171i \(0.782164\pi\)
\(422\) −4.63742 −0.225746
\(423\) −10.7983 −0.525030
\(424\) −8.01315 −0.389153
\(425\) −10.0589 −0.487927
\(426\) 5.77612 0.279854
\(427\) 1.61128 0.0779752
\(428\) −12.0189 −0.580957
\(429\) 2.60808 0.125919
\(430\) −3.08744 −0.148890
\(431\) 10.6520 0.513090 0.256545 0.966532i \(-0.417416\pi\)
0.256545 + 0.966532i \(0.417416\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 7.06019 0.339291 0.169646 0.985505i \(-0.445738\pi\)
0.169646 + 0.985505i \(0.445738\pi\)
\(434\) −7.05356 −0.338582
\(435\) −4.62618 −0.221808
\(436\) −9.77876 −0.468318
\(437\) −1.04299 −0.0498930
\(438\) −5.91373 −0.282569
\(439\) −36.1524 −1.72546 −0.862729 0.505666i \(-0.831247\pi\)
−0.862729 + 0.505666i \(0.831247\pi\)
\(440\) 8.68380 0.413984
\(441\) −5.08334 −0.242064
\(442\) 1.65277 0.0786140
\(443\) 14.1150 0.670626 0.335313 0.942107i \(-0.391158\pi\)
0.335313 + 0.942107i \(0.391158\pi\)
\(444\) −6.25229 −0.296720
\(445\) 57.3583 2.71904
\(446\) −2.11474 −0.100136
\(447\) 5.39722 0.255280
\(448\) −1.38443 −0.0654084
\(449\) 27.6663 1.30565 0.652827 0.757507i \(-0.273583\pi\)
0.652827 + 0.757507i \(0.273583\pi\)
\(450\) −6.08609 −0.286901
\(451\) −7.51171 −0.353713
\(452\) −14.8934 −0.700527
\(453\) 2.23675 0.105092
\(454\) −6.63719 −0.311499
\(455\) −4.60958 −0.216101
\(456\) −2.38443 −0.111661
\(457\) −11.8995 −0.556634 −0.278317 0.960489i \(-0.589777\pi\)
−0.278317 + 0.960489i \(0.589777\pi\)
\(458\) 13.0876 0.611546
\(459\) 1.65277 0.0771445
\(460\) 1.45641 0.0679056
\(461\) −8.74873 −0.407469 −0.203734 0.979026i \(-0.565308\pi\)
−0.203734 + 0.979026i \(0.565308\pi\)
\(462\) 3.61071 0.167986
\(463\) 5.98788 0.278280 0.139140 0.990273i \(-0.455566\pi\)
0.139140 + 0.990273i \(0.455566\pi\)
\(464\) 1.38942 0.0645022
\(465\) 16.9639 0.786681
\(466\) 5.29335 0.245210
\(467\) 42.2930 1.95709 0.978544 0.206038i \(-0.0660569\pi\)
0.978544 + 0.206038i \(0.0660569\pi\)
\(468\) 1.00000 0.0462250
\(469\) −11.1078 −0.512910
\(470\) 35.9537 1.65842
\(471\) −16.1805 −0.745557
\(472\) −3.33907 −0.153693
\(473\) −2.41841 −0.111199
\(474\) 5.61371 0.257846
\(475\) −14.5119 −0.665850
\(476\) 2.28815 0.104877
\(477\) 8.01315 0.366897
\(478\) 14.4156 0.659352
\(479\) −17.9798 −0.821519 −0.410760 0.911744i \(-0.634736\pi\)
−0.410760 + 0.911744i \(0.634736\pi\)
\(480\) 3.32958 0.151974
\(481\) 6.25229 0.285080
\(482\) −13.6057 −0.619721
\(483\) 0.605575 0.0275546
\(484\) −4.19793 −0.190815
\(485\) −6.00067 −0.272476
\(486\) 1.00000 0.0453609
\(487\) 3.71623 0.168398 0.0841992 0.996449i \(-0.473167\pi\)
0.0841992 + 0.996449i \(0.473167\pi\)
\(488\) 1.16385 0.0526852
\(489\) 11.0400 0.499248
\(490\) 16.9254 0.764611
\(491\) 13.0876 0.590637 0.295318 0.955399i \(-0.404574\pi\)
0.295318 + 0.955399i \(0.404574\pi\)
\(492\) −2.88017 −0.129848
\(493\) −2.29638 −0.103424
\(494\) 2.38443 0.107281
\(495\) −8.68380 −0.390308
\(496\) −5.09491 −0.228768
\(497\) −7.99666 −0.358699
\(498\) −7.43809 −0.333309
\(499\) 16.4962 0.738472 0.369236 0.929336i \(-0.379619\pi\)
0.369236 + 0.929336i \(0.379619\pi\)
\(500\) 3.61621 0.161722
\(501\) 16.6481 0.743781
\(502\) −27.1248 −1.21064
\(503\) −25.8610 −1.15309 −0.576543 0.817067i \(-0.695599\pi\)
−0.576543 + 0.817067i \(0.695599\pi\)
\(504\) 1.38443 0.0616676
\(505\) −8.59731 −0.382575
\(506\) 1.14082 0.0507155
\(507\) −1.00000 −0.0444116
\(508\) 6.22507 0.276193
\(509\) 14.7923 0.655659 0.327830 0.944737i \(-0.393683\pi\)
0.327830 + 0.944737i \(0.393683\pi\)
\(510\) −5.50301 −0.243677
\(511\) 8.18717 0.362179
\(512\) −1.00000 −0.0441942
\(513\) 2.38443 0.105275
\(514\) −24.8096 −1.09431
\(515\) 3.32958 0.146719
\(516\) −0.927277 −0.0408211
\(517\) 28.1627 1.23860
\(518\) 8.65588 0.380318
\(519\) 11.4486 0.502539
\(520\) −3.32958 −0.146012
\(521\) −9.53815 −0.417874 −0.208937 0.977929i \(-0.567000\pi\)
−0.208937 + 0.977929i \(0.567000\pi\)
\(522\) −1.38942 −0.0608132
\(523\) −5.66030 −0.247508 −0.123754 0.992313i \(-0.539493\pi\)
−0.123754 + 0.992313i \(0.539493\pi\)
\(524\) −9.84125 −0.429917
\(525\) 8.42579 0.367731
\(526\) −17.4130 −0.759242
\(527\) 8.42069 0.366811
\(528\) 2.60808 0.113502
\(529\) −22.8087 −0.991681
\(530\) −26.6804 −1.15892
\(531\) 3.33907 0.144903
\(532\) 3.30109 0.143121
\(533\) 2.88017 0.124754
\(534\) 17.2269 0.745480
\(535\) −40.0180 −1.73013
\(536\) −8.02334 −0.346556
\(537\) 10.1335 0.437292
\(538\) 4.80067 0.206971
\(539\) 13.2578 0.571052
\(540\) −3.32958 −0.143282
\(541\) 25.4043 1.09222 0.546108 0.837715i \(-0.316109\pi\)
0.546108 + 0.837715i \(0.316109\pi\)
\(542\) −17.6247 −0.757047
\(543\) 20.8197 0.893457
\(544\) 1.65277 0.0708617
\(545\) −32.5592 −1.39468
\(546\) −1.38443 −0.0592483
\(547\) −27.1325 −1.16010 −0.580050 0.814581i \(-0.696967\pi\)
−0.580050 + 0.814581i \(0.696967\pi\)
\(548\) −10.1134 −0.432022
\(549\) −1.16385 −0.0496721
\(550\) 15.8730 0.676826
\(551\) −3.31298 −0.141138
\(552\) 0.437417 0.0186177
\(553\) −7.77182 −0.330491
\(554\) 20.2994 0.862439
\(555\) −20.8175 −0.883653
\(556\) −22.7082 −0.963041
\(557\) −36.5462 −1.54851 −0.774257 0.632872i \(-0.781876\pi\)
−0.774257 + 0.632872i \(0.781876\pi\)
\(558\) 5.09491 0.215685
\(559\) 0.927277 0.0392197
\(560\) −4.60958 −0.194790
\(561\) −4.31054 −0.181991
\(562\) 3.46316 0.146085
\(563\) −18.2633 −0.769708 −0.384854 0.922977i \(-0.625748\pi\)
−0.384854 + 0.922977i \(0.625748\pi\)
\(564\) 10.7983 0.454689
\(565\) −49.5887 −2.08621
\(566\) 16.2956 0.684954
\(567\) −1.38443 −0.0581408
\(568\) −5.77612 −0.242361
\(569\) 5.56719 0.233389 0.116694 0.993168i \(-0.462770\pi\)
0.116694 + 0.993168i \(0.462770\pi\)
\(570\) −7.93916 −0.332535
\(571\) −9.09794 −0.380737 −0.190368 0.981713i \(-0.560968\pi\)
−0.190368 + 0.981713i \(0.560968\pi\)
\(572\) −2.60808 −0.109049
\(573\) 5.92513 0.247526
\(574\) 3.98741 0.166431
\(575\) 2.66215 0.111020
\(576\) 1.00000 0.0416667
\(577\) 11.1487 0.464125 0.232063 0.972701i \(-0.425453\pi\)
0.232063 + 0.972701i \(0.425453\pi\)
\(578\) 14.2684 0.593486
\(579\) −20.0653 −0.833887
\(580\) 4.62618 0.192092
\(581\) 10.2976 0.427215
\(582\) −1.80223 −0.0747049
\(583\) −20.8989 −0.865545
\(584\) 5.91373 0.244712
\(585\) 3.32958 0.137661
\(586\) −16.2465 −0.671138
\(587\) 45.9447 1.89634 0.948170 0.317763i \(-0.102932\pi\)
0.948170 + 0.317763i \(0.102932\pi\)
\(588\) 5.08334 0.209633
\(589\) 12.1485 0.500569
\(590\) −11.1177 −0.457708
\(591\) −11.0734 −0.455500
\(592\) 6.25229 0.256967
\(593\) −27.5944 −1.13317 −0.566583 0.824005i \(-0.691735\pi\)
−0.566583 + 0.824005i \(0.691735\pi\)
\(594\) −2.60808 −0.107011
\(595\) 7.61856 0.312330
\(596\) −5.39722 −0.221079
\(597\) 7.37014 0.301640
\(598\) −0.437417 −0.0178873
\(599\) 11.3793 0.464948 0.232474 0.972603i \(-0.425318\pi\)
0.232474 + 0.972603i \(0.425318\pi\)
\(600\) 6.08609 0.248463
\(601\) 15.5433 0.634025 0.317013 0.948421i \(-0.397320\pi\)
0.317013 + 0.948421i \(0.397320\pi\)
\(602\) 1.28375 0.0523219
\(603\) 8.02334 0.326736
\(604\) −2.23675 −0.0910122
\(605\) −13.9773 −0.568259
\(606\) −2.58210 −0.104891
\(607\) 15.1565 0.615183 0.307591 0.951519i \(-0.400477\pi\)
0.307591 + 0.951519i \(0.400477\pi\)
\(608\) 2.38443 0.0967016
\(609\) 1.92356 0.0779466
\(610\) 3.87514 0.156900
\(611\) −10.7983 −0.436851
\(612\) −1.65277 −0.0668091
\(613\) 6.62987 0.267778 0.133889 0.990996i \(-0.457253\pi\)
0.133889 + 0.990996i \(0.457253\pi\)
\(614\) −22.2353 −0.897342
\(615\) −9.58975 −0.386696
\(616\) −3.61071 −0.145480
\(617\) −8.30759 −0.334451 −0.167225 0.985919i \(-0.553481\pi\)
−0.167225 + 0.985919i \(0.553481\pi\)
\(618\) 1.00000 0.0402259
\(619\) −47.9531 −1.92740 −0.963699 0.266993i \(-0.913970\pi\)
−0.963699 + 0.266993i \(0.913970\pi\)
\(620\) −16.9639 −0.681286
\(621\) −0.437417 −0.0175529
\(622\) −16.5685 −0.664338
\(623\) −23.8495 −0.955510
\(624\) −1.00000 −0.0400320
\(625\) −18.3900 −0.735600
\(626\) 31.5663 1.26164
\(627\) −6.21879 −0.248355
\(628\) 16.1805 0.645671
\(629\) −10.3336 −0.412026
\(630\) 4.60958 0.183650
\(631\) −20.4276 −0.813210 −0.406605 0.913604i \(-0.633287\pi\)
−0.406605 + 0.913604i \(0.633287\pi\)
\(632\) −5.61371 −0.223301
\(633\) −4.63742 −0.184321
\(634\) 21.3357 0.847348
\(635\) 20.7268 0.822520
\(636\) −8.01315 −0.317742
\(637\) −5.08334 −0.201409
\(638\) 3.62371 0.143464
\(639\) 5.77612 0.228500
\(640\) −3.32958 −0.131613
\(641\) 22.1765 0.875918 0.437959 0.898995i \(-0.355701\pi\)
0.437959 + 0.898995i \(0.355701\pi\)
\(642\) −12.0189 −0.474350
\(643\) −14.7045 −0.579889 −0.289945 0.957043i \(-0.593637\pi\)
−0.289945 + 0.957043i \(0.593637\pi\)
\(644\) −0.605575 −0.0238630
\(645\) −3.08744 −0.121568
\(646\) −3.94091 −0.155053
\(647\) 0.604244 0.0237553 0.0118776 0.999929i \(-0.496219\pi\)
0.0118776 + 0.999929i \(0.496219\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −8.70854 −0.341840
\(650\) −6.08609 −0.238716
\(651\) −7.05356 −0.276451
\(652\) −11.0400 −0.432361
\(653\) −7.48013 −0.292720 −0.146360 0.989231i \(-0.546756\pi\)
−0.146360 + 0.989231i \(0.546756\pi\)
\(654\) −9.77876 −0.382380
\(655\) −32.7672 −1.28032
\(656\) 2.88017 0.112452
\(657\) −5.91373 −0.230717
\(658\) −14.9495 −0.582792
\(659\) −43.4268 −1.69167 −0.845834 0.533446i \(-0.820897\pi\)
−0.845834 + 0.533446i \(0.820897\pi\)
\(660\) 8.68380 0.338016
\(661\) −7.59732 −0.295502 −0.147751 0.989025i \(-0.547203\pi\)
−0.147751 + 0.989025i \(0.547203\pi\)
\(662\) 27.7441 1.07830
\(663\) 1.65277 0.0641881
\(664\) 7.43809 0.288654
\(665\) 10.9912 0.426222
\(666\) −6.25229 −0.242271
\(667\) 0.607755 0.0235324
\(668\) −16.6481 −0.644134
\(669\) −2.11474 −0.0817606
\(670\) −26.7143 −1.03206
\(671\) 3.03542 0.117181
\(672\) −1.38443 −0.0534057
\(673\) 33.5644 1.29381 0.646906 0.762570i \(-0.276063\pi\)
0.646906 + 0.762570i \(0.276063\pi\)
\(674\) 20.7986 0.801134
\(675\) −6.08609 −0.234254
\(676\) 1.00000 0.0384615
\(677\) −29.3775 −1.12907 −0.564534 0.825410i \(-0.690944\pi\)
−0.564534 + 0.825410i \(0.690944\pi\)
\(678\) −14.8934 −0.571977
\(679\) 2.49507 0.0957521
\(680\) 5.50301 0.211031
\(681\) −6.63719 −0.254338
\(682\) −13.2879 −0.508821
\(683\) 7.29045 0.278961 0.139481 0.990225i \(-0.455457\pi\)
0.139481 + 0.990225i \(0.455457\pi\)
\(684\) −2.38443 −0.0911711
\(685\) −33.6732 −1.28659
\(686\) −16.7286 −0.638701
\(687\) 13.0876 0.499325
\(688\) 0.927277 0.0353521
\(689\) 8.01315 0.305277
\(690\) 1.45641 0.0554447
\(691\) −36.1981 −1.37704 −0.688521 0.725216i \(-0.741740\pi\)
−0.688521 + 0.725216i \(0.741740\pi\)
\(692\) −11.4486 −0.435212
\(693\) 3.61071 0.137160
\(694\) 25.8264 0.980358
\(695\) −75.6086 −2.86800
\(696\) 1.38942 0.0526658
\(697\) −4.76025 −0.180307
\(698\) −2.17223 −0.0822200
\(699\) 5.29335 0.200213
\(700\) −8.42579 −0.318465
\(701\) 17.7227 0.669376 0.334688 0.942329i \(-0.391369\pi\)
0.334688 + 0.942329i \(0.391369\pi\)
\(702\) 1.00000 0.0377426
\(703\) −14.9082 −0.562272
\(704\) −2.60808 −0.0982956
\(705\) 35.9537 1.35409
\(706\) −16.9804 −0.639064
\(707\) 3.57475 0.134442
\(708\) −3.33907 −0.125490
\(709\) 0.555936 0.0208786 0.0104393 0.999946i \(-0.496677\pi\)
0.0104393 + 0.999946i \(0.496677\pi\)
\(710\) −19.2320 −0.721766
\(711\) 5.61371 0.210531
\(712\) −17.2269 −0.645605
\(713\) −2.22860 −0.0834616
\(714\) 2.28815 0.0856317
\(715\) −8.68380 −0.324756
\(716\) −10.1335 −0.378706
\(717\) 14.4156 0.538359
\(718\) −16.9652 −0.633136
\(719\) 13.0890 0.488139 0.244069 0.969758i \(-0.421518\pi\)
0.244069 + 0.969758i \(0.421518\pi\)
\(720\) 3.32958 0.124086
\(721\) −1.38443 −0.0515590
\(722\) 13.3145 0.495513
\(723\) −13.6057 −0.506000
\(724\) −20.8197 −0.773757
\(725\) 8.45613 0.314053
\(726\) −4.19793 −0.155800
\(727\) 27.6975 1.02724 0.513622 0.858017i \(-0.328303\pi\)
0.513622 + 0.858017i \(0.328303\pi\)
\(728\) 1.38443 0.0513106
\(729\) 1.00000 0.0370370
\(730\) 19.6902 0.728768
\(731\) −1.53257 −0.0566842
\(732\) 1.16385 0.0430173
\(733\) −1.46711 −0.0541888 −0.0270944 0.999633i \(-0.508625\pi\)
−0.0270944 + 0.999633i \(0.508625\pi\)
\(734\) 13.2181 0.487890
\(735\) 16.9254 0.624302
\(736\) −0.437417 −0.0161234
\(737\) −20.9255 −0.770801
\(738\) −2.88017 −0.106021
\(739\) 17.8199 0.655516 0.327758 0.944762i \(-0.393707\pi\)
0.327758 + 0.944762i \(0.393707\pi\)
\(740\) 20.8175 0.765266
\(741\) 2.38443 0.0875944
\(742\) 11.0937 0.407262
\(743\) 0.527700 0.0193594 0.00967972 0.999953i \(-0.496919\pi\)
0.00967972 + 0.999953i \(0.496919\pi\)
\(744\) −5.09491 −0.186788
\(745\) −17.9705 −0.658387
\(746\) 4.80685 0.175991
\(747\) −7.43809 −0.272146
\(748\) 4.31054 0.157609
\(749\) 16.6394 0.607992
\(750\) 3.61621 0.132045
\(751\) 3.74134 0.136524 0.0682618 0.997667i \(-0.478255\pi\)
0.0682618 + 0.997667i \(0.478255\pi\)
\(752\) −10.7983 −0.393772
\(753\) −27.1248 −0.988484
\(754\) −1.38942 −0.0505997
\(755\) −7.44744 −0.271040
\(756\) 1.38443 0.0503514
\(757\) 8.05602 0.292801 0.146401 0.989225i \(-0.453231\pi\)
0.146401 + 0.989225i \(0.453231\pi\)
\(758\) 31.6430 1.14932
\(759\) 1.14082 0.0414090
\(760\) 7.93916 0.287984
\(761\) 32.4969 1.17801 0.589006 0.808129i \(-0.299520\pi\)
0.589006 + 0.808129i \(0.299520\pi\)
\(762\) 6.22507 0.225510
\(763\) 13.5381 0.490111
\(764\) −5.92513 −0.214364
\(765\) −5.50301 −0.198962
\(766\) 0.530233 0.0191581
\(767\) 3.33907 0.120567
\(768\) −1.00000 −0.0360844
\(769\) 0.887902 0.0320186 0.0160093 0.999872i \(-0.494904\pi\)
0.0160093 + 0.999872i \(0.494904\pi\)
\(770\) −12.0221 −0.433248
\(771\) −24.8096 −0.893497
\(772\) 20.0653 0.722167
\(773\) 39.5626 1.42297 0.711484 0.702702i \(-0.248023\pi\)
0.711484 + 0.702702i \(0.248023\pi\)
\(774\) −0.927277 −0.0333303
\(775\) −31.0080 −1.11384
\(776\) 1.80223 0.0646964
\(777\) 8.65588 0.310528
\(778\) −19.6701 −0.705208
\(779\) −6.86758 −0.246057
\(780\) −3.32958 −0.119218
\(781\) −15.0646 −0.539053
\(782\) 0.722947 0.0258525
\(783\) −1.38942 −0.0496538
\(784\) −5.08334 −0.181548
\(785\) 53.8741 1.92285
\(786\) −9.84125 −0.351026
\(787\) 6.84512 0.244002 0.122001 0.992530i \(-0.461069\pi\)
0.122001 + 0.992530i \(0.461069\pi\)
\(788\) 11.0734 0.394474
\(789\) −17.4130 −0.619918
\(790\) −18.6913 −0.665006
\(791\) 20.6189 0.733125
\(792\) 2.60808 0.0926740
\(793\) −1.16385 −0.0413296
\(794\) −8.59657 −0.305081
\(795\) −26.6804 −0.946256
\(796\) −7.37014 −0.261228
\(797\) 25.6291 0.907828 0.453914 0.891046i \(-0.350027\pi\)
0.453914 + 0.891046i \(0.350027\pi\)
\(798\) 3.30109 0.116857
\(799\) 17.8470 0.631382
\(800\) −6.08609 −0.215176
\(801\) 17.2269 0.608682
\(802\) 22.9750 0.811276
\(803\) 15.4235 0.544282
\(804\) −8.02334 −0.282961
\(805\) −2.01631 −0.0710655
\(806\) 5.09491 0.179460
\(807\) 4.80067 0.168991
\(808\) 2.58210 0.0908381
\(809\) −35.4509 −1.24639 −0.623194 0.782067i \(-0.714166\pi\)
−0.623194 + 0.782067i \(0.714166\pi\)
\(810\) −3.32958 −0.116989
\(811\) 15.2520 0.535571 0.267785 0.963479i \(-0.413708\pi\)
0.267785 + 0.963479i \(0.413708\pi\)
\(812\) −1.92356 −0.0675037
\(813\) −17.6247 −0.618126
\(814\) 16.3065 0.571541
\(815\) −36.7586 −1.28760
\(816\) 1.65277 0.0578584
\(817\) −2.21103 −0.0773542
\(818\) 20.0669 0.701623
\(819\) −1.38443 −0.0483761
\(820\) 9.58975 0.334889
\(821\) −26.3835 −0.920792 −0.460396 0.887714i \(-0.652293\pi\)
−0.460396 + 0.887714i \(0.652293\pi\)
\(822\) −10.1134 −0.352744
\(823\) −32.0115 −1.11585 −0.557925 0.829891i \(-0.688402\pi\)
−0.557925 + 0.829891i \(0.688402\pi\)
\(824\) −1.00000 −0.0348367
\(825\) 15.8730 0.552626
\(826\) 4.62272 0.160845
\(827\) −30.7304 −1.06860 −0.534300 0.845295i \(-0.679425\pi\)
−0.534300 + 0.845295i \(0.679425\pi\)
\(828\) 0.437417 0.0152013
\(829\) −3.52821 −0.122540 −0.0612699 0.998121i \(-0.519515\pi\)
−0.0612699 + 0.998121i \(0.519515\pi\)
\(830\) 24.7657 0.859630
\(831\) 20.2994 0.704178
\(832\) 1.00000 0.0346688
\(833\) 8.40157 0.291097
\(834\) −22.7082 −0.786319
\(835\) −55.4311 −1.91827
\(836\) 6.21879 0.215081
\(837\) 5.09491 0.176106
\(838\) −16.5765 −0.572624
\(839\) 1.10550 0.0381662 0.0190831 0.999818i \(-0.493925\pi\)
0.0190831 + 0.999818i \(0.493925\pi\)
\(840\) −4.60958 −0.159046
\(841\) −27.0695 −0.933432
\(842\) 31.7963 1.09577
\(843\) 3.46316 0.119278
\(844\) 4.63742 0.159627
\(845\) 3.32958 0.114541
\(846\) 10.7983 0.371252
\(847\) 5.81176 0.199694
\(848\) 8.01315 0.275173
\(849\) 16.2956 0.559262
\(850\) 10.0589 0.345016
\(851\) 2.73485 0.0937496
\(852\) −5.77612 −0.197887
\(853\) −17.7546 −0.607907 −0.303954 0.952687i \(-0.598307\pi\)
−0.303954 + 0.952687i \(0.598307\pi\)
\(854\) −1.61128 −0.0551368
\(855\) −7.93916 −0.271514
\(856\) 12.0189 0.410799
\(857\) 1.16759 0.0398841 0.0199421 0.999801i \(-0.493652\pi\)
0.0199421 + 0.999801i \(0.493652\pi\)
\(858\) −2.60808 −0.0890383
\(859\) −26.6737 −0.910094 −0.455047 0.890467i \(-0.650378\pi\)
−0.455047 + 0.890467i \(0.650378\pi\)
\(860\) 3.08744 0.105281
\(861\) 3.98741 0.135891
\(862\) −10.6520 −0.362809
\(863\) 16.6001 0.565075 0.282537 0.959256i \(-0.408824\pi\)
0.282537 + 0.959256i \(0.408824\pi\)
\(864\) 1.00000 0.0340207
\(865\) −38.1191 −1.29609
\(866\) −7.06019 −0.239915
\(867\) 14.2684 0.484579
\(868\) 7.05356 0.239414
\(869\) −14.6410 −0.496662
\(870\) 4.62618 0.156842
\(871\) 8.02334 0.271861
\(872\) 9.77876 0.331151
\(873\) −1.80223 −0.0609963
\(874\) 1.04299 0.0352797
\(875\) −5.00640 −0.169247
\(876\) 5.91373 0.199806
\(877\) −45.6635 −1.54195 −0.770974 0.636867i \(-0.780230\pi\)
−0.770974 + 0.636867i \(0.780230\pi\)
\(878\) 36.1524 1.22008
\(879\) −16.2465 −0.547982
\(880\) −8.68380 −0.292731
\(881\) 30.4867 1.02712 0.513561 0.858053i \(-0.328326\pi\)
0.513561 + 0.858053i \(0.328326\pi\)
\(882\) 5.08334 0.171165
\(883\) −24.8086 −0.834877 −0.417439 0.908705i \(-0.637072\pi\)
−0.417439 + 0.908705i \(0.637072\pi\)
\(884\) −1.65277 −0.0555885
\(885\) −11.1177 −0.373717
\(886\) −14.1150 −0.474204
\(887\) 4.40219 0.147811 0.0739055 0.997265i \(-0.476454\pi\)
0.0739055 + 0.997265i \(0.476454\pi\)
\(888\) 6.25229 0.209813
\(889\) −8.61820 −0.289045
\(890\) −57.3583 −1.92265
\(891\) −2.60808 −0.0873739
\(892\) 2.11474 0.0708067
\(893\) 25.7478 0.861616
\(894\) −5.39722 −0.180510
\(895\) −33.7402 −1.12781
\(896\) 1.38443 0.0462507
\(897\) −0.437417 −0.0146049
\(898\) −27.6663 −0.923237
\(899\) −7.07896 −0.236097
\(900\) 6.08609 0.202870
\(901\) −13.2439 −0.441217
\(902\) 7.51171 0.250113
\(903\) 1.28375 0.0427207
\(904\) 14.8934 0.495347
\(905\) −69.3207 −2.30430
\(906\) −2.23675 −0.0743111
\(907\) 35.0714 1.16453 0.582264 0.813000i \(-0.302167\pi\)
0.582264 + 0.813000i \(0.302167\pi\)
\(908\) 6.63719 0.220263
\(909\) −2.58210 −0.0856430
\(910\) 4.60958 0.152806
\(911\) −40.6258 −1.34599 −0.672997 0.739646i \(-0.734993\pi\)
−0.672997 + 0.739646i \(0.734993\pi\)
\(912\) 2.38443 0.0789565
\(913\) 19.3991 0.642018
\(914\) 11.8995 0.393599
\(915\) 3.87514 0.128108
\(916\) −13.0876 −0.432428
\(917\) 13.6246 0.449923
\(918\) −1.65277 −0.0545494
\(919\) −52.0533 −1.71708 −0.858540 0.512746i \(-0.828628\pi\)
−0.858540 + 0.512746i \(0.828628\pi\)
\(920\) −1.45641 −0.0480165
\(921\) −22.2353 −0.732677
\(922\) 8.74873 0.288124
\(923\) 5.77612 0.190123
\(924\) −3.61071 −0.118784
\(925\) 38.0520 1.25114
\(926\) −5.98788 −0.196774
\(927\) 1.00000 0.0328443
\(928\) −1.38942 −0.0456099
\(929\) −50.7854 −1.66622 −0.833108 0.553111i \(-0.813441\pi\)
−0.833108 + 0.553111i \(0.813441\pi\)
\(930\) −16.9639 −0.556268
\(931\) 12.1209 0.397246
\(932\) −5.29335 −0.173389
\(933\) −16.5685 −0.542429
\(934\) −42.2930 −1.38387
\(935\) 14.3523 0.469370
\(936\) −1.00000 −0.0326860
\(937\) 8.67062 0.283257 0.141628 0.989920i \(-0.454766\pi\)
0.141628 + 0.989920i \(0.454766\pi\)
\(938\) 11.1078 0.362682
\(939\) 31.5663 1.03013
\(940\) −35.9537 −1.17268
\(941\) −12.9461 −0.422032 −0.211016 0.977483i \(-0.567677\pi\)
−0.211016 + 0.977483i \(0.567677\pi\)
\(942\) 16.1805 0.527188
\(943\) 1.25983 0.0410259
\(944\) 3.33907 0.108677
\(945\) 4.60958 0.149950
\(946\) 2.41841 0.0786294
\(947\) −34.0803 −1.10746 −0.553730 0.832696i \(-0.686796\pi\)
−0.553730 + 0.832696i \(0.686796\pi\)
\(948\) −5.61371 −0.182325
\(949\) −5.91373 −0.191968
\(950\) 14.5119 0.470827
\(951\) 21.3357 0.691856
\(952\) −2.28815 −0.0741592
\(953\) 13.7710 0.446087 0.223044 0.974808i \(-0.428401\pi\)
0.223044 + 0.974808i \(0.428401\pi\)
\(954\) −8.01315 −0.259435
\(955\) −19.7282 −0.638389
\(956\) −14.4156 −0.466232
\(957\) 3.62371 0.117138
\(958\) 17.9798 0.580902
\(959\) 14.0013 0.452125
\(960\) −3.32958 −0.107462
\(961\) −5.04192 −0.162643
\(962\) −6.25229 −0.201582
\(963\) −12.0189 −0.387305
\(964\) 13.6057 0.438209
\(965\) 66.8091 2.15066
\(966\) −0.605575 −0.0194840
\(967\) 27.4535 0.882844 0.441422 0.897300i \(-0.354474\pi\)
0.441422 + 0.897300i \(0.354474\pi\)
\(968\) 4.19793 0.134927
\(969\) −3.94091 −0.126600
\(970\) 6.00067 0.192670
\(971\) −57.3187 −1.83945 −0.919723 0.392568i \(-0.871587\pi\)
−0.919723 + 0.392568i \(0.871587\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 31.4380 1.00785
\(974\) −3.71623 −0.119076
\(975\) −6.08609 −0.194911
\(976\) −1.16385 −0.0372540
\(977\) 24.8339 0.794505 0.397253 0.917709i \(-0.369964\pi\)
0.397253 + 0.917709i \(0.369964\pi\)
\(978\) −11.0400 −0.353021
\(979\) −44.9291 −1.43594
\(980\) −16.9254 −0.540661
\(981\) −9.77876 −0.312212
\(982\) −13.0876 −0.417643
\(983\) 29.2824 0.933964 0.466982 0.884267i \(-0.345341\pi\)
0.466982 + 0.884267i \(0.345341\pi\)
\(984\) 2.88017 0.0918165
\(985\) 36.8698 1.17477
\(986\) 2.29638 0.0731318
\(987\) −14.9495 −0.475848
\(988\) −2.38443 −0.0758590
\(989\) 0.405607 0.0128975
\(990\) 8.68380 0.275989
\(991\) −17.4497 −0.554309 −0.277154 0.960825i \(-0.589391\pi\)
−0.277154 + 0.960825i \(0.589391\pi\)
\(992\) 5.09491 0.161763
\(993\) 27.7441 0.880431
\(994\) 7.99666 0.253639
\(995\) −24.5394 −0.777953
\(996\) 7.43809 0.235685
\(997\) −44.9473 −1.42350 −0.711748 0.702435i \(-0.752096\pi\)
−0.711748 + 0.702435i \(0.752096\pi\)
\(998\) −16.4962 −0.522179
\(999\) −6.25229 −0.197814
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 \(a_p\))