Properties

Label 4026.2.a.bc.1.4
Level 4026
Weight 2
Character 4026.1
Self dual Yes
Analytic conductor 32.148
Analytic rank 0
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1477718538\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(0.731055\)
Character \(\chi\) = 4026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+0.268945 q^{5}\) \(+1.00000 q^{6}\) \(+3.42672 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+0.268945 q^{5}\) \(+1.00000 q^{6}\) \(+3.42672 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+0.268945 q^{10}\) \(+1.00000 q^{11}\) \(+1.00000 q^{12}\) \(+1.26655 q^{13}\) \(+3.42672 q^{14}\) \(+0.268945 q^{15}\) \(+1.00000 q^{16}\) \(+0.867540 q^{17}\) \(+1.00000 q^{18}\) \(+6.18750 q^{19}\) \(+0.268945 q^{20}\) \(+3.42672 q^{21}\) \(+1.00000 q^{22}\) \(-8.86224 q^{23}\) \(+1.00000 q^{24}\) \(-4.92767 q^{25}\) \(+1.26655 q^{26}\) \(+1.00000 q^{27}\) \(+3.42672 q^{28}\) \(+1.57247 q^{29}\) \(+0.268945 q^{30}\) \(-6.59330 q^{31}\) \(+1.00000 q^{32}\) \(+1.00000 q^{33}\) \(+0.867540 q^{34}\) \(+0.921599 q^{35}\) \(+1.00000 q^{36}\) \(+8.55030 q^{37}\) \(+6.18750 q^{38}\) \(+1.26655 q^{39}\) \(+0.268945 q^{40}\) \(+3.44241 q^{41}\) \(+3.42672 q^{42}\) \(+12.3719 q^{43}\) \(+1.00000 q^{44}\) \(+0.268945 q^{45}\) \(-8.86224 q^{46}\) \(+5.99112 q^{47}\) \(+1.00000 q^{48}\) \(+4.74240 q^{49}\) \(-4.92767 q^{50}\) \(+0.867540 q^{51}\) \(+1.26655 q^{52}\) \(+4.13724 q^{53}\) \(+1.00000 q^{54}\) \(+0.268945 q^{55}\) \(+3.42672 q^{56}\) \(+6.18750 q^{57}\) \(+1.57247 q^{58}\) \(-13.3632 q^{59}\) \(+0.268945 q^{60}\) \(-1.00000 q^{61}\) \(-6.59330 q^{62}\) \(+3.42672 q^{63}\) \(+1.00000 q^{64}\) \(+0.340633 q^{65}\) \(+1.00000 q^{66}\) \(-0.380487 q^{67}\) \(+0.867540 q^{68}\) \(-8.86224 q^{69}\) \(+0.921599 q^{70}\) \(-10.4281 q^{71}\) \(+1.00000 q^{72}\) \(-2.36638 q^{73}\) \(+8.55030 q^{74}\) \(-4.92767 q^{75}\) \(+6.18750 q^{76}\) \(+3.42672 q^{77}\) \(+1.26655 q^{78}\) \(-8.37132 q^{79}\) \(+0.268945 q^{80}\) \(+1.00000 q^{81}\) \(+3.44241 q^{82}\) \(+2.32547 q^{83}\) \(+3.42672 q^{84}\) \(+0.233320 q^{85}\) \(+12.3719 q^{86}\) \(+1.57247 q^{87}\) \(+1.00000 q^{88}\) \(-11.6165 q^{89}\) \(+0.268945 q^{90}\) \(+4.34011 q^{91}\) \(-8.86224 q^{92}\) \(-6.59330 q^{93}\) \(+5.99112 q^{94}\) \(+1.66410 q^{95}\) \(+1.00000 q^{96}\) \(-11.5077 q^{97}\) \(+4.74240 q^{98}\) \(+1.00000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 9q^{12} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 9q^{16} \) \(\mathstrut +\mathstrut q^{17} \) \(\mathstrut +\mathstrut 9q^{18} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 9q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 9q^{24} \) \(\mathstrut +\mathstrut 23q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut +\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 8q^{30} \) \(\mathstrut +\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut +\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 9q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 5q^{38} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 9q^{42} \) \(\mathstrut +\mathstrut 5q^{43} \) \(\mathstrut +\mathstrut 9q^{44} \) \(\mathstrut +\mathstrut 8q^{45} \) \(\mathstrut -\mathstrut q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 9q^{48} \) \(\mathstrut +\mathstrut 30q^{49} \) \(\mathstrut +\mathstrut 23q^{50} \) \(\mathstrut +\mathstrut q^{51} \) \(\mathstrut +\mathstrut 8q^{52} \) \(\mathstrut +\mathstrut q^{53} \) \(\mathstrut +\mathstrut 9q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut +\mathstrut 25q^{62} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut q^{68} \) \(\mathstrut -\mathstrut q^{69} \) \(\mathstrut +\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 15q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 5q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut +\mathstrut 5q^{82} \) \(\mathstrut +\mathstrut 21q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 5q^{86} \) \(\mathstrut -\mathstrut 14q^{87} \) \(\mathstrut +\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 8q^{90} \) \(\mathstrut -\mathstrut 19q^{91} \) \(\mathstrut -\mathstrut q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 30q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 0.268945 0.120276 0.0601379 0.998190i \(-0.480846\pi\)
0.0601379 + 0.998190i \(0.480846\pi\)
\(6\) 1.00000 0.408248
\(7\) 3.42672 1.29518 0.647589 0.761990i \(-0.275777\pi\)
0.647589 + 0.761990i \(0.275777\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0.268945 0.0850479
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) 1.26655 0.351278 0.175639 0.984455i \(-0.443801\pi\)
0.175639 + 0.984455i \(0.443801\pi\)
\(14\) 3.42672 0.915829
\(15\) 0.268945 0.0694413
\(16\) 1.00000 0.250000
\(17\) 0.867540 0.210409 0.105205 0.994451i \(-0.466450\pi\)
0.105205 + 0.994451i \(0.466450\pi\)
\(18\) 1.00000 0.235702
\(19\) 6.18750 1.41951 0.709755 0.704449i \(-0.248806\pi\)
0.709755 + 0.704449i \(0.248806\pi\)
\(20\) 0.268945 0.0601379
\(21\) 3.42672 0.747771
\(22\) 1.00000 0.213201
\(23\) −8.86224 −1.84791 −0.923953 0.382506i \(-0.875061\pi\)
−0.923953 + 0.382506i \(0.875061\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.92767 −0.985534
\(26\) 1.26655 0.248391
\(27\) 1.00000 0.192450
\(28\) 3.42672 0.647589
\(29\) 1.57247 0.292001 0.146001 0.989285i \(-0.453360\pi\)
0.146001 + 0.989285i \(0.453360\pi\)
\(30\) 0.268945 0.0491024
\(31\) −6.59330 −1.18419 −0.592096 0.805868i \(-0.701699\pi\)
−0.592096 + 0.805868i \(0.701699\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) 0.867540 0.148782
\(35\) 0.921599 0.155779
\(36\) 1.00000 0.166667
\(37\) 8.55030 1.40566 0.702830 0.711358i \(-0.251919\pi\)
0.702830 + 0.711358i \(0.251919\pi\)
\(38\) 6.18750 1.00374
\(39\) 1.26655 0.202811
\(40\) 0.268945 0.0425239
\(41\) 3.44241 0.537614 0.268807 0.963194i \(-0.413371\pi\)
0.268807 + 0.963194i \(0.413371\pi\)
\(42\) 3.42672 0.528754
\(43\) 12.3719 1.88669 0.943345 0.331813i \(-0.107660\pi\)
0.943345 + 0.331813i \(0.107660\pi\)
\(44\) 1.00000 0.150756
\(45\) 0.268945 0.0400920
\(46\) −8.86224 −1.30667
\(47\) 5.99112 0.873894 0.436947 0.899487i \(-0.356060\pi\)
0.436947 + 0.899487i \(0.356060\pi\)
\(48\) 1.00000 0.144338
\(49\) 4.74240 0.677485
\(50\) −4.92767 −0.696878
\(51\) 0.867540 0.121480
\(52\) 1.26655 0.175639
\(53\) 4.13724 0.568293 0.284147 0.958781i \(-0.408290\pi\)
0.284147 + 0.958781i \(0.408290\pi\)
\(54\) 1.00000 0.136083
\(55\) 0.268945 0.0362645
\(56\) 3.42672 0.457914
\(57\) 6.18750 0.819554
\(58\) 1.57247 0.206476
\(59\) −13.3632 −1.73974 −0.869870 0.493281i \(-0.835797\pi\)
−0.869870 + 0.493281i \(0.835797\pi\)
\(60\) 0.268945 0.0347207
\(61\) −1.00000 −0.128037
\(62\) −6.59330 −0.837350
\(63\) 3.42672 0.431726
\(64\) 1.00000 0.125000
\(65\) 0.340633 0.0422503
\(66\) 1.00000 0.123091
\(67\) −0.380487 −0.0464839 −0.0232420 0.999730i \(-0.507399\pi\)
−0.0232420 + 0.999730i \(0.507399\pi\)
\(68\) 0.867540 0.105205
\(69\) −8.86224 −1.06689
\(70\) 0.921599 0.110152
\(71\) −10.4281 −1.23759 −0.618796 0.785551i \(-0.712379\pi\)
−0.618796 + 0.785551i \(0.712379\pi\)
\(72\) 1.00000 0.117851
\(73\) −2.36638 −0.276964 −0.138482 0.990365i \(-0.544222\pi\)
−0.138482 + 0.990365i \(0.544222\pi\)
\(74\) 8.55030 0.993952
\(75\) −4.92767 −0.568998
\(76\) 6.18750 0.709755
\(77\) 3.42672 0.390511
\(78\) 1.26655 0.143409
\(79\) −8.37132 −0.941847 −0.470924 0.882174i \(-0.656079\pi\)
−0.470924 + 0.882174i \(0.656079\pi\)
\(80\) 0.268945 0.0300690
\(81\) 1.00000 0.111111
\(82\) 3.44241 0.380150
\(83\) 2.32547 0.255254 0.127627 0.991822i \(-0.459264\pi\)
0.127627 + 0.991822i \(0.459264\pi\)
\(84\) 3.42672 0.373886
\(85\) 0.233320 0.0253072
\(86\) 12.3719 1.33409
\(87\) 1.57247 0.168587
\(88\) 1.00000 0.106600
\(89\) −11.6165 −1.23134 −0.615671 0.788004i \(-0.711115\pi\)
−0.615671 + 0.788004i \(0.711115\pi\)
\(90\) 0.268945 0.0283493
\(91\) 4.34011 0.454968
\(92\) −8.86224 −0.923953
\(93\) −6.59330 −0.683693
\(94\) 5.99112 0.617937
\(95\) 1.66410 0.170733
\(96\) 1.00000 0.102062
\(97\) −11.5077 −1.16843 −0.584215 0.811599i \(-0.698597\pi\)
−0.584215 + 0.811599i \(0.698597\pi\)
\(98\) 4.74240 0.479054
\(99\) 1.00000 0.100504
\(100\) −4.92767 −0.492767
\(101\) −10.6426 −1.05898 −0.529489 0.848317i \(-0.677616\pi\)
−0.529489 + 0.848317i \(0.677616\pi\)
\(102\) 0.867540 0.0858992
\(103\) 1.00764 0.0992852 0.0496426 0.998767i \(-0.484192\pi\)
0.0496426 + 0.998767i \(0.484192\pi\)
\(104\) 1.26655 0.124196
\(105\) 0.921599 0.0899388
\(106\) 4.13724 0.401844
\(107\) −6.78676 −0.656101 −0.328051 0.944660i \(-0.606392\pi\)
−0.328051 + 0.944660i \(0.606392\pi\)
\(108\) 1.00000 0.0962250
\(109\) −10.9790 −1.05160 −0.525800 0.850608i \(-0.676234\pi\)
−0.525800 + 0.850608i \(0.676234\pi\)
\(110\) 0.268945 0.0256429
\(111\) 8.55030 0.811558
\(112\) 3.42672 0.323794
\(113\) −0.304968 −0.0286890 −0.0143445 0.999897i \(-0.504566\pi\)
−0.0143445 + 0.999897i \(0.504566\pi\)
\(114\) 6.18750 0.579512
\(115\) −2.38346 −0.222258
\(116\) 1.57247 0.146001
\(117\) 1.26655 0.117093
\(118\) −13.3632 −1.23018
\(119\) 2.97281 0.272517
\(120\) 0.268945 0.0245512
\(121\) 1.00000 0.0909091
\(122\) −1.00000 −0.0905357
\(123\) 3.44241 0.310391
\(124\) −6.59330 −0.592096
\(125\) −2.67000 −0.238812
\(126\) 3.42672 0.305276
\(127\) 18.8689 1.67435 0.837174 0.546936i \(-0.184206\pi\)
0.837174 + 0.546936i \(0.184206\pi\)
\(128\) 1.00000 0.0883883
\(129\) 12.3719 1.08928
\(130\) 0.340633 0.0298755
\(131\) 3.68893 0.322304 0.161152 0.986930i \(-0.448479\pi\)
0.161152 + 0.986930i \(0.448479\pi\)
\(132\) 1.00000 0.0870388
\(133\) 21.2028 1.83852
\(134\) −0.380487 −0.0328691
\(135\) 0.268945 0.0231471
\(136\) 0.867540 0.0743909
\(137\) 8.47305 0.723901 0.361951 0.932197i \(-0.382111\pi\)
0.361951 + 0.932197i \(0.382111\pi\)
\(138\) −8.86224 −0.754404
\(139\) 14.3911 1.22064 0.610320 0.792155i \(-0.291041\pi\)
0.610320 + 0.792155i \(0.291041\pi\)
\(140\) 0.921599 0.0778893
\(141\) 5.99112 0.504543
\(142\) −10.4281 −0.875110
\(143\) 1.26655 0.105914
\(144\) 1.00000 0.0833333
\(145\) 0.422909 0.0351207
\(146\) −2.36638 −0.195843
\(147\) 4.74240 0.391146
\(148\) 8.55030 0.702830
\(149\) 19.6765 1.61196 0.805980 0.591943i \(-0.201639\pi\)
0.805980 + 0.591943i \(0.201639\pi\)
\(150\) −4.92767 −0.402342
\(151\) 8.71508 0.709223 0.354611 0.935014i \(-0.384613\pi\)
0.354611 + 0.935014i \(0.384613\pi\)
\(152\) 6.18750 0.501872
\(153\) 0.867540 0.0701364
\(154\) 3.42672 0.276133
\(155\) −1.77324 −0.142430
\(156\) 1.26655 0.101405
\(157\) 22.7483 1.81551 0.907755 0.419501i \(-0.137795\pi\)
0.907755 + 0.419501i \(0.137795\pi\)
\(158\) −8.37132 −0.665986
\(159\) 4.13724 0.328104
\(160\) 0.268945 0.0212620
\(161\) −30.3684 −2.39337
\(162\) 1.00000 0.0785674
\(163\) −16.9197 −1.32526 −0.662628 0.748948i \(-0.730559\pi\)
−0.662628 + 0.748948i \(0.730559\pi\)
\(164\) 3.44241 0.268807
\(165\) 0.268945 0.0209373
\(166\) 2.32547 0.180492
\(167\) 24.5798 1.90204 0.951021 0.309125i \(-0.100036\pi\)
0.951021 + 0.309125i \(0.100036\pi\)
\(168\) 3.42672 0.264377
\(169\) −11.3958 −0.876604
\(170\) 0.233320 0.0178949
\(171\) 6.18750 0.473170
\(172\) 12.3719 0.943345
\(173\) 16.0917 1.22343 0.611715 0.791078i \(-0.290480\pi\)
0.611715 + 0.791078i \(0.290480\pi\)
\(174\) 1.57247 0.119209
\(175\) −16.8857 −1.27644
\(176\) 1.00000 0.0753778
\(177\) −13.3632 −1.00444
\(178\) −11.6165 −0.870690
\(179\) −20.5271 −1.53427 −0.767133 0.641488i \(-0.778317\pi\)
−0.767133 + 0.641488i \(0.778317\pi\)
\(180\) 0.268945 0.0200460
\(181\) −14.6239 −1.08699 −0.543494 0.839413i \(-0.682899\pi\)
−0.543494 + 0.839413i \(0.682899\pi\)
\(182\) 4.34011 0.321711
\(183\) −1.00000 −0.0739221
\(184\) −8.86224 −0.653333
\(185\) 2.29956 0.169067
\(186\) −6.59330 −0.483444
\(187\) 0.867540 0.0634408
\(188\) 5.99112 0.436947
\(189\) 3.42672 0.249257
\(190\) 1.66410 0.120726
\(191\) −5.11491 −0.370102 −0.185051 0.982729i \(-0.559245\pi\)
−0.185051 + 0.982729i \(0.559245\pi\)
\(192\) 1.00000 0.0721688
\(193\) −18.9293 −1.36256 −0.681281 0.732022i \(-0.738577\pi\)
−0.681281 + 0.732022i \(0.738577\pi\)
\(194\) −11.5077 −0.826204
\(195\) 0.340633 0.0243932
\(196\) 4.74240 0.338743
\(197\) 8.98440 0.640112 0.320056 0.947399i \(-0.396298\pi\)
0.320056 + 0.947399i \(0.396298\pi\)
\(198\) 1.00000 0.0710669
\(199\) 15.1438 1.07352 0.536758 0.843736i \(-0.319649\pi\)
0.536758 + 0.843736i \(0.319649\pi\)
\(200\) −4.92767 −0.348439
\(201\) −0.380487 −0.0268375
\(202\) −10.6426 −0.748810
\(203\) 5.38842 0.378193
\(204\) 0.867540 0.0607399
\(205\) 0.925818 0.0646620
\(206\) 1.00764 0.0702053
\(207\) −8.86224 −0.615969
\(208\) 1.26655 0.0878196
\(209\) 6.18750 0.427998
\(210\) 0.921599 0.0635964
\(211\) 25.8348 1.77854 0.889271 0.457381i \(-0.151212\pi\)
0.889271 + 0.457381i \(0.151212\pi\)
\(212\) 4.13724 0.284147
\(213\) −10.4281 −0.714525
\(214\) −6.78676 −0.463934
\(215\) 3.32735 0.226923
\(216\) 1.00000 0.0680414
\(217\) −22.5934 −1.53374
\(218\) −10.9790 −0.743594
\(219\) −2.36638 −0.159905
\(220\) 0.268945 0.0181323
\(221\) 1.09878 0.0739122
\(222\) 8.55030 0.573858
\(223\) 9.89572 0.662666 0.331333 0.943514i \(-0.392502\pi\)
0.331333 + 0.943514i \(0.392502\pi\)
\(224\) 3.42672 0.228957
\(225\) −4.92767 −0.328511
\(226\) −0.304968 −0.0202862
\(227\) 1.05470 0.0700032 0.0350016 0.999387i \(-0.488856\pi\)
0.0350016 + 0.999387i \(0.488856\pi\)
\(228\) 6.18750 0.409777
\(229\) −6.19110 −0.409119 −0.204560 0.978854i \(-0.565576\pi\)
−0.204560 + 0.978854i \(0.565576\pi\)
\(230\) −2.38346 −0.157160
\(231\) 3.42672 0.225461
\(232\) 1.57247 0.103238
\(233\) −28.9847 −1.89885 −0.949426 0.313990i \(-0.898334\pi\)
−0.949426 + 0.313990i \(0.898334\pi\)
\(234\) 1.26655 0.0827971
\(235\) 1.61128 0.105108
\(236\) −13.3632 −0.869870
\(237\) −8.37132 −0.543776
\(238\) 2.97281 0.192699
\(239\) −4.63720 −0.299955 −0.149978 0.988689i \(-0.547920\pi\)
−0.149978 + 0.988689i \(0.547920\pi\)
\(240\) 0.268945 0.0173603
\(241\) 13.8531 0.892354 0.446177 0.894945i \(-0.352785\pi\)
0.446177 + 0.894945i \(0.352785\pi\)
\(242\) 1.00000 0.0642824
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) 1.27544 0.0814851
\(246\) 3.44241 0.219480
\(247\) 7.83679 0.498643
\(248\) −6.59330 −0.418675
\(249\) 2.32547 0.147371
\(250\) −2.67000 −0.168865
\(251\) −8.63040 −0.544746 −0.272373 0.962192i \(-0.587808\pi\)
−0.272373 + 0.962192i \(0.587808\pi\)
\(252\) 3.42672 0.215863
\(253\) −8.86224 −0.557165
\(254\) 18.8689 1.18394
\(255\) 0.233320 0.0146111
\(256\) 1.00000 0.0625000
\(257\) 1.33011 0.0829700 0.0414850 0.999139i \(-0.486791\pi\)
0.0414850 + 0.999139i \(0.486791\pi\)
\(258\) 12.3719 0.770238
\(259\) 29.2995 1.82058
\(260\) 0.340633 0.0211251
\(261\) 1.57247 0.0973337
\(262\) 3.68893 0.227903
\(263\) −29.1042 −1.79464 −0.897321 0.441378i \(-0.854490\pi\)
−0.897321 + 0.441378i \(0.854490\pi\)
\(264\) 1.00000 0.0615457
\(265\) 1.11269 0.0683520
\(266\) 21.2028 1.30003
\(267\) −11.6165 −0.710915
\(268\) −0.380487 −0.0232420
\(269\) −2.29032 −0.139643 −0.0698215 0.997560i \(-0.522243\pi\)
−0.0698215 + 0.997560i \(0.522243\pi\)
\(270\) 0.268945 0.0163675
\(271\) −23.4290 −1.42321 −0.711604 0.702580i \(-0.752031\pi\)
−0.711604 + 0.702580i \(0.752031\pi\)
\(272\) 0.867540 0.0526023
\(273\) 4.34011 0.262676
\(274\) 8.47305 0.511875
\(275\) −4.92767 −0.297150
\(276\) −8.86224 −0.533444
\(277\) 18.8839 1.13463 0.567313 0.823502i \(-0.307983\pi\)
0.567313 + 0.823502i \(0.307983\pi\)
\(278\) 14.3911 0.863123
\(279\) −6.59330 −0.394730
\(280\) 0.921599 0.0550761
\(281\) −10.0216 −0.597840 −0.298920 0.954278i \(-0.596626\pi\)
−0.298920 + 0.954278i \(0.596626\pi\)
\(282\) 5.99112 0.356766
\(283\) 2.41609 0.143622 0.0718108 0.997418i \(-0.477122\pi\)
0.0718108 + 0.997418i \(0.477122\pi\)
\(284\) −10.4281 −0.618796
\(285\) 1.66410 0.0985726
\(286\) 1.26655 0.0748928
\(287\) 11.7962 0.696305
\(288\) 1.00000 0.0589256
\(289\) −16.2474 −0.955728
\(290\) 0.422909 0.0248341
\(291\) −11.5077 −0.674593
\(292\) −2.36638 −0.138482
\(293\) 4.40067 0.257090 0.128545 0.991704i \(-0.458969\pi\)
0.128545 + 0.991704i \(0.458969\pi\)
\(294\) 4.74240 0.276582
\(295\) −3.59396 −0.209249
\(296\) 8.55030 0.496976
\(297\) 1.00000 0.0580259
\(298\) 19.6765 1.13983
\(299\) −11.2245 −0.649129
\(300\) −4.92767 −0.284499
\(301\) 42.3949 2.44360
\(302\) 8.71508 0.501496
\(303\) −10.6426 −0.611401
\(304\) 6.18750 0.354877
\(305\) −0.268945 −0.0153997
\(306\) 0.867540 0.0495939
\(307\) −17.0682 −0.974136 −0.487068 0.873364i \(-0.661934\pi\)
−0.487068 + 0.873364i \(0.661934\pi\)
\(308\) 3.42672 0.195255
\(309\) 1.00764 0.0573224
\(310\) −1.77324 −0.100713
\(311\) −28.3715 −1.60880 −0.804400 0.594088i \(-0.797513\pi\)
−0.804400 + 0.594088i \(0.797513\pi\)
\(312\) 1.26655 0.0717044
\(313\) −9.88599 −0.558789 −0.279395 0.960176i \(-0.590134\pi\)
−0.279395 + 0.960176i \(0.590134\pi\)
\(314\) 22.7483 1.28376
\(315\) 0.921599 0.0519262
\(316\) −8.37132 −0.470924
\(317\) 5.91378 0.332151 0.166075 0.986113i \(-0.446890\pi\)
0.166075 + 0.986113i \(0.446890\pi\)
\(318\) 4.13724 0.232005
\(319\) 1.57247 0.0880416
\(320\) 0.268945 0.0150345
\(321\) −6.78676 −0.378800
\(322\) −30.3684 −1.69237
\(323\) 5.36790 0.298678
\(324\) 1.00000 0.0555556
\(325\) −6.24115 −0.346197
\(326\) −16.9197 −0.937098
\(327\) −10.9790 −0.607142
\(328\) 3.44241 0.190075
\(329\) 20.5299 1.13185
\(330\) 0.268945 0.0148049
\(331\) 18.4377 1.01343 0.506714 0.862114i \(-0.330860\pi\)
0.506714 + 0.862114i \(0.330860\pi\)
\(332\) 2.32547 0.127627
\(333\) 8.55030 0.468553
\(334\) 24.5798 1.34495
\(335\) −0.102330 −0.00559090
\(336\) 3.42672 0.186943
\(337\) 35.4326 1.93014 0.965069 0.261998i \(-0.0843813\pi\)
0.965069 + 0.261998i \(0.0843813\pi\)
\(338\) −11.3958 −0.619852
\(339\) −0.304968 −0.0165636
\(340\) 0.233320 0.0126536
\(341\) −6.59330 −0.357047
\(342\) 6.18750 0.334582
\(343\) −7.73617 −0.417714
\(344\) 12.3719 0.667046
\(345\) −2.38346 −0.128321
\(346\) 16.0917 0.865096
\(347\) 32.0180 1.71881 0.859407 0.511292i \(-0.170833\pi\)
0.859407 + 0.511292i \(0.170833\pi\)
\(348\) 1.57247 0.0842935
\(349\) 0.763609 0.0408751 0.0204375 0.999791i \(-0.493494\pi\)
0.0204375 + 0.999791i \(0.493494\pi\)
\(350\) −16.8857 −0.902580
\(351\) 1.26655 0.0676035
\(352\) 1.00000 0.0533002
\(353\) 16.4468 0.875376 0.437688 0.899127i \(-0.355798\pi\)
0.437688 + 0.899127i \(0.355798\pi\)
\(354\) −13.3632 −0.710246
\(355\) −2.80460 −0.148853
\(356\) −11.6165 −0.615671
\(357\) 2.97281 0.157338
\(358\) −20.5271 −1.08489
\(359\) 19.7050 1.03999 0.519995 0.854169i \(-0.325934\pi\)
0.519995 + 0.854169i \(0.325934\pi\)
\(360\) 0.268945 0.0141746
\(361\) 19.2851 1.01501
\(362\) −14.6239 −0.768616
\(363\) 1.00000 0.0524864
\(364\) 4.34011 0.227484
\(365\) −0.636427 −0.0333121
\(366\) −1.00000 −0.0522708
\(367\) −20.4095 −1.06537 −0.532684 0.846314i \(-0.678817\pi\)
−0.532684 + 0.846314i \(0.678817\pi\)
\(368\) −8.86224 −0.461976
\(369\) 3.44241 0.179205
\(370\) 2.29956 0.119548
\(371\) 14.1772 0.736041
\(372\) −6.59330 −0.341847
\(373\) −35.9190 −1.85982 −0.929908 0.367793i \(-0.880114\pi\)
−0.929908 + 0.367793i \(0.880114\pi\)
\(374\) 0.867540 0.0448594
\(375\) −2.67000 −0.137878
\(376\) 5.99112 0.308968
\(377\) 1.99162 0.102574
\(378\) 3.42672 0.176251
\(379\) 29.2039 1.50010 0.750051 0.661380i \(-0.230029\pi\)
0.750051 + 0.661380i \(0.230029\pi\)
\(380\) 1.66410 0.0853664
\(381\) 18.8689 0.966686
\(382\) −5.11491 −0.261702
\(383\) −30.2591 −1.54617 −0.773083 0.634305i \(-0.781286\pi\)
−0.773083 + 0.634305i \(0.781286\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0.921599 0.0469690
\(386\) −18.9293 −0.963477
\(387\) 12.3719 0.628897
\(388\) −11.5077 −0.584215
\(389\) −6.13420 −0.311016 −0.155508 0.987835i \(-0.549702\pi\)
−0.155508 + 0.987835i \(0.549702\pi\)
\(390\) 0.340633 0.0172486
\(391\) −7.68835 −0.388816
\(392\) 4.74240 0.239527
\(393\) 3.68893 0.186082
\(394\) 8.98440 0.452628
\(395\) −2.25142 −0.113281
\(396\) 1.00000 0.0502519
\(397\) 7.09173 0.355924 0.177962 0.984037i \(-0.443050\pi\)
0.177962 + 0.984037i \(0.443050\pi\)
\(398\) 15.1438 0.759091
\(399\) 21.2028 1.06147
\(400\) −4.92767 −0.246383
\(401\) −29.9023 −1.49325 −0.746626 0.665244i \(-0.768328\pi\)
−0.746626 + 0.665244i \(0.768328\pi\)
\(402\) −0.380487 −0.0189770
\(403\) −8.35075 −0.415981
\(404\) −10.6426 −0.529489
\(405\) 0.268945 0.0133640
\(406\) 5.38842 0.267423
\(407\) 8.55030 0.423822
\(408\) 0.867540 0.0429496
\(409\) −31.4377 −1.55449 −0.777246 0.629197i \(-0.783384\pi\)
−0.777246 + 0.629197i \(0.783384\pi\)
\(410\) 0.925818 0.0457229
\(411\) 8.47305 0.417945
\(412\) 1.00764 0.0496426
\(413\) −45.7919 −2.25327
\(414\) −8.86224 −0.435556
\(415\) 0.625425 0.0307009
\(416\) 1.26655 0.0620978
\(417\) 14.3911 0.704737
\(418\) 6.18750 0.302640
\(419\) −6.06492 −0.296291 −0.148145 0.988966i \(-0.547330\pi\)
−0.148145 + 0.988966i \(0.547330\pi\)
\(420\) 0.921599 0.0449694
\(421\) −11.9703 −0.583397 −0.291698 0.956510i \(-0.594220\pi\)
−0.291698 + 0.956510i \(0.594220\pi\)
\(422\) 25.8348 1.25762
\(423\) 5.99112 0.291298
\(424\) 4.13724 0.200922
\(425\) −4.27495 −0.207365
\(426\) −10.4281 −0.505245
\(427\) −3.42672 −0.165831
\(428\) −6.78676 −0.328051
\(429\) 1.26655 0.0611497
\(430\) 3.32735 0.160459
\(431\) 4.23679 0.204079 0.102039 0.994780i \(-0.467463\pi\)
0.102039 + 0.994780i \(0.467463\pi\)
\(432\) 1.00000 0.0481125
\(433\) −12.6590 −0.608352 −0.304176 0.952616i \(-0.598381\pi\)
−0.304176 + 0.952616i \(0.598381\pi\)
\(434\) −22.5934 −1.08452
\(435\) 0.422909 0.0202769
\(436\) −10.9790 −0.525800
\(437\) −54.8351 −2.62312
\(438\) −2.36638 −0.113070
\(439\) −26.5844 −1.26881 −0.634403 0.773003i \(-0.718754\pi\)
−0.634403 + 0.773003i \(0.718754\pi\)
\(440\) 0.268945 0.0128215
\(441\) 4.74240 0.225828
\(442\) 1.09878 0.0522638
\(443\) 26.5443 1.26116 0.630579 0.776125i \(-0.282817\pi\)
0.630579 + 0.776125i \(0.282817\pi\)
\(444\) 8.55030 0.405779
\(445\) −3.12419 −0.148101
\(446\) 9.89572 0.468576
\(447\) 19.6765 0.930665
\(448\) 3.42672 0.161897
\(449\) 33.4432 1.57828 0.789140 0.614213i \(-0.210526\pi\)
0.789140 + 0.614213i \(0.210526\pi\)
\(450\) −4.92767 −0.232293
\(451\) 3.44241 0.162097
\(452\) −0.304968 −0.0143445
\(453\) 8.71508 0.409470
\(454\) 1.05470 0.0494997
\(455\) 1.16725 0.0547216
\(456\) 6.18750 0.289756
\(457\) −39.3979 −1.84296 −0.921479 0.388428i \(-0.873018\pi\)
−0.921479 + 0.388428i \(0.873018\pi\)
\(458\) −6.19110 −0.289291
\(459\) 0.867540 0.0404933
\(460\) −2.38346 −0.111129
\(461\) 2.36247 0.110031 0.0550155 0.998485i \(-0.482479\pi\)
0.0550155 + 0.998485i \(0.482479\pi\)
\(462\) 3.42672 0.159425
\(463\) 29.4582 1.36904 0.684520 0.728994i \(-0.260012\pi\)
0.684520 + 0.728994i \(0.260012\pi\)
\(464\) 1.57247 0.0730003
\(465\) −1.77324 −0.0822318
\(466\) −28.9847 −1.34269
\(467\) −1.97701 −0.0914850 −0.0457425 0.998953i \(-0.514565\pi\)
−0.0457425 + 0.998953i \(0.514565\pi\)
\(468\) 1.26655 0.0585464
\(469\) −1.30382 −0.0602050
\(470\) 1.61128 0.0743229
\(471\) 22.7483 1.04818
\(472\) −13.3632 −0.615091
\(473\) 12.3719 0.568859
\(474\) −8.37132 −0.384507
\(475\) −30.4899 −1.39897
\(476\) 2.97281 0.136259
\(477\) 4.13724 0.189431
\(478\) −4.63720 −0.212100
\(479\) −26.1584 −1.19521 −0.597604 0.801791i \(-0.703880\pi\)
−0.597604 + 0.801791i \(0.703880\pi\)
\(480\) 0.268945 0.0122756
\(481\) 10.8294 0.493778
\(482\) 13.8531 0.630990
\(483\) −30.3684 −1.38181
\(484\) 1.00000 0.0454545
\(485\) −3.09494 −0.140534
\(486\) 1.00000 0.0453609
\(487\) −28.6097 −1.29643 −0.648215 0.761457i \(-0.724484\pi\)
−0.648215 + 0.761457i \(0.724484\pi\)
\(488\) −1.00000 −0.0452679
\(489\) −16.9197 −0.765137
\(490\) 1.27544 0.0576187
\(491\) −12.1722 −0.549322 −0.274661 0.961541i \(-0.588566\pi\)
−0.274661 + 0.961541i \(0.588566\pi\)
\(492\) 3.44241 0.155196
\(493\) 1.36418 0.0614397
\(494\) 7.83679 0.352594
\(495\) 0.268945 0.0120882
\(496\) −6.59330 −0.296048
\(497\) −35.7343 −1.60290
\(498\) 2.32547 0.104207
\(499\) −18.9089 −0.846481 −0.423240 0.906017i \(-0.639107\pi\)
−0.423240 + 0.906017i \(0.639107\pi\)
\(500\) −2.67000 −0.119406
\(501\) 24.5798 1.09814
\(502\) −8.63040 −0.385194
\(503\) −16.0313 −0.714800 −0.357400 0.933951i \(-0.616337\pi\)
−0.357400 + 0.933951i \(0.616337\pi\)
\(504\) 3.42672 0.152638
\(505\) −2.86227 −0.127369
\(506\) −8.86224 −0.393975
\(507\) −11.3958 −0.506107
\(508\) 18.8689 0.837174
\(509\) 41.6067 1.84418 0.922092 0.386971i \(-0.126479\pi\)
0.922092 + 0.386971i \(0.126479\pi\)
\(510\) 0.233320 0.0103316
\(511\) −8.10893 −0.358718
\(512\) 1.00000 0.0441942
\(513\) 6.18750 0.273185
\(514\) 1.33011 0.0586687
\(515\) 0.270998 0.0119416
\(516\) 12.3719 0.544641
\(517\) 5.99112 0.263489
\(518\) 29.2995 1.28734
\(519\) 16.0917 0.706348
\(520\) 0.340633 0.0149377
\(521\) 28.9241 1.26719 0.633593 0.773667i \(-0.281579\pi\)
0.633593 + 0.773667i \(0.281579\pi\)
\(522\) 1.57247 0.0688253
\(523\) 18.7161 0.818400 0.409200 0.912445i \(-0.365808\pi\)
0.409200 + 0.912445i \(0.365808\pi\)
\(524\) 3.68893 0.161152
\(525\) −16.8857 −0.736954
\(526\) −29.1042 −1.26900
\(527\) −5.71995 −0.249165
\(528\) 1.00000 0.0435194
\(529\) 55.5394 2.41476
\(530\) 1.11269 0.0483322
\(531\) −13.3632 −0.579913
\(532\) 21.2028 0.919259
\(533\) 4.35999 0.188852
\(534\) −11.6165 −0.502693
\(535\) −1.82527 −0.0789131
\(536\) −0.380487 −0.0164346
\(537\) −20.5271 −0.885809
\(538\) −2.29032 −0.0987425
\(539\) 4.74240 0.204269
\(540\) 0.268945 0.0115736
\(541\) −6.77164 −0.291136 −0.145568 0.989348i \(-0.546501\pi\)
−0.145568 + 0.989348i \(0.546501\pi\)
\(542\) −23.4290 −1.00636
\(543\) −14.6239 −0.627573
\(544\) 0.867540 0.0371955
\(545\) −2.95276 −0.126482
\(546\) 4.34011 0.185740
\(547\) 11.8955 0.508616 0.254308 0.967123i \(-0.418152\pi\)
0.254308 + 0.967123i \(0.418152\pi\)
\(548\) 8.47305 0.361951
\(549\) −1.00000 −0.0426790
\(550\) −4.92767 −0.210116
\(551\) 9.72968 0.414498
\(552\) −8.86224 −0.377202
\(553\) −28.6861 −1.21986
\(554\) 18.8839 0.802301
\(555\) 2.29956 0.0976109
\(556\) 14.3911 0.610320
\(557\) −28.9513 −1.22671 −0.613354 0.789808i \(-0.710180\pi\)
−0.613354 + 0.789808i \(0.710180\pi\)
\(558\) −6.59330 −0.279117
\(559\) 15.6696 0.662753
\(560\) 0.921599 0.0389447
\(561\) 0.867540 0.0366276
\(562\) −10.0216 −0.422737
\(563\) −41.4776 −1.74807 −0.874036 0.485861i \(-0.838506\pi\)
−0.874036 + 0.485861i \(0.838506\pi\)
\(564\) 5.99112 0.252272
\(565\) −0.0820196 −0.00345059
\(566\) 2.41609 0.101556
\(567\) 3.42672 0.143909
\(568\) −10.4281 −0.437555
\(569\) −8.47596 −0.355331 −0.177665 0.984091i \(-0.556854\pi\)
−0.177665 + 0.984091i \(0.556854\pi\)
\(570\) 1.66410 0.0697014
\(571\) −14.6693 −0.613892 −0.306946 0.951727i \(-0.599307\pi\)
−0.306946 + 0.951727i \(0.599307\pi\)
\(572\) 1.26655 0.0529572
\(573\) −5.11491 −0.213679
\(574\) 11.7962 0.492362
\(575\) 43.6702 1.82117
\(576\) 1.00000 0.0416667
\(577\) −34.5189 −1.43704 −0.718520 0.695506i \(-0.755180\pi\)
−0.718520 + 0.695506i \(0.755180\pi\)
\(578\) −16.2474 −0.675802
\(579\) −18.9293 −0.786676
\(580\) 0.422909 0.0175603
\(581\) 7.96874 0.330599
\(582\) −11.5077 −0.477009
\(583\) 4.13724 0.171347
\(584\) −2.36638 −0.0979216
\(585\) 0.340633 0.0140834
\(586\) 4.40067 0.181790
\(587\) −38.5034 −1.58920 −0.794602 0.607131i \(-0.792320\pi\)
−0.794602 + 0.607131i \(0.792320\pi\)
\(588\) 4.74240 0.195573
\(589\) −40.7960 −1.68097
\(590\) −3.59396 −0.147961
\(591\) 8.98440 0.369569
\(592\) 8.55030 0.351415
\(593\) −13.1113 −0.538416 −0.269208 0.963082i \(-0.586762\pi\)
−0.269208 + 0.963082i \(0.586762\pi\)
\(594\) 1.00000 0.0410305
\(595\) 0.799523 0.0327773
\(596\) 19.6765 0.805980
\(597\) 15.1438 0.619795
\(598\) −11.2245 −0.459004
\(599\) −34.2308 −1.39863 −0.699316 0.714813i \(-0.746512\pi\)
−0.699316 + 0.714813i \(0.746512\pi\)
\(600\) −4.92767 −0.201171
\(601\) −2.51772 −0.102700 −0.0513499 0.998681i \(-0.516352\pi\)
−0.0513499 + 0.998681i \(0.516352\pi\)
\(602\) 42.3949 1.72789
\(603\) −0.380487 −0.0154946
\(604\) 8.71508 0.354611
\(605\) 0.268945 0.0109342
\(606\) −10.6426 −0.432326
\(607\) −24.5474 −0.996349 −0.498174 0.867077i \(-0.665996\pi\)
−0.498174 + 0.867077i \(0.665996\pi\)
\(608\) 6.18750 0.250936
\(609\) 5.38842 0.218350
\(610\) −0.268945 −0.0108893
\(611\) 7.58806 0.306980
\(612\) 0.867540 0.0350682
\(613\) 25.2944 1.02163 0.510816 0.859690i \(-0.329343\pi\)
0.510816 + 0.859690i \(0.329343\pi\)
\(614\) −17.0682 −0.688818
\(615\) 0.925818 0.0373326
\(616\) 3.42672 0.138066
\(617\) 7.83562 0.315450 0.157725 0.987483i \(-0.449584\pi\)
0.157725 + 0.987483i \(0.449584\pi\)
\(618\) 1.00764 0.0405330
\(619\) 28.4337 1.14285 0.571424 0.820655i \(-0.306391\pi\)
0.571424 + 0.820655i \(0.306391\pi\)
\(620\) −1.77324 −0.0712148
\(621\) −8.86224 −0.355630
\(622\) −28.3715 −1.13759
\(623\) −39.8063 −1.59481
\(624\) 1.26655 0.0507026
\(625\) 23.9203 0.956810
\(626\) −9.88599 −0.395124
\(627\) 6.18750 0.247105
\(628\) 22.7483 0.907755
\(629\) 7.41772 0.295764
\(630\) 0.921599 0.0367174
\(631\) 13.6904 0.545006 0.272503 0.962155i \(-0.412149\pi\)
0.272503 + 0.962155i \(0.412149\pi\)
\(632\) −8.37132 −0.332993
\(633\) 25.8348 1.02684
\(634\) 5.91378 0.234866
\(635\) 5.07471 0.201384
\(636\) 4.13724 0.164052
\(637\) 6.00649 0.237986
\(638\) 1.57247 0.0622548
\(639\) −10.4281 −0.412531
\(640\) 0.268945 0.0106310
\(641\) −16.9952 −0.671271 −0.335636 0.941992i \(-0.608951\pi\)
−0.335636 + 0.941992i \(0.608951\pi\)
\(642\) −6.78676 −0.267852
\(643\) −25.4697 −1.00443 −0.502214 0.864743i \(-0.667481\pi\)
−0.502214 + 0.864743i \(0.667481\pi\)
\(644\) −30.3684 −1.19668
\(645\) 3.32735 0.131014
\(646\) 5.36790 0.211197
\(647\) −23.3764 −0.919021 −0.459510 0.888172i \(-0.651975\pi\)
−0.459510 + 0.888172i \(0.651975\pi\)
\(648\) 1.00000 0.0392837
\(649\) −13.3632 −0.524551
\(650\) −6.24115 −0.244798
\(651\) −22.5934 −0.885504
\(652\) −16.9197 −0.662628
\(653\) −14.5309 −0.568638 −0.284319 0.958730i \(-0.591767\pi\)
−0.284319 + 0.958730i \(0.591767\pi\)
\(654\) −10.9790 −0.429314
\(655\) 0.992120 0.0387654
\(656\) 3.44241 0.134403
\(657\) −2.36638 −0.0923214
\(658\) 20.5299 0.800338
\(659\) −1.83670 −0.0715475 −0.0357738 0.999360i \(-0.511390\pi\)
−0.0357738 + 0.999360i \(0.511390\pi\)
\(660\) 0.268945 0.0104687
\(661\) 27.0191 1.05092 0.525460 0.850818i \(-0.323893\pi\)
0.525460 + 0.850818i \(0.323893\pi\)
\(662\) 18.4377 0.716602
\(663\) 1.09878 0.0426732
\(664\) 2.32547 0.0902459
\(665\) 5.70239 0.221129
\(666\) 8.55030 0.331317
\(667\) −13.9356 −0.539590
\(668\) 24.5798 0.951021
\(669\) 9.89572 0.382591
\(670\) −0.102330 −0.00395336
\(671\) −1.00000 −0.0386046
\(672\) 3.42672 0.132189
\(673\) 31.5860 1.21755 0.608775 0.793343i \(-0.291661\pi\)
0.608775 + 0.793343i \(0.291661\pi\)
\(674\) 35.4326 1.36481
\(675\) −4.92767 −0.189666
\(676\) −11.3958 −0.438302
\(677\) 33.9490 1.30477 0.652384 0.757889i \(-0.273769\pi\)
0.652384 + 0.757889i \(0.273769\pi\)
\(678\) −0.304968 −0.0117122
\(679\) −39.4336 −1.51332
\(680\) 0.233320 0.00894743
\(681\) 1.05470 0.0404164
\(682\) −6.59330 −0.252470
\(683\) −5.96961 −0.228421 −0.114210 0.993457i \(-0.536434\pi\)
−0.114210 + 0.993457i \(0.536434\pi\)
\(684\) 6.18750 0.236585
\(685\) 2.27878 0.0870679
\(686\) −7.73617 −0.295368
\(687\) −6.19110 −0.236205
\(688\) 12.3719 0.471673
\(689\) 5.24003 0.199629
\(690\) −2.38346 −0.0907366
\(691\) −17.1589 −0.652757 −0.326378 0.945239i \(-0.605828\pi\)
−0.326378 + 0.945239i \(0.605828\pi\)
\(692\) 16.0917 0.611715
\(693\) 3.42672 0.130170
\(694\) 32.0180 1.21538
\(695\) 3.87043 0.146814
\(696\) 1.57247 0.0596045
\(697\) 2.98642 0.113119
\(698\) 0.763609 0.0289030
\(699\) −28.9847 −1.09630
\(700\) −16.8857 −0.638221
\(701\) −23.4422 −0.885399 −0.442699 0.896670i \(-0.645979\pi\)
−0.442699 + 0.896670i \(0.645979\pi\)
\(702\) 1.26655 0.0478029
\(703\) 52.9049 1.99535
\(704\) 1.00000 0.0376889
\(705\) 1.61128 0.0606844
\(706\) 16.4468 0.618984
\(707\) −36.4692 −1.37156
\(708\) −13.3632 −0.502220
\(709\) −12.4098 −0.466061 −0.233030 0.972469i \(-0.574864\pi\)
−0.233030 + 0.972469i \(0.574864\pi\)
\(710\) −2.80460 −0.105255
\(711\) −8.37132 −0.313949
\(712\) −11.6165 −0.435345
\(713\) 58.4314 2.18827
\(714\) 2.97281 0.111255
\(715\) 0.340633 0.0127389
\(716\) −20.5271 −0.767133
\(717\) −4.63720 −0.173179
\(718\) 19.7050 0.735385
\(719\) 5.73145 0.213747 0.106874 0.994273i \(-0.465916\pi\)
0.106874 + 0.994273i \(0.465916\pi\)
\(720\) 0.268945 0.0100230
\(721\) 3.45288 0.128592
\(722\) 19.2851 0.717719
\(723\) 13.8531 0.515201
\(724\) −14.6239 −0.543494
\(725\) −7.74863 −0.287777
\(726\) 1.00000 0.0371135
\(727\) −38.7317 −1.43648 −0.718240 0.695795i \(-0.755052\pi\)
−0.718240 + 0.695795i \(0.755052\pi\)
\(728\) 4.34011 0.160855
\(729\) 1.00000 0.0370370
\(730\) −0.636427 −0.0235552
\(731\) 10.7331 0.396977
\(732\) −1.00000 −0.0369611
\(733\) 30.5487 1.12834 0.564171 0.825658i \(-0.309196\pi\)
0.564171 + 0.825658i \(0.309196\pi\)
\(734\) −20.4095 −0.753329
\(735\) 1.27544 0.0470454
\(736\) −8.86224 −0.326667
\(737\) −0.380487 −0.0140154
\(738\) 3.44241 0.126717
\(739\) 13.3787 0.492142 0.246071 0.969252i \(-0.420860\pi\)
0.246071 + 0.969252i \(0.420860\pi\)
\(740\) 2.29956 0.0845335
\(741\) 7.83679 0.287892
\(742\) 14.1772 0.520460
\(743\) 41.2178 1.51213 0.756067 0.654494i \(-0.227118\pi\)
0.756067 + 0.654494i \(0.227118\pi\)
\(744\) −6.59330 −0.241722
\(745\) 5.29189 0.193880
\(746\) −35.9190 −1.31509
\(747\) 2.32547 0.0850846
\(748\) 0.867540 0.0317204
\(749\) −23.2563 −0.849768
\(750\) −2.67000 −0.0974945
\(751\) 17.5229 0.639420 0.319710 0.947515i \(-0.396414\pi\)
0.319710 + 0.947515i \(0.396414\pi\)
\(752\) 5.99112 0.218474
\(753\) −8.63040 −0.314509
\(754\) 1.99162 0.0725305
\(755\) 2.34388 0.0853024
\(756\) 3.42672 0.124629
\(757\) −17.5737 −0.638726 −0.319363 0.947632i \(-0.603469\pi\)
−0.319363 + 0.947632i \(0.603469\pi\)
\(758\) 29.2039 1.06073
\(759\) −8.86224 −0.321679
\(760\) 1.66410 0.0603631
\(761\) −41.5905 −1.50765 −0.753827 0.657073i \(-0.771794\pi\)
−0.753827 + 0.657073i \(0.771794\pi\)
\(762\) 18.8689 0.683550
\(763\) −37.6220 −1.36201
\(764\) −5.11491 −0.185051
\(765\) 0.233320 0.00843572
\(766\) −30.2591 −1.09330
\(767\) −16.9252 −0.611133
\(768\) 1.00000 0.0360844
\(769\) 22.8539 0.824132 0.412066 0.911154i \(-0.364807\pi\)
0.412066 + 0.911154i \(0.364807\pi\)
\(770\) 0.921599 0.0332121
\(771\) 1.33011 0.0479028
\(772\) −18.9293 −0.681281
\(773\) −47.8479 −1.72097 −0.860485 0.509476i \(-0.829839\pi\)
−0.860485 + 0.509476i \(0.829839\pi\)
\(774\) 12.3719 0.444697
\(775\) 32.4896 1.16706
\(776\) −11.5077 −0.413102
\(777\) 29.2995 1.05111
\(778\) −6.13420 −0.219922
\(779\) 21.2999 0.763148
\(780\) 0.340633 0.0121966
\(781\) −10.4281 −0.373148
\(782\) −7.68835 −0.274935
\(783\) 1.57247 0.0561956
\(784\) 4.74240 0.169371
\(785\) 6.11803 0.218362
\(786\) 3.68893 0.131580
\(787\) 6.39840 0.228078 0.114039 0.993476i \(-0.463621\pi\)
0.114039 + 0.993476i \(0.463621\pi\)
\(788\) 8.98440 0.320056
\(789\) −29.1042 −1.03614
\(790\) −2.25142 −0.0801021
\(791\) −1.04504 −0.0371573
\(792\) 1.00000 0.0355335
\(793\) −1.26655 −0.0449766
\(794\) 7.09173 0.251676
\(795\) 1.11269 0.0394630
\(796\) 15.1438 0.536758
\(797\) 23.0083 0.814996 0.407498 0.913206i \(-0.366401\pi\)
0.407498 + 0.913206i \(0.366401\pi\)
\(798\) 21.2028 0.750571
\(799\) 5.19753 0.183875
\(800\) −4.92767 −0.174219
\(801\) −11.6165 −0.410447
\(802\) −29.9023 −1.05589
\(803\) −2.36638 −0.0835079
\(804\) −0.380487 −0.0134188
\(805\) −8.16743 −0.287864
\(806\) −8.35075 −0.294143
\(807\) −2.29032 −0.0806229
\(808\) −10.6426 −0.374405
\(809\) 23.5409 0.827653 0.413827 0.910356i \(-0.364192\pi\)
0.413827 + 0.910356i \(0.364192\pi\)
\(810\) 0.268945 0.00944976
\(811\) 13.2119 0.463932 0.231966 0.972724i \(-0.425484\pi\)
0.231966 + 0.972724i \(0.425484\pi\)
\(812\) 5.38842 0.189097
\(813\) −23.4290 −0.821690
\(814\) 8.55030 0.299688
\(815\) −4.55048 −0.159396
\(816\) 0.867540 0.0303700
\(817\) 76.5509 2.67818
\(818\) −31.4377 −1.09919
\(819\) 4.34011 0.151656
\(820\) 0.925818 0.0323310
\(821\) 17.7547 0.619643 0.309821 0.950795i \(-0.399731\pi\)
0.309821 + 0.950795i \(0.399731\pi\)
\(822\) 8.47305 0.295531
\(823\) 32.3631 1.12811 0.564054 0.825738i \(-0.309241\pi\)
0.564054 + 0.825738i \(0.309241\pi\)
\(824\) 1.00764 0.0351026
\(825\) −4.92767 −0.171559
\(826\) −45.7919 −1.59330
\(827\) −40.4152 −1.40537 −0.702686 0.711500i \(-0.748016\pi\)
−0.702686 + 0.711500i \(0.748016\pi\)
\(828\) −8.86224 −0.307984
\(829\) 22.9984 0.798767 0.399384 0.916784i \(-0.369224\pi\)
0.399384 + 0.916784i \(0.369224\pi\)
\(830\) 0.625425 0.0217088
\(831\) 18.8839 0.655076
\(832\) 1.26655 0.0439098
\(833\) 4.11422 0.142549
\(834\) 14.3911 0.498325
\(835\) 6.61062 0.228770
\(836\) 6.18750 0.213999
\(837\) −6.59330 −0.227898
\(838\) −6.06492 −0.209509
\(839\) −1.45169 −0.0501179 −0.0250589 0.999686i \(-0.507977\pi\)
−0.0250589 + 0.999686i \(0.507977\pi\)
\(840\) 0.921599 0.0317982
\(841\) −26.5273 −0.914735
\(842\) −11.9703 −0.412524
\(843\) −10.0216 −0.345163
\(844\) 25.8348 0.889271
\(845\) −3.06486 −0.105434
\(846\) 5.99112 0.205979
\(847\) 3.42672 0.117743
\(848\) 4.13724 0.142073
\(849\) 2.41609 0.0829200
\(850\) −4.27495 −0.146629
\(851\) −75.7748 −2.59753
\(852\) −10.4281 −0.357262
\(853\) 42.6983 1.46196 0.730981 0.682398i \(-0.239063\pi\)
0.730981 + 0.682398i \(0.239063\pi\)
\(854\) −3.42672 −0.117260
\(855\) 1.66410 0.0569109
\(856\) −6.78676 −0.231967
\(857\) −4.02296 −0.137422 −0.0687108 0.997637i \(-0.521889\pi\)
−0.0687108 + 0.997637i \(0.521889\pi\)
\(858\) 1.26655 0.0432394
\(859\) −11.2054 −0.382323 −0.191162 0.981559i \(-0.561225\pi\)
−0.191162 + 0.981559i \(0.561225\pi\)
\(860\) 3.32735 0.113462
\(861\) 11.7962 0.402012
\(862\) 4.23679 0.144306
\(863\) −38.2809 −1.30310 −0.651548 0.758607i \(-0.725880\pi\)
−0.651548 + 0.758607i \(0.725880\pi\)
\(864\) 1.00000 0.0340207
\(865\) 4.32779 0.147149
\(866\) −12.6590 −0.430170
\(867\) −16.2474 −0.551790
\(868\) −22.5934 −0.766869
\(869\) −8.37132 −0.283978
\(870\) 0.422909 0.0143380
\(871\) −0.481907 −0.0163288
\(872\) −10.9790 −0.371797
\(873\) −11.5077 −0.389476
\(874\) −54.8351 −1.85483
\(875\) −9.14933 −0.309304
\(876\) −2.36638 −0.0799527
\(877\) 14.9533 0.504937 0.252468 0.967605i \(-0.418758\pi\)
0.252468 + 0.967605i \(0.418758\pi\)
\(878\) −26.5844 −0.897181
\(879\) 4.40067 0.148431
\(880\) 0.268945 0.00906613
\(881\) −13.4894 −0.454469 −0.227234 0.973840i \(-0.572968\pi\)
−0.227234 + 0.973840i \(0.572968\pi\)
\(882\) 4.74240 0.159685
\(883\) −53.1259 −1.78783 −0.893915 0.448236i \(-0.852052\pi\)
−0.893915 + 0.448236i \(0.852052\pi\)
\(884\) 1.09878 0.0369561
\(885\) −3.59396 −0.120810
\(886\) 26.5443 0.891773
\(887\) 33.1287 1.11235 0.556176 0.831065i \(-0.312268\pi\)
0.556176 + 0.831065i \(0.312268\pi\)
\(888\) 8.55030 0.286929
\(889\) 64.6586 2.16858
\(890\) −3.12419 −0.104723
\(891\) 1.00000 0.0335013
\(892\) 9.89572 0.331333
\(893\) 37.0700 1.24050
\(894\) 19.6765 0.658080
\(895\) −5.52066 −0.184535
\(896\) 3.42672 0.114479
\(897\) −11.2245 −0.374775
\(898\) 33.4432 1.11601
\(899\) −10.3678 −0.345785
\(900\) −4.92767 −0.164256
\(901\) 3.58922 0.119574
\(902\) 3.44241 0.114620
\(903\) 42.3949 1.41081
\(904\) −0.304968 −0.0101431
\(905\) −3.93303 −0.130738
\(906\) 8.71508 0.289539
\(907\) 35.6391 1.18338 0.591688 0.806167i \(-0.298462\pi\)
0.591688 + 0.806167i \(0.298462\pi\)
\(908\) 1.05470 0.0350016
\(909\) −10.6426 −0.352993
\(910\) 1.16725 0.0386940
\(911\) −40.8527 −1.35351 −0.676755 0.736208i \(-0.736614\pi\)
−0.676755 + 0.736208i \(0.736614\pi\)
\(912\) 6.18750 0.204889
\(913\) 2.32547 0.0769619
\(914\) −39.3979 −1.30317
\(915\) −0.268945 −0.00889105
\(916\) −6.19110 −0.204560
\(917\) 12.6409 0.417440
\(918\) 0.867540 0.0286331
\(919\) −6.75599 −0.222860 −0.111430 0.993772i \(-0.535543\pi\)
−0.111430 + 0.993772i \(0.535543\pi\)
\(920\) −2.38346 −0.0785802
\(921\) −17.0682 −0.562418
\(922\) 2.36247 0.0778037
\(923\) −13.2078 −0.434739
\(924\) 3.42672 0.112731
\(925\) −42.1330 −1.38533
\(926\) 29.4582 0.968057
\(927\) 1.00764 0.0330951
\(928\) 1.57247 0.0516190
\(929\) −30.3584 −0.996026 −0.498013 0.867170i \(-0.665937\pi\)
−0.498013 + 0.867170i \(0.665937\pi\)
\(930\) −1.77324 −0.0581467
\(931\) 29.3436 0.961697
\(932\) −28.9847 −0.949426
\(933\) −28.3715 −0.928841
\(934\) −1.97701 −0.0646896
\(935\) 0.233320 0.00763040
\(936\) 1.26655 0.0413985
\(937\) −7.42112 −0.242437 −0.121219 0.992626i \(-0.538680\pi\)
−0.121219 + 0.992626i \(0.538680\pi\)
\(938\) −1.30382 −0.0425713
\(939\) −9.88599 −0.322617
\(940\) 1.61128 0.0525542
\(941\) −36.7139 −1.19684 −0.598419 0.801183i \(-0.704204\pi\)
−0.598419 + 0.801183i \(0.704204\pi\)
\(942\) 22.7483 0.741179
\(943\) −30.5075 −0.993459
\(944\) −13.3632 −0.434935
\(945\) 0.921599 0.0299796
\(946\) 12.3719 0.402244
\(947\) 27.1926 0.883641 0.441821 0.897103i \(-0.354333\pi\)
0.441821 + 0.897103i \(0.354333\pi\)
\(948\) −8.37132 −0.271888
\(949\) −2.99715 −0.0972915
\(950\) −30.4899 −0.989224
\(951\) 5.91378 0.191767
\(952\) 2.97281 0.0963494
\(953\) −11.2829 −0.365488 −0.182744 0.983161i \(-0.558498\pi\)
−0.182744 + 0.983161i \(0.558498\pi\)
\(954\) 4.13724 0.133948
\(955\) −1.37563 −0.0445144
\(956\) −4.63720 −0.149978
\(957\) 1.57247 0.0508309
\(958\) −26.1584 −0.845140
\(959\) 29.0347 0.937581
\(960\) 0.268945 0.00868016
\(961\) 12.4716 0.402309
\(962\) 10.8294 0.349154
\(963\) −6.78676 −0.218700
\(964\) 13.8531 0.446177
\(965\) −5.09095 −0.163883
\(966\) −30.3684 −0.977088
\(967\) 47.9113 1.54072 0.770361 0.637608i \(-0.220076\pi\)
0.770361 + 0.637608i \(0.220076\pi\)
\(968\) 1.00000 0.0321412
\(969\) 5.36790 0.172442
\(970\) −3.09494 −0.0993724
\(971\) 27.4932 0.882298 0.441149 0.897434i \(-0.354571\pi\)
0.441149 + 0.897434i \(0.354571\pi\)
\(972\) 1.00000 0.0320750
\(973\) 49.3144 1.58095
\(974\) −28.6097 −0.916715
\(975\) −6.24115 −0.199877
\(976\) −1.00000 −0.0320092
\(977\) 7.09610 0.227024 0.113512 0.993537i \(-0.463790\pi\)
0.113512 + 0.993537i \(0.463790\pi\)
\(978\) −16.9197 −0.541034
\(979\) −11.6165 −0.371263
\(980\) 1.27544 0.0407426
\(981\) −10.9790 −0.350533
\(982\) −12.1722 −0.388429
\(983\) 49.9351 1.59268 0.796342 0.604847i \(-0.206766\pi\)
0.796342 + 0.604847i \(0.206766\pi\)
\(984\) 3.44241 0.109740
\(985\) 2.41631 0.0769901
\(986\) 1.36418 0.0434445
\(987\) 20.5299 0.653473
\(988\) 7.83679 0.249321
\(989\) −109.642 −3.48643
\(990\) 0.268945 0.00854763
\(991\) 25.0878 0.796942 0.398471 0.917181i \(-0.369541\pi\)
0.398471 + 0.917181i \(0.369541\pi\)
\(992\) −6.59330 −0.209337
\(993\) 18.4377 0.585103
\(994\) −35.7343 −1.13342
\(995\) 4.07286 0.129118
\(996\) 2.32547 0.0736855
\(997\) 55.0312 1.74285 0.871427 0.490525i \(-0.163195\pi\)
0.871427 + 0.490525i \(0.163195\pi\)
\(998\) −18.9089 −0.598552
\(999\) 8.55030 0.270519
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 \(a_p\))