Properties

Label 6010.2.a.c.1.3
Level 6010
Weight 2
Character 6010.1
Self dual Yes
Analytic conductor 47.990
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6010 = 2 \cdot 5 \cdot 601 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9900916148\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
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 1.3
Root \(-1.28136\)
Character \(\chi\) = 6010.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.28136 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-2.28136 q^{6}\) \(+1.99437 q^{7}\) \(+1.00000 q^{8}\) \(+2.20462 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.28136 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-2.28136 q^{6}\) \(+1.99437 q^{7}\) \(+1.00000 q^{8}\) \(+2.20462 q^{9}\) \(+1.00000 q^{10}\) \(+1.87428 q^{11}\) \(-2.28136 q^{12}\) \(-4.38275 q^{13}\) \(+1.99437 q^{14}\) \(-2.28136 q^{15}\) \(+1.00000 q^{16}\) \(-2.44884 q^{17}\) \(+2.20462 q^{18}\) \(-5.14004 q^{19}\) \(+1.00000 q^{20}\) \(-4.54988 q^{21}\) \(+1.87428 q^{22}\) \(+5.32780 q^{23}\) \(-2.28136 q^{24}\) \(+1.00000 q^{25}\) \(-4.38275 q^{26}\) \(+1.81455 q^{27}\) \(+1.99437 q^{28}\) \(+8.18089 q^{29}\) \(-2.28136 q^{30}\) \(-9.68099 q^{31}\) \(+1.00000 q^{32}\) \(-4.27591 q^{33}\) \(-2.44884 q^{34}\) \(+1.99437 q^{35}\) \(+2.20462 q^{36}\) \(-4.69319 q^{37}\) \(-5.14004 q^{38}\) \(+9.99864 q^{39}\) \(+1.00000 q^{40}\) \(-2.34952 q^{41}\) \(-4.54988 q^{42}\) \(-9.31769 q^{43}\) \(+1.87428 q^{44}\) \(+2.20462 q^{45}\) \(+5.32780 q^{46}\) \(-1.00015 q^{47}\) \(-2.28136 q^{48}\) \(-3.02249 q^{49}\) \(+1.00000 q^{50}\) \(+5.58669 q^{51}\) \(-4.38275 q^{52}\) \(-3.26390 q^{53}\) \(+1.81455 q^{54}\) \(+1.87428 q^{55}\) \(+1.99437 q^{56}\) \(+11.7263 q^{57}\) \(+8.18089 q^{58}\) \(-2.78044 q^{59}\) \(-2.28136 q^{60}\) \(-0.527106 q^{61}\) \(-9.68099 q^{62}\) \(+4.39683 q^{63}\) \(+1.00000 q^{64}\) \(-4.38275 q^{65}\) \(-4.27591 q^{66}\) \(+6.25111 q^{67}\) \(-2.44884 q^{68}\) \(-12.1546 q^{69}\) \(+1.99437 q^{70}\) \(-12.4228 q^{71}\) \(+2.20462 q^{72}\) \(-9.22198 q^{73}\) \(-4.69319 q^{74}\) \(-2.28136 q^{75}\) \(-5.14004 q^{76}\) \(+3.73801 q^{77}\) \(+9.99864 q^{78}\) \(-4.06354 q^{79}\) \(+1.00000 q^{80}\) \(-10.7535 q^{81}\) \(-2.34952 q^{82}\) \(+10.7147 q^{83}\) \(-4.54988 q^{84}\) \(-2.44884 q^{85}\) \(-9.31769 q^{86}\) \(-18.6636 q^{87}\) \(+1.87428 q^{88}\) \(+1.69710 q^{89}\) \(+2.20462 q^{90}\) \(-8.74082 q^{91}\) \(+5.32780 q^{92}\) \(+22.0859 q^{93}\) \(-1.00015 q^{94}\) \(-5.14004 q^{95}\) \(-2.28136 q^{96}\) \(+13.8088 q^{97}\) \(-3.02249 q^{98}\) \(+4.13207 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut +\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 8q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 16q^{8} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 20q^{13} \) \(\mathstrut -\mathstrut 10q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut -\mathstrut 27q^{17} \) \(\mathstrut -\mathstrut 2q^{18} \) \(\mathstrut -\mathstrut 17q^{19} \) \(\mathstrut +\mathstrut 16q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 14q^{22} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut -\mathstrut 8q^{24} \) \(\mathstrut +\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 20q^{26} \) \(\mathstrut -\mathstrut 11q^{27} \) \(\mathstrut -\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 16q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut -\mathstrut 27q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 17q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut -\mathstrut 35q^{41} \) \(\mathstrut -\mathstrut 12q^{42} \) \(\mathstrut +\mathstrut 3q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 9q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut -\mathstrut 24q^{49} \) \(\mathstrut +\mathstrut 16q^{50} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut -\mathstrut 20q^{52} \) \(\mathstrut -\mathstrut 39q^{53} \) \(\mathstrut -\mathstrut 11q^{54} \) \(\mathstrut -\mathstrut 14q^{55} \) \(\mathstrut -\mathstrut 10q^{56} \) \(\mathstrut -\mathstrut 6q^{57} \) \(\mathstrut -\mathstrut 23q^{58} \) \(\mathstrut -\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 21q^{62} \) \(\mathstrut +\mathstrut q^{63} \) \(\mathstrut +\mathstrut 16q^{64} \) \(\mathstrut -\mathstrut 20q^{65} \) \(\mathstrut -\mathstrut 9q^{66} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 27q^{68} \) \(\mathstrut -\mathstrut 25q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut -\mathstrut 2q^{72} \) \(\mathstrut -\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 17q^{76} \) \(\mathstrut -\mathstrut 34q^{77} \) \(\mathstrut -\mathstrut 6q^{78} \) \(\mathstrut -\mathstrut 40q^{79} \) \(\mathstrut +\mathstrut 16q^{80} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut -\mathstrut 35q^{82} \) \(\mathstrut -\mathstrut 22q^{83} \) \(\mathstrut -\mathstrut 12q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut +\mathstrut 3q^{86} \) \(\mathstrut +\mathstrut 10q^{87} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut q^{91} \) \(\mathstrut -\mathstrut 9q^{92} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut -\mathstrut 25q^{94} \) \(\mathstrut -\mathstrut 17q^{95} \) \(\mathstrut -\mathstrut 8q^{96} \) \(\mathstrut -\mathstrut 21q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.28136 −1.31715 −0.658573 0.752517i \(-0.728840\pi\)
−0.658573 + 0.752517i \(0.728840\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −2.28136 −0.931363
\(7\) 1.99437 0.753801 0.376901 0.926254i \(-0.376990\pi\)
0.376901 + 0.926254i \(0.376990\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.20462 0.734873
\(10\) 1.00000 0.316228
\(11\) 1.87428 0.565116 0.282558 0.959250i \(-0.408817\pi\)
0.282558 + 0.959250i \(0.408817\pi\)
\(12\) −2.28136 −0.658573
\(13\) −4.38275 −1.21556 −0.607778 0.794107i \(-0.707939\pi\)
−0.607778 + 0.794107i \(0.707939\pi\)
\(14\) 1.99437 0.533018
\(15\) −2.28136 −0.589046
\(16\) 1.00000 0.250000
\(17\) −2.44884 −0.593931 −0.296965 0.954888i \(-0.595975\pi\)
−0.296965 + 0.954888i \(0.595975\pi\)
\(18\) 2.20462 0.519634
\(19\) −5.14004 −1.17921 −0.589603 0.807693i \(-0.700716\pi\)
−0.589603 + 0.807693i \(0.700716\pi\)
\(20\) 1.00000 0.223607
\(21\) −4.54988 −0.992866
\(22\) 1.87428 0.399598
\(23\) 5.32780 1.11092 0.555462 0.831542i \(-0.312542\pi\)
0.555462 + 0.831542i \(0.312542\pi\)
\(24\) −2.28136 −0.465681
\(25\) 1.00000 0.200000
\(26\) −4.38275 −0.859528
\(27\) 1.81455 0.349210
\(28\) 1.99437 0.376901
\(29\) 8.18089 1.51915 0.759576 0.650418i \(-0.225406\pi\)
0.759576 + 0.650418i \(0.225406\pi\)
\(30\) −2.28136 −0.416518
\(31\) −9.68099 −1.73876 −0.869379 0.494146i \(-0.835481\pi\)
−0.869379 + 0.494146i \(0.835481\pi\)
\(32\) 1.00000 0.176777
\(33\) −4.27591 −0.744341
\(34\) −2.44884 −0.419973
\(35\) 1.99437 0.337110
\(36\) 2.20462 0.367437
\(37\) −4.69319 −0.771556 −0.385778 0.922592i \(-0.626067\pi\)
−0.385778 + 0.922592i \(0.626067\pi\)
\(38\) −5.14004 −0.833825
\(39\) 9.99864 1.60106
\(40\) 1.00000 0.158114
\(41\) −2.34952 −0.366934 −0.183467 0.983026i \(-0.558732\pi\)
−0.183467 + 0.983026i \(0.558732\pi\)
\(42\) −4.54988 −0.702062
\(43\) −9.31769 −1.42093 −0.710467 0.703731i \(-0.751516\pi\)
−0.710467 + 0.703731i \(0.751516\pi\)
\(44\) 1.87428 0.282558
\(45\) 2.20462 0.328645
\(46\) 5.32780 0.785541
\(47\) −1.00015 −0.145887 −0.0729436 0.997336i \(-0.523239\pi\)
−0.0729436 + 0.997336i \(0.523239\pi\)
\(48\) −2.28136 −0.329286
\(49\) −3.02249 −0.431784
\(50\) 1.00000 0.141421
\(51\) 5.58669 0.782294
\(52\) −4.38275 −0.607778
\(53\) −3.26390 −0.448331 −0.224165 0.974551i \(-0.571966\pi\)
−0.224165 + 0.974551i \(0.571966\pi\)
\(54\) 1.81455 0.246929
\(55\) 1.87428 0.252728
\(56\) 1.99437 0.266509
\(57\) 11.7263 1.55319
\(58\) 8.18089 1.07420
\(59\) −2.78044 −0.361983 −0.180991 0.983485i \(-0.557931\pi\)
−0.180991 + 0.983485i \(0.557931\pi\)
\(60\) −2.28136 −0.294523
\(61\) −0.527106 −0.0674890 −0.0337445 0.999430i \(-0.510743\pi\)
−0.0337445 + 0.999430i \(0.510743\pi\)
\(62\) −9.68099 −1.22949
\(63\) 4.39683 0.553948
\(64\) 1.00000 0.125000
\(65\) −4.38275 −0.543613
\(66\) −4.27591 −0.526328
\(67\) 6.25111 0.763695 0.381848 0.924225i \(-0.375288\pi\)
0.381848 + 0.924225i \(0.375288\pi\)
\(68\) −2.44884 −0.296965
\(69\) −12.1546 −1.46325
\(70\) 1.99437 0.238373
\(71\) −12.4228 −1.47432 −0.737158 0.675721i \(-0.763832\pi\)
−0.737158 + 0.675721i \(0.763832\pi\)
\(72\) 2.20462 0.259817
\(73\) −9.22198 −1.07935 −0.539675 0.841873i \(-0.681453\pi\)
−0.539675 + 0.841873i \(0.681453\pi\)
\(74\) −4.69319 −0.545573
\(75\) −2.28136 −0.263429
\(76\) −5.14004 −0.589603
\(77\) 3.73801 0.425985
\(78\) 9.99864 1.13212
\(79\) −4.06354 −0.457184 −0.228592 0.973522i \(-0.573412\pi\)
−0.228592 + 0.973522i \(0.573412\pi\)
\(80\) 1.00000 0.111803
\(81\) −10.7535 −1.19483
\(82\) −2.34952 −0.259461
\(83\) 10.7147 1.17610 0.588048 0.808826i \(-0.299897\pi\)
0.588048 + 0.808826i \(0.299897\pi\)
\(84\) −4.54988 −0.496433
\(85\) −2.44884 −0.265614
\(86\) −9.31769 −1.00475
\(87\) −18.6636 −2.00095
\(88\) 1.87428 0.199799
\(89\) 1.69710 0.179892 0.0899461 0.995947i \(-0.471331\pi\)
0.0899461 + 0.995947i \(0.471331\pi\)
\(90\) 2.20462 0.232387
\(91\) −8.74082 −0.916287
\(92\) 5.32780 0.555462
\(93\) 22.0859 2.29020
\(94\) −1.00015 −0.103158
\(95\) −5.14004 −0.527357
\(96\) −2.28136 −0.232841
\(97\) 13.8088 1.40208 0.701038 0.713124i \(-0.252720\pi\)
0.701038 + 0.713124i \(0.252720\pi\)
\(98\) −3.02249 −0.305317
\(99\) 4.13207 0.415289
\(100\) 1.00000 0.100000
\(101\) −1.36351 −0.135675 −0.0678374 0.997696i \(-0.521610\pi\)
−0.0678374 + 0.997696i \(0.521610\pi\)
\(102\) 5.58669 0.553165
\(103\) −6.73160 −0.663284 −0.331642 0.943405i \(-0.607603\pi\)
−0.331642 + 0.943405i \(0.607603\pi\)
\(104\) −4.38275 −0.429764
\(105\) −4.54988 −0.444023
\(106\) −3.26390 −0.317018
\(107\) −1.21947 −0.117890 −0.0589452 0.998261i \(-0.518774\pi\)
−0.0589452 + 0.998261i \(0.518774\pi\)
\(108\) 1.81455 0.174605
\(109\) 7.55973 0.724091 0.362046 0.932160i \(-0.382078\pi\)
0.362046 + 0.932160i \(0.382078\pi\)
\(110\) 1.87428 0.178705
\(111\) 10.7069 1.01625
\(112\) 1.99437 0.188450
\(113\) 16.9666 1.59608 0.798042 0.602602i \(-0.205869\pi\)
0.798042 + 0.602602i \(0.205869\pi\)
\(114\) 11.7263 1.09827
\(115\) 5.32780 0.496820
\(116\) 8.18089 0.759576
\(117\) −9.66230 −0.893280
\(118\) −2.78044 −0.255961
\(119\) −4.88389 −0.447706
\(120\) −2.28136 −0.208259
\(121\) −7.48708 −0.680644
\(122\) −0.527106 −0.0477219
\(123\) 5.36011 0.483305
\(124\) −9.68099 −0.869379
\(125\) 1.00000 0.0894427
\(126\) 4.39683 0.391701
\(127\) −6.40287 −0.568163 −0.284081 0.958800i \(-0.591689\pi\)
−0.284081 + 0.958800i \(0.591689\pi\)
\(128\) 1.00000 0.0883883
\(129\) 21.2570 1.87158
\(130\) −4.38275 −0.384392
\(131\) 7.53069 0.657959 0.328980 0.944337i \(-0.393295\pi\)
0.328980 + 0.944337i \(0.393295\pi\)
\(132\) −4.27591 −0.372170
\(133\) −10.2511 −0.888887
\(134\) 6.25111 0.540014
\(135\) 1.81455 0.156172
\(136\) −2.44884 −0.209986
\(137\) 17.6455 1.50755 0.753777 0.657130i \(-0.228230\pi\)
0.753777 + 0.657130i \(0.228230\pi\)
\(138\) −12.1546 −1.03467
\(139\) −11.7390 −0.995692 −0.497846 0.867265i \(-0.665875\pi\)
−0.497846 + 0.867265i \(0.665875\pi\)
\(140\) 1.99437 0.168555
\(141\) 2.28171 0.192155
\(142\) −12.4228 −1.04250
\(143\) −8.21449 −0.686930
\(144\) 2.20462 0.183718
\(145\) 8.18089 0.679386
\(146\) −9.22198 −0.763216
\(147\) 6.89540 0.568723
\(148\) −4.69319 −0.385778
\(149\) −7.41774 −0.607685 −0.303842 0.952722i \(-0.598270\pi\)
−0.303842 + 0.952722i \(0.598270\pi\)
\(150\) −2.28136 −0.186273
\(151\) −13.2359 −1.07712 −0.538562 0.842586i \(-0.681032\pi\)
−0.538562 + 0.842586i \(0.681032\pi\)
\(152\) −5.14004 −0.416913
\(153\) −5.39876 −0.436464
\(154\) 3.73801 0.301217
\(155\) −9.68099 −0.777596
\(156\) 9.99864 0.800532
\(157\) −11.5379 −0.920822 −0.460411 0.887706i \(-0.652298\pi\)
−0.460411 + 0.887706i \(0.652298\pi\)
\(158\) −4.06354 −0.323278
\(159\) 7.44614 0.590517
\(160\) 1.00000 0.0790569
\(161\) 10.6256 0.837415
\(162\) −10.7535 −0.844876
\(163\) 6.06917 0.475374 0.237687 0.971342i \(-0.423611\pi\)
0.237687 + 0.971342i \(0.423611\pi\)
\(164\) −2.34952 −0.183467
\(165\) −4.27591 −0.332879
\(166\) 10.7147 0.831625
\(167\) 13.6921 1.05953 0.529765 0.848145i \(-0.322280\pi\)
0.529765 + 0.848145i \(0.322280\pi\)
\(168\) −4.54988 −0.351031
\(169\) 6.20849 0.477576
\(170\) −2.44884 −0.187817
\(171\) −11.3318 −0.866568
\(172\) −9.31769 −0.710467
\(173\) −19.4834 −1.48130 −0.740648 0.671893i \(-0.765481\pi\)
−0.740648 + 0.671893i \(0.765481\pi\)
\(174\) −18.6636 −1.41488
\(175\) 1.99437 0.150760
\(176\) 1.87428 0.141279
\(177\) 6.34320 0.476784
\(178\) 1.69710 0.127203
\(179\) 7.94386 0.593752 0.296876 0.954916i \(-0.404055\pi\)
0.296876 + 0.954916i \(0.404055\pi\)
\(180\) 2.20462 0.164323
\(181\) −12.1441 −0.902660 −0.451330 0.892357i \(-0.649050\pi\)
−0.451330 + 0.892357i \(0.649050\pi\)
\(182\) −8.74082 −0.647913
\(183\) 1.20252 0.0888928
\(184\) 5.32780 0.392771
\(185\) −4.69319 −0.345051
\(186\) 22.0859 1.61941
\(187\) −4.58981 −0.335640
\(188\) −1.00015 −0.0729436
\(189\) 3.61888 0.263235
\(190\) −5.14004 −0.372898
\(191\) 21.8649 1.58209 0.791045 0.611758i \(-0.209537\pi\)
0.791045 + 0.611758i \(0.209537\pi\)
\(192\) −2.28136 −0.164643
\(193\) −25.8490 −1.86065 −0.930324 0.366738i \(-0.880475\pi\)
−0.930324 + 0.366738i \(0.880475\pi\)
\(194\) 13.8088 0.991418
\(195\) 9.99864 0.716018
\(196\) −3.02249 −0.215892
\(197\) −7.50208 −0.534501 −0.267250 0.963627i \(-0.586115\pi\)
−0.267250 + 0.963627i \(0.586115\pi\)
\(198\) 4.13207 0.293654
\(199\) 1.81387 0.128582 0.0642908 0.997931i \(-0.479521\pi\)
0.0642908 + 0.997931i \(0.479521\pi\)
\(200\) 1.00000 0.0707107
\(201\) −14.2611 −1.00590
\(202\) −1.36351 −0.0959365
\(203\) 16.3157 1.14514
\(204\) 5.58669 0.391147
\(205\) −2.34952 −0.164098
\(206\) −6.73160 −0.469013
\(207\) 11.7458 0.816388
\(208\) −4.38275 −0.303889
\(209\) −9.63387 −0.666389
\(210\) −4.54988 −0.313972
\(211\) 12.3024 0.846931 0.423466 0.905912i \(-0.360813\pi\)
0.423466 + 0.905912i \(0.360813\pi\)
\(212\) −3.26390 −0.224165
\(213\) 28.3409 1.94189
\(214\) −1.21947 −0.0833611
\(215\) −9.31769 −0.635461
\(216\) 1.81455 0.123465
\(217\) −19.3075 −1.31068
\(218\) 7.55973 0.512010
\(219\) 21.0387 1.42166
\(220\) 1.87428 0.126364
\(221\) 10.7326 0.721956
\(222\) 10.7069 0.718599
\(223\) −5.44946 −0.364923 −0.182461 0.983213i \(-0.558406\pi\)
−0.182461 + 0.983213i \(0.558406\pi\)
\(224\) 1.99437 0.133254
\(225\) 2.20462 0.146975
\(226\) 16.9666 1.12860
\(227\) −17.8644 −1.18570 −0.592852 0.805311i \(-0.701998\pi\)
−0.592852 + 0.805311i \(0.701998\pi\)
\(228\) 11.7263 0.776594
\(229\) −13.3168 −0.879996 −0.439998 0.897999i \(-0.645021\pi\)
−0.439998 + 0.897999i \(0.645021\pi\)
\(230\) 5.32780 0.351305
\(231\) −8.52775 −0.561085
\(232\) 8.18089 0.537101
\(233\) −4.00562 −0.262417 −0.131209 0.991355i \(-0.541886\pi\)
−0.131209 + 0.991355i \(0.541886\pi\)
\(234\) −9.66230 −0.631644
\(235\) −1.00015 −0.0652427
\(236\) −2.78044 −0.180991
\(237\) 9.27042 0.602179
\(238\) −4.88389 −0.316576
\(239\) 10.2326 0.661893 0.330946 0.943650i \(-0.392632\pi\)
0.330946 + 0.943650i \(0.392632\pi\)
\(240\) −2.28136 −0.147261
\(241\) −29.0639 −1.87217 −0.936084 0.351777i \(-0.885578\pi\)
−0.936084 + 0.351777i \(0.885578\pi\)
\(242\) −7.48708 −0.481288
\(243\) 19.0890 1.22456
\(244\) −0.527106 −0.0337445
\(245\) −3.02249 −0.193100
\(246\) 5.36011 0.341748
\(247\) 22.5275 1.43339
\(248\) −9.68099 −0.614744
\(249\) −24.4442 −1.54909
\(250\) 1.00000 0.0632456
\(251\) −10.3519 −0.653406 −0.326703 0.945127i \(-0.605938\pi\)
−0.326703 + 0.945127i \(0.605938\pi\)
\(252\) 4.39683 0.276974
\(253\) 9.98578 0.627801
\(254\) −6.40287 −0.401752
\(255\) 5.58669 0.349852
\(256\) 1.00000 0.0625000
\(257\) −27.5708 −1.71982 −0.859909 0.510448i \(-0.829480\pi\)
−0.859909 + 0.510448i \(0.829480\pi\)
\(258\) 21.2570 1.32340
\(259\) −9.35997 −0.581600
\(260\) −4.38275 −0.271807
\(261\) 18.0357 1.11638
\(262\) 7.53069 0.465247
\(263\) 31.1715 1.92212 0.961058 0.276347i \(-0.0891237\pi\)
0.961058 + 0.276347i \(0.0891237\pi\)
\(264\) −4.27591 −0.263164
\(265\) −3.26390 −0.200500
\(266\) −10.2511 −0.628538
\(267\) −3.87170 −0.236944
\(268\) 6.25111 0.381848
\(269\) −8.33487 −0.508186 −0.254093 0.967180i \(-0.581777\pi\)
−0.254093 + 0.967180i \(0.581777\pi\)
\(270\) 1.81455 0.110430
\(271\) −19.7981 −1.20265 −0.601324 0.799005i \(-0.705360\pi\)
−0.601324 + 0.799005i \(0.705360\pi\)
\(272\) −2.44884 −0.148483
\(273\) 19.9410 1.20688
\(274\) 17.6455 1.06600
\(275\) 1.87428 0.113023
\(276\) −12.1546 −0.731624
\(277\) −13.6513 −0.820227 −0.410114 0.912034i \(-0.634511\pi\)
−0.410114 + 0.912034i \(0.634511\pi\)
\(278\) −11.7390 −0.704060
\(279\) −21.3429 −1.27777
\(280\) 1.99437 0.119186
\(281\) −14.9118 −0.889564 −0.444782 0.895639i \(-0.646719\pi\)
−0.444782 + 0.895639i \(0.646719\pi\)
\(282\) 2.28171 0.135874
\(283\) 14.8349 0.881843 0.440921 0.897546i \(-0.354652\pi\)
0.440921 + 0.897546i \(0.354652\pi\)
\(284\) −12.4228 −0.737158
\(285\) 11.7263 0.694607
\(286\) −8.21449 −0.485733
\(287\) −4.68582 −0.276595
\(288\) 2.20462 0.129908
\(289\) −11.0032 −0.647246
\(290\) 8.18089 0.480398
\(291\) −31.5030 −1.84674
\(292\) −9.22198 −0.539675
\(293\) 15.8005 0.923076 0.461538 0.887120i \(-0.347298\pi\)
0.461538 + 0.887120i \(0.347298\pi\)
\(294\) 6.89540 0.402148
\(295\) −2.78044 −0.161884
\(296\) −4.69319 −0.272786
\(297\) 3.40097 0.197344
\(298\) −7.41774 −0.429698
\(299\) −23.3504 −1.35039
\(300\) −2.28136 −0.131715
\(301\) −18.5829 −1.07110
\(302\) −13.2359 −0.761642
\(303\) 3.11067 0.178703
\(304\) −5.14004 −0.294802
\(305\) −0.527106 −0.0301820
\(306\) −5.39876 −0.308627
\(307\) −19.8280 −1.13165 −0.565823 0.824527i \(-0.691442\pi\)
−0.565823 + 0.824527i \(0.691442\pi\)
\(308\) 3.73801 0.212993
\(309\) 15.3572 0.873642
\(310\) −9.68099 −0.549843
\(311\) −4.80236 −0.272317 −0.136158 0.990687i \(-0.543476\pi\)
−0.136158 + 0.990687i \(0.543476\pi\)
\(312\) 9.99864 0.566062
\(313\) −9.73399 −0.550198 −0.275099 0.961416i \(-0.588711\pi\)
−0.275099 + 0.961416i \(0.588711\pi\)
\(314\) −11.5379 −0.651119
\(315\) 4.39683 0.247733
\(316\) −4.06354 −0.228592
\(317\) −3.27762 −0.184090 −0.0920448 0.995755i \(-0.529340\pi\)
−0.0920448 + 0.995755i \(0.529340\pi\)
\(318\) 7.44614 0.417559
\(319\) 15.3333 0.858498
\(320\) 1.00000 0.0559017
\(321\) 2.78205 0.155279
\(322\) 10.6256 0.592142
\(323\) 12.5871 0.700367
\(324\) −10.7535 −0.597417
\(325\) −4.38275 −0.243111
\(326\) 6.06917 0.336140
\(327\) −17.2465 −0.953734
\(328\) −2.34952 −0.129731
\(329\) −1.99467 −0.109970
\(330\) −4.27591 −0.235381
\(331\) 6.01441 0.330582 0.165291 0.986245i \(-0.447144\pi\)
0.165291 + 0.986245i \(0.447144\pi\)
\(332\) 10.7147 0.588048
\(333\) −10.3467 −0.566996
\(334\) 13.6921 0.749201
\(335\) 6.25111 0.341535
\(336\) −4.54988 −0.248216
\(337\) −16.7042 −0.909934 −0.454967 0.890508i \(-0.650349\pi\)
−0.454967 + 0.890508i \(0.650349\pi\)
\(338\) 6.20849 0.337697
\(339\) −38.7070 −2.10227
\(340\) −2.44884 −0.132807
\(341\) −18.1449 −0.982600
\(342\) −11.3318 −0.612756
\(343\) −19.9886 −1.07928
\(344\) −9.31769 −0.502376
\(345\) −12.1546 −0.654384
\(346\) −19.4834 −1.04743
\(347\) −20.2128 −1.08508 −0.542540 0.840030i \(-0.682537\pi\)
−0.542540 + 0.840030i \(0.682537\pi\)
\(348\) −18.6636 −1.00047
\(349\) 32.1542 1.72118 0.860588 0.509302i \(-0.170096\pi\)
0.860588 + 0.509302i \(0.170096\pi\)
\(350\) 1.99437 0.106604
\(351\) −7.95272 −0.424485
\(352\) 1.87428 0.0998994
\(353\) 20.1440 1.07216 0.536080 0.844167i \(-0.319905\pi\)
0.536080 + 0.844167i \(0.319905\pi\)
\(354\) 6.34320 0.337137
\(355\) −12.4228 −0.659334
\(356\) 1.69710 0.0899461
\(357\) 11.1419 0.589694
\(358\) 7.94386 0.419846
\(359\) −27.2113 −1.43616 −0.718078 0.695963i \(-0.754978\pi\)
−0.718078 + 0.695963i \(0.754978\pi\)
\(360\) 2.20462 0.116194
\(361\) 7.42004 0.390529
\(362\) −12.1441 −0.638277
\(363\) 17.0808 0.896507
\(364\) −8.74082 −0.458144
\(365\) −9.22198 −0.482700
\(366\) 1.20252 0.0628567
\(367\) 28.2878 1.47661 0.738306 0.674466i \(-0.235626\pi\)
0.738306 + 0.674466i \(0.235626\pi\)
\(368\) 5.32780 0.277731
\(369\) −5.17980 −0.269650
\(370\) −4.69319 −0.243988
\(371\) −6.50942 −0.337952
\(372\) 22.0859 1.14510
\(373\) −0.976114 −0.0505413 −0.0252706 0.999681i \(-0.508045\pi\)
−0.0252706 + 0.999681i \(0.508045\pi\)
\(374\) −4.58981 −0.237333
\(375\) −2.28136 −0.117809
\(376\) −1.00015 −0.0515789
\(377\) −35.8548 −1.84661
\(378\) 3.61888 0.186135
\(379\) 8.48882 0.436042 0.218021 0.975944i \(-0.430040\pi\)
0.218021 + 0.975944i \(0.430040\pi\)
\(380\) −5.14004 −0.263679
\(381\) 14.6073 0.748354
\(382\) 21.8649 1.11871
\(383\) −10.1052 −0.516354 −0.258177 0.966098i \(-0.583122\pi\)
−0.258177 + 0.966098i \(0.583122\pi\)
\(384\) −2.28136 −0.116420
\(385\) 3.73801 0.190506
\(386\) −25.8490 −1.31568
\(387\) −20.5420 −1.04421
\(388\) 13.8088 0.701038
\(389\) −18.1330 −0.919380 −0.459690 0.888080i \(-0.652039\pi\)
−0.459690 + 0.888080i \(0.652039\pi\)
\(390\) 9.99864 0.506301
\(391\) −13.0469 −0.659811
\(392\) −3.02249 −0.152659
\(393\) −17.1802 −0.866628
\(394\) −7.50208 −0.377949
\(395\) −4.06354 −0.204459
\(396\) 4.13207 0.207644
\(397\) 13.6402 0.684584 0.342292 0.939594i \(-0.388797\pi\)
0.342292 + 0.939594i \(0.388797\pi\)
\(398\) 1.81387 0.0909209
\(399\) 23.3866 1.17079
\(400\) 1.00000 0.0500000
\(401\) −2.29121 −0.114417 −0.0572087 0.998362i \(-0.518220\pi\)
−0.0572087 + 0.998362i \(0.518220\pi\)
\(402\) −14.2611 −0.711277
\(403\) 42.4294 2.11356
\(404\) −1.36351 −0.0678374
\(405\) −10.7535 −0.534346
\(406\) 16.3157 0.809735
\(407\) −8.79635 −0.436019
\(408\) 5.58669 0.276583
\(409\) −18.8708 −0.933101 −0.466551 0.884495i \(-0.654503\pi\)
−0.466551 + 0.884495i \(0.654503\pi\)
\(410\) −2.34952 −0.116035
\(411\) −40.2557 −1.98567
\(412\) −6.73160 −0.331642
\(413\) −5.54523 −0.272863
\(414\) 11.7458 0.577273
\(415\) 10.7147 0.525966
\(416\) −4.38275 −0.214882
\(417\) 26.7810 1.31147
\(418\) −9.63387 −0.471208
\(419\) 8.02753 0.392170 0.196085 0.980587i \(-0.437177\pi\)
0.196085 + 0.980587i \(0.437177\pi\)
\(420\) −4.54988 −0.222012
\(421\) −32.1899 −1.56884 −0.784420 0.620230i \(-0.787039\pi\)
−0.784420 + 0.620230i \(0.787039\pi\)
\(422\) 12.3024 0.598871
\(423\) −2.20496 −0.107209
\(424\) −3.26390 −0.158509
\(425\) −2.44884 −0.118786
\(426\) 28.3409 1.37312
\(427\) −1.05124 −0.0508733
\(428\) −1.21947 −0.0589452
\(429\) 18.7402 0.904788
\(430\) −9.31769 −0.449339
\(431\) −38.2579 −1.84282 −0.921408 0.388597i \(-0.872960\pi\)
−0.921408 + 0.388597i \(0.872960\pi\)
\(432\) 1.81455 0.0873026
\(433\) −0.870006 −0.0418098 −0.0209049 0.999781i \(-0.506655\pi\)
−0.0209049 + 0.999781i \(0.506655\pi\)
\(434\) −19.3075 −0.926789
\(435\) −18.6636 −0.894850
\(436\) 7.55973 0.362046
\(437\) −27.3851 −1.31001
\(438\) 21.0387 1.00527
\(439\) 15.3880 0.734431 0.367216 0.930136i \(-0.380311\pi\)
0.367216 + 0.930136i \(0.380311\pi\)
\(440\) 1.87428 0.0893527
\(441\) −6.66344 −0.317307
\(442\) 10.7326 0.510500
\(443\) 13.5024 0.641519 0.320759 0.947161i \(-0.396062\pi\)
0.320759 + 0.947161i \(0.396062\pi\)
\(444\) 10.7069 0.508126
\(445\) 1.69710 0.0804502
\(446\) −5.44946 −0.258039
\(447\) 16.9226 0.800409
\(448\) 1.99437 0.0942251
\(449\) 1.21920 0.0575376 0.0287688 0.999586i \(-0.490841\pi\)
0.0287688 + 0.999586i \(0.490841\pi\)
\(450\) 2.20462 0.103927
\(451\) −4.40366 −0.207360
\(452\) 16.9666 0.798042
\(453\) 30.1960 1.41873
\(454\) −17.8644 −0.838420
\(455\) −8.74082 −0.409776
\(456\) 11.7263 0.549135
\(457\) −14.6280 −0.684267 −0.342133 0.939651i \(-0.611149\pi\)
−0.342133 + 0.939651i \(0.611149\pi\)
\(458\) −13.3168 −0.622251
\(459\) −4.44354 −0.207407
\(460\) 5.32780 0.248410
\(461\) −38.2518 −1.78156 −0.890782 0.454430i \(-0.849843\pi\)
−0.890782 + 0.454430i \(0.849843\pi\)
\(462\) −8.52775 −0.396747
\(463\) 29.1991 1.35700 0.678498 0.734602i \(-0.262631\pi\)
0.678498 + 0.734602i \(0.262631\pi\)
\(464\) 8.18089 0.379788
\(465\) 22.0859 1.02421
\(466\) −4.00562 −0.185557
\(467\) 32.0814 1.48455 0.742276 0.670094i \(-0.233746\pi\)
0.742276 + 0.670094i \(0.233746\pi\)
\(468\) −9.66230 −0.446640
\(469\) 12.4670 0.575674
\(470\) −1.00015 −0.0461336
\(471\) 26.3221 1.21286
\(472\) −2.78044 −0.127980
\(473\) −17.4639 −0.802993
\(474\) 9.27042 0.425805
\(475\) −5.14004 −0.235841
\(476\) −4.88389 −0.223853
\(477\) −7.19566 −0.329467
\(478\) 10.2326 0.468029
\(479\) 2.21543 0.101226 0.0506129 0.998718i \(-0.483883\pi\)
0.0506129 + 0.998718i \(0.483883\pi\)
\(480\) −2.28136 −0.104130
\(481\) 20.5691 0.937870
\(482\) −29.0639 −1.32382
\(483\) −24.2409 −1.10300
\(484\) −7.48708 −0.340322
\(485\) 13.8088 0.627028
\(486\) 19.0890 0.865895
\(487\) 6.19322 0.280642 0.140321 0.990106i \(-0.455187\pi\)
0.140321 + 0.990106i \(0.455187\pi\)
\(488\) −0.527106 −0.0238610
\(489\) −13.8460 −0.626137
\(490\) −3.02249 −0.136542
\(491\) 7.75169 0.349829 0.174914 0.984584i \(-0.444035\pi\)
0.174914 + 0.984584i \(0.444035\pi\)
\(492\) 5.36011 0.241653
\(493\) −20.0337 −0.902271
\(494\) 22.5275 1.01356
\(495\) 4.13207 0.185723
\(496\) −9.68099 −0.434689
\(497\) −24.7757 −1.11134
\(498\) −24.4442 −1.09537
\(499\) −1.76473 −0.0790003 −0.0395002 0.999220i \(-0.512577\pi\)
−0.0395002 + 0.999220i \(0.512577\pi\)
\(500\) 1.00000 0.0447214
\(501\) −31.2368 −1.39556
\(502\) −10.3519 −0.462028
\(503\) −16.8768 −0.752499 −0.376249 0.926518i \(-0.622786\pi\)
−0.376249 + 0.926518i \(0.622786\pi\)
\(504\) 4.39683 0.195850
\(505\) −1.36351 −0.0606756
\(506\) 9.98578 0.443922
\(507\) −14.1638 −0.629037
\(508\) −6.40287 −0.284081
\(509\) 45.0177 1.99538 0.997688 0.0679615i \(-0.0216495\pi\)
0.997688 + 0.0679615i \(0.0216495\pi\)
\(510\) 5.58669 0.247383
\(511\) −18.3920 −0.813616
\(512\) 1.00000 0.0441942
\(513\) −9.32687 −0.411791
\(514\) −27.5708 −1.21609
\(515\) −6.73160 −0.296630
\(516\) 21.2570 0.935789
\(517\) −1.87456 −0.0824432
\(518\) −9.35997 −0.411253
\(519\) 44.4488 1.95108
\(520\) −4.38275 −0.192196
\(521\) −6.30714 −0.276321 −0.138160 0.990410i \(-0.544119\pi\)
−0.138160 + 0.990410i \(0.544119\pi\)
\(522\) 18.0357 0.789403
\(523\) −37.5327 −1.64119 −0.820595 0.571510i \(-0.806358\pi\)
−0.820595 + 0.571510i \(0.806358\pi\)
\(524\) 7.53069 0.328980
\(525\) −4.54988 −0.198573
\(526\) 31.1715 1.35914
\(527\) 23.7072 1.03270
\(528\) −4.27591 −0.186085
\(529\) 5.38545 0.234150
\(530\) −3.26390 −0.141775
\(531\) −6.12982 −0.266012
\(532\) −10.2511 −0.444444
\(533\) 10.2974 0.446028
\(534\) −3.87170 −0.167545
\(535\) −1.21947 −0.0527222
\(536\) 6.25111 0.270007
\(537\) −18.1228 −0.782058
\(538\) −8.33487 −0.359342
\(539\) −5.66499 −0.244008
\(540\) 1.81455 0.0780858
\(541\) −4.46479 −0.191956 −0.0959782 0.995383i \(-0.530598\pi\)
−0.0959782 + 0.995383i \(0.530598\pi\)
\(542\) −19.7981 −0.850401
\(543\) 27.7050 1.18894
\(544\) −2.44884 −0.104993
\(545\) 7.55973 0.323823
\(546\) 19.9410 0.853396
\(547\) 26.3218 1.12544 0.562720 0.826648i \(-0.309755\pi\)
0.562720 + 0.826648i \(0.309755\pi\)
\(548\) 17.6455 0.753777
\(549\) −1.16207 −0.0495959
\(550\) 1.87428 0.0799195
\(551\) −42.0501 −1.79139
\(552\) −12.1546 −0.517336
\(553\) −8.10421 −0.344626
\(554\) −13.6513 −0.579988
\(555\) 10.7069 0.454482
\(556\) −11.7390 −0.497846
\(557\) 1.70559 0.0722680 0.0361340 0.999347i \(-0.488496\pi\)
0.0361340 + 0.999347i \(0.488496\pi\)
\(558\) −21.3429 −0.903518
\(559\) 40.8371 1.72722
\(560\) 1.99437 0.0842775
\(561\) 10.4710 0.442087
\(562\) −14.9118 −0.629017
\(563\) 44.0436 1.85622 0.928109 0.372309i \(-0.121434\pi\)
0.928109 + 0.372309i \(0.121434\pi\)
\(564\) 2.28171 0.0960774
\(565\) 16.9666 0.713790
\(566\) 14.8349 0.623557
\(567\) −21.4465 −0.900667
\(568\) −12.4228 −0.521249
\(569\) 14.8842 0.623978 0.311989 0.950086i \(-0.399005\pi\)
0.311989 + 0.950086i \(0.399005\pi\)
\(570\) 11.7263 0.491161
\(571\) 29.4256 1.23142 0.615712 0.787972i \(-0.288869\pi\)
0.615712 + 0.787972i \(0.288869\pi\)
\(572\) −8.21449 −0.343465
\(573\) −49.8818 −2.08384
\(574\) −4.68582 −0.195582
\(575\) 5.32780 0.222185
\(576\) 2.20462 0.0918592
\(577\) 9.19120 0.382635 0.191317 0.981528i \(-0.438724\pi\)
0.191317 + 0.981528i \(0.438724\pi\)
\(578\) −11.0032 −0.457672
\(579\) 58.9709 2.45075
\(580\) 8.18089 0.339693
\(581\) 21.3692 0.886542
\(582\) −31.5030 −1.30584
\(583\) −6.11746 −0.253359
\(584\) −9.22198 −0.381608
\(585\) −9.66230 −0.399487
\(586\) 15.8005 0.652714
\(587\) 47.8954 1.97685 0.988426 0.151701i \(-0.0484752\pi\)
0.988426 + 0.151701i \(0.0484752\pi\)
\(588\) 6.89540 0.284361
\(589\) 49.7607 2.05035
\(590\) −2.78044 −0.114469
\(591\) 17.1150 0.704016
\(592\) −4.69319 −0.192889
\(593\) 6.26015 0.257073 0.128537 0.991705i \(-0.458972\pi\)
0.128537 + 0.991705i \(0.458972\pi\)
\(594\) 3.40097 0.139544
\(595\) −4.88389 −0.200220
\(596\) −7.41774 −0.303842
\(597\) −4.13809 −0.169361
\(598\) −23.3504 −0.954869
\(599\) −9.68059 −0.395538 −0.197769 0.980249i \(-0.563370\pi\)
−0.197769 + 0.980249i \(0.563370\pi\)
\(600\) −2.28136 −0.0931363
\(601\) −1.00000 −0.0407909
\(602\) −18.5829 −0.757383
\(603\) 13.7813 0.561219
\(604\) −13.2359 −0.538562
\(605\) −7.48708 −0.304393
\(606\) 3.11067 0.126362
\(607\) −36.2345 −1.47071 −0.735357 0.677680i \(-0.762986\pi\)
−0.735357 + 0.677680i \(0.762986\pi\)
\(608\) −5.14004 −0.208456
\(609\) −37.2221 −1.50831
\(610\) −0.527106 −0.0213419
\(611\) 4.38342 0.177334
\(612\) −5.39876 −0.218232
\(613\) 36.1691 1.46086 0.730428 0.682990i \(-0.239321\pi\)
0.730428 + 0.682990i \(0.239321\pi\)
\(614\) −19.8280 −0.800195
\(615\) 5.36011 0.216141
\(616\) 3.73801 0.150609
\(617\) −28.2435 −1.13704 −0.568520 0.822669i \(-0.692484\pi\)
−0.568520 + 0.822669i \(0.692484\pi\)
\(618\) 15.3572 0.617758
\(619\) 35.3820 1.42212 0.711061 0.703130i \(-0.248215\pi\)
0.711061 + 0.703130i \(0.248215\pi\)
\(620\) −9.68099 −0.388798
\(621\) 9.66756 0.387946
\(622\) −4.80236 −0.192557
\(623\) 3.38464 0.135603
\(624\) 9.99864 0.400266
\(625\) 1.00000 0.0400000
\(626\) −9.73399 −0.389049
\(627\) 21.9784 0.877731
\(628\) −11.5379 −0.460411
\(629\) 11.4929 0.458251
\(630\) 4.39683 0.175174
\(631\) −20.1738 −0.803107 −0.401553 0.915836i \(-0.631530\pi\)
−0.401553 + 0.915836i \(0.631530\pi\)
\(632\) −4.06354 −0.161639
\(633\) −28.0662 −1.11553
\(634\) −3.27762 −0.130171
\(635\) −6.40287 −0.254090
\(636\) 7.44614 0.295259
\(637\) 13.2468 0.524858
\(638\) 15.3333 0.607050
\(639\) −27.3876 −1.08343
\(640\) 1.00000 0.0395285
\(641\) 23.3534 0.922405 0.461203 0.887295i \(-0.347418\pi\)
0.461203 + 0.887295i \(0.347418\pi\)
\(642\) 2.78205 0.109799
\(643\) 39.7730 1.56849 0.784247 0.620449i \(-0.213049\pi\)
0.784247 + 0.620449i \(0.213049\pi\)
\(644\) 10.6256 0.418707
\(645\) 21.2570 0.836995
\(646\) 12.5871 0.495234
\(647\) −28.9077 −1.13648 −0.568240 0.822863i \(-0.692376\pi\)
−0.568240 + 0.822863i \(0.692376\pi\)
\(648\) −10.7535 −0.422438
\(649\) −5.21132 −0.204562
\(650\) −4.38275 −0.171906
\(651\) 44.0474 1.72635
\(652\) 6.06917 0.237687
\(653\) 23.0429 0.901737 0.450869 0.892590i \(-0.351114\pi\)
0.450869 + 0.892590i \(0.351114\pi\)
\(654\) −17.2465 −0.674391
\(655\) 7.53069 0.294248
\(656\) −2.34952 −0.0917334
\(657\) −20.3310 −0.793186
\(658\) −1.99467 −0.0777605
\(659\) −11.5214 −0.448811 −0.224405 0.974496i \(-0.572044\pi\)
−0.224405 + 0.974496i \(0.572044\pi\)
\(660\) −4.27591 −0.166440
\(661\) 34.2954 1.33394 0.666969 0.745086i \(-0.267591\pi\)
0.666969 + 0.745086i \(0.267591\pi\)
\(662\) 6.01441 0.233757
\(663\) −24.4851 −0.950922
\(664\) 10.7147 0.415813
\(665\) −10.2511 −0.397522
\(666\) −10.3467 −0.400927
\(667\) 43.5861 1.68766
\(668\) 13.6921 0.529765
\(669\) 12.4322 0.480656
\(670\) 6.25111 0.241502
\(671\) −0.987943 −0.0381391
\(672\) −4.54988 −0.175516
\(673\) 1.47480 0.0568495 0.0284247 0.999596i \(-0.490951\pi\)
0.0284247 + 0.999596i \(0.490951\pi\)
\(674\) −16.7042 −0.643420
\(675\) 1.81455 0.0698421
\(676\) 6.20849 0.238788
\(677\) −1.61020 −0.0618849 −0.0309424 0.999521i \(-0.509851\pi\)
−0.0309424 + 0.999521i \(0.509851\pi\)
\(678\) −38.7070 −1.48653
\(679\) 27.5400 1.05689
\(680\) −2.44884 −0.0939087
\(681\) 40.7553 1.56175
\(682\) −18.1449 −0.694803
\(683\) 47.2327 1.80731 0.903655 0.428261i \(-0.140874\pi\)
0.903655 + 0.428261i \(0.140874\pi\)
\(684\) −11.3318 −0.433284
\(685\) 17.6455 0.674199
\(686\) −19.9886 −0.763166
\(687\) 30.3804 1.15908
\(688\) −9.31769 −0.355233
\(689\) 14.3048 0.544971
\(690\) −12.1546 −0.462720
\(691\) −30.5215 −1.16109 −0.580547 0.814227i \(-0.697161\pi\)
−0.580547 + 0.814227i \(0.697161\pi\)
\(692\) −19.4834 −0.740648
\(693\) 8.24088 0.313045
\(694\) −20.2128 −0.767268
\(695\) −11.7390 −0.445287
\(696\) −18.6636 −0.707441
\(697\) 5.75360 0.217933
\(698\) 32.1542 1.21706
\(699\) 9.13828 0.345642
\(700\) 1.99437 0.0753801
\(701\) 43.5429 1.64459 0.822296 0.569059i \(-0.192693\pi\)
0.822296 + 0.569059i \(0.192693\pi\)
\(702\) −7.95272 −0.300156
\(703\) 24.1232 0.909824
\(704\) 1.87428 0.0706395
\(705\) 2.28171 0.0859342
\(706\) 20.1440 0.758131
\(707\) −2.71935 −0.102272
\(708\) 6.34320 0.238392
\(709\) −23.2550 −0.873361 −0.436680 0.899617i \(-0.643846\pi\)
−0.436680 + 0.899617i \(0.643846\pi\)
\(710\) −12.4228 −0.466219
\(711\) −8.95857 −0.335973
\(712\) 1.69710 0.0636015
\(713\) −51.5784 −1.93163
\(714\) 11.1419 0.416976
\(715\) −8.21449 −0.307205
\(716\) 7.94386 0.296876
\(717\) −23.3443 −0.871809
\(718\) −27.2113 −1.01552
\(719\) −29.4691 −1.09901 −0.549506 0.835490i \(-0.685184\pi\)
−0.549506 + 0.835490i \(0.685184\pi\)
\(720\) 2.20462 0.0821613
\(721\) −13.4253 −0.499984
\(722\) 7.42004 0.276145
\(723\) 66.3052 2.46592
\(724\) −12.1441 −0.451330
\(725\) 8.18089 0.303830
\(726\) 17.0808 0.633926
\(727\) 7.82904 0.290363 0.145182 0.989405i \(-0.453623\pi\)
0.145182 + 0.989405i \(0.453623\pi\)
\(728\) −8.74082 −0.323956
\(729\) −11.2885 −0.418091
\(730\) −9.22198 −0.341321
\(731\) 22.8175 0.843936
\(732\) 1.20252 0.0444464
\(733\) −17.0264 −0.628883 −0.314441 0.949277i \(-0.601817\pi\)
−0.314441 + 0.949277i \(0.601817\pi\)
\(734\) 28.2878 1.04412
\(735\) 6.89540 0.254340
\(736\) 5.32780 0.196385
\(737\) 11.7163 0.431577
\(738\) −5.17980 −0.190671
\(739\) 42.5442 1.56502 0.782508 0.622641i \(-0.213940\pi\)
0.782508 + 0.622641i \(0.213940\pi\)
\(740\) −4.69319 −0.172525
\(741\) −51.3935 −1.88799
\(742\) −6.50942 −0.238968
\(743\) −13.0719 −0.479561 −0.239780 0.970827i \(-0.577075\pi\)
−0.239780 + 0.970827i \(0.577075\pi\)
\(744\) 22.0859 0.809707
\(745\) −7.41774 −0.271765
\(746\) −0.976114 −0.0357381
\(747\) 23.6219 0.864281
\(748\) −4.58981 −0.167820
\(749\) −2.43207 −0.0888659
\(750\) −2.28136 −0.0833036
\(751\) −40.7815 −1.48814 −0.744069 0.668103i \(-0.767107\pi\)
−0.744069 + 0.668103i \(0.767107\pi\)
\(752\) −1.00015 −0.0364718
\(753\) 23.6164 0.860631
\(754\) −35.8548 −1.30575
\(755\) −13.2359 −0.481705
\(756\) 3.61888 0.131618
\(757\) −46.8948 −1.70442 −0.852210 0.523200i \(-0.824738\pi\)
−0.852210 + 0.523200i \(0.824738\pi\)
\(758\) 8.48882 0.308328
\(759\) −22.7812 −0.826905
\(760\) −5.14004 −0.186449
\(761\) 35.6949 1.29394 0.646970 0.762516i \(-0.276036\pi\)
0.646970 + 0.762516i \(0.276036\pi\)
\(762\) 14.6073 0.529166
\(763\) 15.0769 0.545821
\(764\) 21.8649 0.791045
\(765\) −5.39876 −0.195193
\(766\) −10.1052 −0.365118
\(767\) 12.1860 0.440010
\(768\) −2.28136 −0.0823216
\(769\) −15.2231 −0.548958 −0.274479 0.961593i \(-0.588505\pi\)
−0.274479 + 0.961593i \(0.588505\pi\)
\(770\) 3.73801 0.134708
\(771\) 62.8989 2.26525
\(772\) −25.8490 −0.930324
\(773\) −2.98771 −0.107461 −0.0537303 0.998555i \(-0.517111\pi\)
−0.0537303 + 0.998555i \(0.517111\pi\)
\(774\) −20.5420 −0.738366
\(775\) −9.68099 −0.347752
\(776\) 13.8088 0.495709
\(777\) 21.3535 0.766052
\(778\) −18.1330 −0.650100
\(779\) 12.0766 0.432691
\(780\) 9.99864 0.358009
\(781\) −23.2838 −0.833159
\(782\) −13.0469 −0.466557
\(783\) 14.8446 0.530504
\(784\) −3.02249 −0.107946
\(785\) −11.5379 −0.411804
\(786\) −17.1802 −0.612799
\(787\) −4.70167 −0.167596 −0.0837982 0.996483i \(-0.526705\pi\)
−0.0837982 + 0.996483i \(0.526705\pi\)
\(788\) −7.50208 −0.267250
\(789\) −71.1135 −2.53171
\(790\) −4.06354 −0.144574
\(791\) 33.8377 1.20313
\(792\) 4.13207 0.146827
\(793\) 2.31017 0.0820366
\(794\) 13.6402 0.484074
\(795\) 7.44614 0.264087
\(796\) 1.81387 0.0642908
\(797\) 33.6753 1.19284 0.596420 0.802672i \(-0.296589\pi\)
0.596420 + 0.802672i \(0.296589\pi\)
\(798\) 23.3866 0.827877
\(799\) 2.44921 0.0866469
\(800\) 1.00000 0.0353553
\(801\) 3.74146 0.132198
\(802\) −2.29121 −0.0809053
\(803\) −17.2846 −0.609959
\(804\) −14.2611 −0.502949
\(805\) 10.6256 0.374503
\(806\) 42.4294 1.49451
\(807\) 19.0149 0.669355
\(808\) −1.36351 −0.0479683
\(809\) −36.1134 −1.26968 −0.634839 0.772644i \(-0.718934\pi\)
−0.634839 + 0.772644i \(0.718934\pi\)
\(810\) −10.7535 −0.377840
\(811\) 28.2962 0.993614 0.496807 0.867861i \(-0.334506\pi\)
0.496807 + 0.867861i \(0.334506\pi\)
\(812\) 16.3157 0.572569
\(813\) 45.1666 1.58406
\(814\) −8.79635 −0.308312
\(815\) 6.06917 0.212594
\(816\) 5.58669 0.195573
\(817\) 47.8933 1.67557
\(818\) −18.8708 −0.659802
\(819\) −19.2702 −0.673355
\(820\) −2.34952 −0.0820489
\(821\) −13.2379 −0.462004 −0.231002 0.972953i \(-0.574200\pi\)
−0.231002 + 0.972953i \(0.574200\pi\)
\(822\) −40.2557 −1.40408
\(823\) 27.9186 0.973180 0.486590 0.873630i \(-0.338240\pi\)
0.486590 + 0.873630i \(0.338240\pi\)
\(824\) −6.73160 −0.234506
\(825\) −4.27591 −0.148868
\(826\) −5.54523 −0.192943
\(827\) −51.3407 −1.78529 −0.892646 0.450759i \(-0.851153\pi\)
−0.892646 + 0.450759i \(0.851153\pi\)
\(828\) 11.7458 0.408194
\(829\) 6.35055 0.220564 0.110282 0.993900i \(-0.464825\pi\)
0.110282 + 0.993900i \(0.464825\pi\)
\(830\) 10.7147 0.371914
\(831\) 31.1436 1.08036
\(832\) −4.38275 −0.151944
\(833\) 7.40159 0.256450
\(834\) 26.7810 0.927350
\(835\) 13.6921 0.473836
\(836\) −9.63387 −0.333194
\(837\) −17.5666 −0.607192
\(838\) 8.02753 0.277306
\(839\) 14.6234 0.504857 0.252429 0.967615i \(-0.418771\pi\)
0.252429 + 0.967615i \(0.418771\pi\)
\(840\) −4.54988 −0.156986
\(841\) 37.9269 1.30782
\(842\) −32.1899 −1.10934
\(843\) 34.0193 1.17169
\(844\) 12.3024 0.423466
\(845\) 6.20849 0.213578
\(846\) −2.20496 −0.0758080
\(847\) −14.9320 −0.513070
\(848\) −3.26390 −0.112083
\(849\) −33.8438 −1.16152
\(850\) −2.44884 −0.0839945
\(851\) −25.0044 −0.857140
\(852\) 28.3409 0.970944
\(853\) −23.5105 −0.804985 −0.402493 0.915423i \(-0.631856\pi\)
−0.402493 + 0.915423i \(0.631856\pi\)
\(854\) −1.05124 −0.0359728
\(855\) −11.3318 −0.387541
\(856\) −1.21947 −0.0416805
\(857\) −1.38976 −0.0474732 −0.0237366 0.999718i \(-0.507556\pi\)
−0.0237366 + 0.999718i \(0.507556\pi\)
\(858\) 18.7402 0.639781
\(859\) −18.0488 −0.615817 −0.307909 0.951416i \(-0.599629\pi\)
−0.307909 + 0.951416i \(0.599629\pi\)
\(860\) −9.31769 −0.317730
\(861\) 10.6901 0.364316
\(862\) −38.2579 −1.30307
\(863\) 1.45594 0.0495606 0.0247803 0.999693i \(-0.492111\pi\)
0.0247803 + 0.999693i \(0.492111\pi\)
\(864\) 1.81455 0.0617323
\(865\) −19.4834 −0.662456
\(866\) −0.870006 −0.0295640
\(867\) 25.1023 0.852518
\(868\) −19.3075 −0.655339
\(869\) −7.61621 −0.258362
\(870\) −18.6636 −0.632754
\(871\) −27.3971 −0.928314
\(872\) 7.55973 0.256005
\(873\) 30.4433 1.03035
\(874\) −27.3851 −0.926315
\(875\) 1.99437 0.0674220
\(876\) 21.0387 0.710831
\(877\) −0.775510 −0.0261871 −0.0130936 0.999914i \(-0.504168\pi\)
−0.0130936 + 0.999914i \(0.504168\pi\)
\(878\) 15.3880 0.519321
\(879\) −36.0467 −1.21583
\(880\) 1.87428 0.0631819
\(881\) 5.60615 0.188876 0.0944381 0.995531i \(-0.469895\pi\)
0.0944381 + 0.995531i \(0.469895\pi\)
\(882\) −6.66344 −0.224370
\(883\) 23.5277 0.791769 0.395885 0.918300i \(-0.370438\pi\)
0.395885 + 0.918300i \(0.370438\pi\)
\(884\) 10.7326 0.360978
\(885\) 6.34320 0.213224
\(886\) 13.5024 0.453622
\(887\) 49.6539 1.66721 0.833607 0.552358i \(-0.186272\pi\)
0.833607 + 0.552358i \(0.186272\pi\)
\(888\) 10.7069 0.359299
\(889\) −12.7697 −0.428282
\(890\) 1.69710 0.0568869
\(891\) −20.1551 −0.675220
\(892\) −5.44946 −0.182461
\(893\) 5.14083 0.172031
\(894\) 16.9226 0.565975
\(895\) 7.94386 0.265534
\(896\) 1.99437 0.0666272
\(897\) 53.2708 1.77866
\(898\) 1.21920 0.0406852
\(899\) −79.1991 −2.64144
\(900\) 2.20462 0.0734873
\(901\) 7.99276 0.266278
\(902\) −4.40366 −0.146626
\(903\) 42.3944 1.41080
\(904\) 16.9666 0.564301
\(905\) −12.1441 −0.403682
\(906\) 30.1960 1.00319
\(907\) 22.4359 0.744971 0.372485 0.928038i \(-0.378506\pi\)
0.372485 + 0.928038i \(0.378506\pi\)
\(908\) −17.8644 −0.592852
\(909\) −3.00603 −0.0997038
\(910\) −8.74082 −0.289755
\(911\) 26.1208 0.865421 0.432711 0.901533i \(-0.357557\pi\)
0.432711 + 0.901533i \(0.357557\pi\)
\(912\) 11.7263 0.388297
\(913\) 20.0824 0.664631
\(914\) −14.6280 −0.483850
\(915\) 1.20252 0.0397541
\(916\) −13.3168 −0.439998
\(917\) 15.0190 0.495970
\(918\) −4.44354 −0.146659
\(919\) 8.28053 0.273149 0.136575 0.990630i \(-0.456391\pi\)
0.136575 + 0.990630i \(0.456391\pi\)
\(920\) 5.32780 0.175652
\(921\) 45.2350 1.49054
\(922\) −38.2518 −1.25976
\(923\) 54.4460 1.79211
\(924\) −8.52775 −0.280542
\(925\) −4.69319 −0.154311
\(926\) 29.1991 0.959541
\(927\) −14.8406 −0.487430
\(928\) 8.18089 0.268551
\(929\) −21.3883 −0.701726 −0.350863 0.936427i \(-0.614112\pi\)
−0.350863 + 0.936427i \(0.614112\pi\)
\(930\) 22.0859 0.724224
\(931\) 15.5357 0.509163
\(932\) −4.00562 −0.131209
\(933\) 10.9559 0.358681
\(934\) 32.0814 1.04974
\(935\) −4.58981 −0.150103
\(936\) −9.66230 −0.315822
\(937\) −3.48138 −0.113732 −0.0568659 0.998382i \(-0.518111\pi\)
−0.0568659 + 0.998382i \(0.518111\pi\)
\(938\) 12.4670 0.407063
\(939\) 22.2068 0.724691
\(940\) −1.00015 −0.0326214
\(941\) −35.1196 −1.14486 −0.572432 0.819952i \(-0.694000\pi\)
−0.572432 + 0.819952i \(0.694000\pi\)
\(942\) 26.3221 0.857619
\(943\) −12.5178 −0.407635
\(944\) −2.78044 −0.0904957
\(945\) 3.61888 0.117722
\(946\) −17.4639 −0.567802
\(947\) 7.69518 0.250060 0.125030 0.992153i \(-0.460097\pi\)
0.125030 + 0.992153i \(0.460097\pi\)
\(948\) 9.27042 0.301089
\(949\) 40.4176 1.31201
\(950\) −5.14004 −0.166765
\(951\) 7.47744 0.242473
\(952\) −4.88389 −0.158288
\(953\) −2.58696 −0.0837999 −0.0419000 0.999122i \(-0.513341\pi\)
−0.0419000 + 0.999122i \(0.513341\pi\)
\(954\) −7.19566 −0.232968
\(955\) 21.8649 0.707532
\(956\) 10.2326 0.330946
\(957\) −34.9807 −1.13077
\(958\) 2.21543 0.0715774
\(959\) 35.1916 1.13640
\(960\) −2.28136 −0.0736307
\(961\) 62.7216 2.02328
\(962\) 20.5691 0.663174
\(963\) −2.68846 −0.0866345
\(964\) −29.0639 −0.936084
\(965\) −25.8490 −0.832107
\(966\) −24.2409 −0.779937
\(967\) 5.67466 0.182485 0.0912424 0.995829i \(-0.470916\pi\)
0.0912424 + 0.995829i \(0.470916\pi\)
\(968\) −7.48708 −0.240644
\(969\) −28.7158 −0.922486
\(970\) 13.8088 0.443375
\(971\) −26.5535 −0.852142 −0.426071 0.904690i \(-0.640103\pi\)
−0.426071 + 0.904690i \(0.640103\pi\)
\(972\) 19.0890 0.612281
\(973\) −23.4120 −0.750554
\(974\) 6.19322 0.198444
\(975\) 9.99864 0.320213
\(976\) −0.527106 −0.0168722
\(977\) −26.7138 −0.854651 −0.427325 0.904098i \(-0.640544\pi\)
−0.427325 + 0.904098i \(0.640544\pi\)
\(978\) −13.8460 −0.442746
\(979\) 3.18084 0.101660
\(980\) −3.02249 −0.0965498
\(981\) 16.6663 0.532115
\(982\) 7.75169 0.247366
\(983\) 54.5247 1.73907 0.869535 0.493872i \(-0.164419\pi\)
0.869535 + 0.493872i \(0.164419\pi\)
\(984\) 5.36011 0.170874
\(985\) −7.50208 −0.239036
\(986\) −20.0337 −0.638002
\(987\) 4.55058 0.144846
\(988\) 22.5275 0.716696
\(989\) −49.6428 −1.57855
\(990\) 4.13207 0.131326
\(991\) −20.7124 −0.657952 −0.328976 0.944338i \(-0.606704\pi\)
−0.328976 + 0.944338i \(0.606704\pi\)
\(992\) −9.68099 −0.307372
\(993\) −13.7211 −0.435425
\(994\) −24.7757 −0.785836
\(995\) 1.81387 0.0575034
\(996\) −24.4442 −0.774545
\(997\) 42.7101 1.35264 0.676321 0.736607i \(-0.263573\pi\)
0.676321 + 0.736607i \(0.263573\pi\)
\(998\) −1.76473 −0.0558617
\(999\) −8.51604 −0.269435
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 \(a_p\))