Properties

Label 6041.2.a.f.1.12
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

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Newspace parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2376278611\)
Analytic rank: \(0\)
Dimension: \(132\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.56875 q^{2}\) \(-3.19690 q^{3}\) \(+4.59849 q^{4}\) \(-1.91049 q^{5}\) \(+8.21205 q^{6}\) \(+1.00000 q^{7}\) \(-6.67489 q^{8}\) \(+7.22017 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.56875 q^{2}\) \(-3.19690 q^{3}\) \(+4.59849 q^{4}\) \(-1.91049 q^{5}\) \(+8.21205 q^{6}\) \(+1.00000 q^{7}\) \(-6.67489 q^{8}\) \(+7.22017 q^{9}\) \(+4.90758 q^{10}\) \(+5.45473 q^{11}\) \(-14.7009 q^{12}\) \(-2.75875 q^{13}\) \(-2.56875 q^{14}\) \(+6.10765 q^{15}\) \(+7.94917 q^{16}\) \(-1.52927 q^{17}\) \(-18.5468 q^{18}\) \(+2.74225 q^{19}\) \(-8.78538 q^{20}\) \(-3.19690 q^{21}\) \(-14.0119 q^{22}\) \(-8.61124 q^{23}\) \(+21.3390 q^{24}\) \(-1.35002 q^{25}\) \(+7.08656 q^{26}\) \(-13.4914 q^{27}\) \(+4.59849 q^{28}\) \(-3.64687 q^{29}\) \(-15.6890 q^{30}\) \(-6.70859 q^{31}\) \(-7.06966 q^{32}\) \(-17.4382 q^{33}\) \(+3.92833 q^{34}\) \(-1.91049 q^{35}\) \(+33.2019 q^{36}\) \(+4.87651 q^{37}\) \(-7.04417 q^{38}\) \(+8.81946 q^{39}\) \(+12.7523 q^{40}\) \(+5.17648 q^{41}\) \(+8.21205 q^{42}\) \(+5.42937 q^{43}\) \(+25.0835 q^{44}\) \(-13.7941 q^{45}\) \(+22.1202 q^{46}\) \(+10.0340 q^{47}\) \(-25.4127 q^{48}\) \(+1.00000 q^{49}\) \(+3.46788 q^{50}\) \(+4.88893 q^{51}\) \(-12.6861 q^{52}\) \(-3.15331 q^{53}\) \(+34.6562 q^{54}\) \(-10.4212 q^{55}\) \(-6.67489 q^{56}\) \(-8.76671 q^{57}\) \(+9.36790 q^{58}\) \(-6.50781 q^{59}\) \(+28.0860 q^{60}\) \(+4.62860 q^{61}\) \(+17.2327 q^{62}\) \(+7.22017 q^{63}\) \(+2.26189 q^{64}\) \(+5.27058 q^{65}\) \(+44.7945 q^{66}\) \(+4.17921 q^{67}\) \(-7.03236 q^{68}\) \(+27.5293 q^{69}\) \(+4.90758 q^{70}\) \(-7.98204 q^{71}\) \(-48.1938 q^{72}\) \(+3.87065 q^{73}\) \(-12.5266 q^{74}\) \(+4.31589 q^{75}\) \(+12.6102 q^{76}\) \(+5.45473 q^{77}\) \(-22.6550 q^{78}\) \(+10.2824 q^{79}\) \(-15.1868 q^{80}\) \(+21.4703 q^{81}\) \(-13.2971 q^{82}\) \(-7.69439 q^{83}\) \(-14.7009 q^{84}\) \(+2.92166 q^{85}\) \(-13.9467 q^{86}\) \(+11.6587 q^{87}\) \(-36.4097 q^{88}\) \(-6.10370 q^{89}\) \(+35.4335 q^{90}\) \(-2.75875 q^{91}\) \(-39.5987 q^{92}\) \(+21.4467 q^{93}\) \(-25.7749 q^{94}\) \(-5.23905 q^{95}\) \(+22.6010 q^{96}\) \(-7.71647 q^{97}\) \(-2.56875 q^{98}\) \(+39.3840 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56875 −1.81638 −0.908192 0.418555i \(-0.862537\pi\)
−0.908192 + 0.418555i \(0.862537\pi\)
\(3\) −3.19690 −1.84573 −0.922865 0.385123i \(-0.874159\pi\)
−0.922865 + 0.385123i \(0.874159\pi\)
\(4\) 4.59849 2.29925
\(5\) −1.91049 −0.854398 −0.427199 0.904158i \(-0.640500\pi\)
−0.427199 + 0.904158i \(0.640500\pi\)
\(6\) 8.21205 3.35255
\(7\) 1.00000 0.377964
\(8\) −6.67489 −2.35993
\(9\) 7.22017 2.40672
\(10\) 4.90758 1.55191
\(11\) 5.45473 1.64466 0.822331 0.569009i \(-0.192673\pi\)
0.822331 + 0.569009i \(0.192673\pi\)
\(12\) −14.7009 −4.24379
\(13\) −2.75875 −0.765141 −0.382570 0.923926i \(-0.624961\pi\)
−0.382570 + 0.923926i \(0.624961\pi\)
\(14\) −2.56875 −0.686528
\(15\) 6.10765 1.57699
\(16\) 7.94917 1.98729
\(17\) −1.52927 −0.370903 −0.185452 0.982653i \(-0.559375\pi\)
−0.185452 + 0.982653i \(0.559375\pi\)
\(18\) −18.5468 −4.37153
\(19\) 2.74225 0.629116 0.314558 0.949238i \(-0.398144\pi\)
0.314558 + 0.949238i \(0.398144\pi\)
\(20\) −8.78538 −1.96447
\(21\) −3.19690 −0.697621
\(22\) −14.0119 −2.98734
\(23\) −8.61124 −1.79557 −0.897784 0.440436i \(-0.854824\pi\)
−0.897784 + 0.440436i \(0.854824\pi\)
\(24\) 21.3390 4.35580
\(25\) −1.35002 −0.270005
\(26\) 7.08656 1.38979
\(27\) −13.4914 −2.59643
\(28\) 4.59849 0.869034
\(29\) −3.64687 −0.677206 −0.338603 0.940929i \(-0.609954\pi\)
−0.338603 + 0.940929i \(0.609954\pi\)
\(30\) −15.6890 −2.86441
\(31\) −6.70859 −1.20490 −0.602449 0.798157i \(-0.705808\pi\)
−0.602449 + 0.798157i \(0.705808\pi\)
\(32\) −7.06966 −1.24975
\(33\) −17.4382 −3.03560
\(34\) 3.92833 0.673702
\(35\) −1.91049 −0.322932
\(36\) 33.2019 5.53365
\(37\) 4.87651 0.801693 0.400847 0.916145i \(-0.368716\pi\)
0.400847 + 0.916145i \(0.368716\pi\)
\(38\) −7.04417 −1.14272
\(39\) 8.81946 1.41224
\(40\) 12.7523 2.01632
\(41\) 5.17648 0.808431 0.404215 0.914664i \(-0.367545\pi\)
0.404215 + 0.914664i \(0.367545\pi\)
\(42\) 8.21205 1.26715
\(43\) 5.42937 0.827971 0.413986 0.910283i \(-0.364136\pi\)
0.413986 + 0.910283i \(0.364136\pi\)
\(44\) 25.0835 3.78149
\(45\) −13.7941 −2.05630
\(46\) 22.1202 3.26144
\(47\) 10.0340 1.46361 0.731807 0.681512i \(-0.238677\pi\)
0.731807 + 0.681512i \(0.238677\pi\)
\(48\) −25.4127 −3.66800
\(49\) 1.00000 0.142857
\(50\) 3.46788 0.490432
\(51\) 4.88893 0.684588
\(52\) −12.6861 −1.75925
\(53\) −3.15331 −0.433140 −0.216570 0.976267i \(-0.569487\pi\)
−0.216570 + 0.976267i \(0.569487\pi\)
\(54\) 34.6562 4.71611
\(55\) −10.4212 −1.40520
\(56\) −6.67489 −0.891970
\(57\) −8.76671 −1.16118
\(58\) 9.36790 1.23007
\(59\) −6.50781 −0.847245 −0.423622 0.905839i \(-0.639242\pi\)
−0.423622 + 0.905839i \(0.639242\pi\)
\(60\) 28.0860 3.62589
\(61\) 4.62860 0.592632 0.296316 0.955090i \(-0.404242\pi\)
0.296316 + 0.955090i \(0.404242\pi\)
\(62\) 17.2327 2.18856
\(63\) 7.22017 0.909655
\(64\) 2.26189 0.282736
\(65\) 5.27058 0.653734
\(66\) 44.7945 5.51382
\(67\) 4.17921 0.510572 0.255286 0.966866i \(-0.417830\pi\)
0.255286 + 0.966866i \(0.417830\pi\)
\(68\) −7.03236 −0.852798
\(69\) 27.5293 3.31413
\(70\) 4.90758 0.586568
\(71\) −7.98204 −0.947294 −0.473647 0.880715i \(-0.657063\pi\)
−0.473647 + 0.880715i \(0.657063\pi\)
\(72\) −48.1938 −5.67970
\(73\) 3.87065 0.453025 0.226512 0.974008i \(-0.427268\pi\)
0.226512 + 0.974008i \(0.427268\pi\)
\(74\) −12.5266 −1.45618
\(75\) 4.31589 0.498356
\(76\) 12.6102 1.44649
\(77\) 5.45473 0.621624
\(78\) −22.6550 −2.56518
\(79\) 10.2824 1.15686 0.578432 0.815731i \(-0.303665\pi\)
0.578432 + 0.815731i \(0.303665\pi\)
\(80\) −15.1868 −1.69794
\(81\) 21.4703 2.38559
\(82\) −13.2971 −1.46842
\(83\) −7.69439 −0.844569 −0.422285 0.906463i \(-0.638772\pi\)
−0.422285 + 0.906463i \(0.638772\pi\)
\(84\) −14.7009 −1.60400
\(85\) 2.92166 0.316899
\(86\) −13.9467 −1.50391
\(87\) 11.6587 1.24994
\(88\) −36.4097 −3.88129
\(89\) −6.10370 −0.646991 −0.323495 0.946230i \(-0.604858\pi\)
−0.323495 + 0.946230i \(0.604858\pi\)
\(90\) 35.4335 3.73502
\(91\) −2.75875 −0.289196
\(92\) −39.5987 −4.12845
\(93\) 21.4467 2.22392
\(94\) −25.7749 −2.65848
\(95\) −5.23905 −0.537515
\(96\) 22.6010 2.30670
\(97\) −7.71647 −0.783489 −0.391744 0.920074i \(-0.628128\pi\)
−0.391744 + 0.920074i \(0.628128\pi\)
\(98\) −2.56875 −0.259483
\(99\) 39.3840 3.95824
\(100\) −6.20808 −0.620808
\(101\) 0.454038 0.0451785 0.0225893 0.999745i \(-0.492809\pi\)
0.0225893 + 0.999745i \(0.492809\pi\)
\(102\) −12.5585 −1.24347
\(103\) −7.54078 −0.743015 −0.371508 0.928430i \(-0.621159\pi\)
−0.371508 + 0.928430i \(0.621159\pi\)
\(104\) 18.4144 1.80568
\(105\) 6.10765 0.596045
\(106\) 8.10007 0.786748
\(107\) −7.86993 −0.760815 −0.380408 0.924819i \(-0.624216\pi\)
−0.380408 + 0.924819i \(0.624216\pi\)
\(108\) −62.0404 −5.96984
\(109\) 13.5078 1.29381 0.646906 0.762570i \(-0.276063\pi\)
0.646906 + 0.762570i \(0.276063\pi\)
\(110\) 26.7695 2.55237
\(111\) −15.5897 −1.47971
\(112\) 7.94917 0.751126
\(113\) 13.1272 1.23490 0.617451 0.786610i \(-0.288165\pi\)
0.617451 + 0.786610i \(0.288165\pi\)
\(114\) 22.5195 2.10915
\(115\) 16.4517 1.53413
\(116\) −16.7701 −1.55706
\(117\) −19.9187 −1.84148
\(118\) 16.7170 1.53892
\(119\) −1.52927 −0.140188
\(120\) −40.7679 −3.72158
\(121\) 18.7541 1.70491
\(122\) −11.8897 −1.07645
\(123\) −16.5487 −1.49215
\(124\) −30.8494 −2.77036
\(125\) 12.1317 1.08509
\(126\) −18.5468 −1.65228
\(127\) 4.84167 0.429629 0.214815 0.976655i \(-0.431085\pi\)
0.214815 + 0.976655i \(0.431085\pi\)
\(128\) 8.32909 0.736195
\(129\) −17.3572 −1.52821
\(130\) −13.5388 −1.18743
\(131\) −15.0343 −1.31355 −0.656775 0.754086i \(-0.728080\pi\)
−0.656775 + 0.754086i \(0.728080\pi\)
\(132\) −80.1895 −6.97960
\(133\) 2.74225 0.237784
\(134\) −10.7354 −0.927395
\(135\) 25.7753 2.21838
\(136\) 10.2077 0.875306
\(137\) −18.6789 −1.59584 −0.797922 0.602761i \(-0.794067\pi\)
−0.797922 + 0.602761i \(0.794067\pi\)
\(138\) −70.7159 −6.01974
\(139\) −1.84353 −0.156366 −0.0781829 0.996939i \(-0.524912\pi\)
−0.0781829 + 0.996939i \(0.524912\pi\)
\(140\) −8.78538 −0.742500
\(141\) −32.0778 −2.70144
\(142\) 20.5039 1.72065
\(143\) −15.0483 −1.25840
\(144\) 57.3943 4.78286
\(145\) 6.96730 0.578603
\(146\) −9.94274 −0.822867
\(147\) −3.19690 −0.263676
\(148\) 22.4246 1.84329
\(149\) 22.7532 1.86401 0.932006 0.362442i \(-0.118057\pi\)
0.932006 + 0.362442i \(0.118057\pi\)
\(150\) −11.0865 −0.905206
\(151\) −15.1476 −1.23269 −0.616345 0.787476i \(-0.711387\pi\)
−0.616345 + 0.787476i \(0.711387\pi\)
\(152\) −18.3043 −1.48467
\(153\) −11.0416 −0.892661
\(154\) −14.0119 −1.12911
\(155\) 12.8167 1.02946
\(156\) 40.5562 3.24710
\(157\) −3.72481 −0.297272 −0.148636 0.988892i \(-0.547488\pi\)
−0.148636 + 0.988892i \(0.547488\pi\)
\(158\) −26.4130 −2.10131
\(159\) 10.0808 0.799460
\(160\) 13.5065 1.06778
\(161\) −8.61124 −0.678661
\(162\) −55.1519 −4.33314
\(163\) 18.9092 1.48108 0.740542 0.672010i \(-0.234569\pi\)
0.740542 + 0.672010i \(0.234569\pi\)
\(164\) 23.8040 1.85878
\(165\) 33.3156 2.59361
\(166\) 19.7650 1.53406
\(167\) 17.4820 1.35280 0.676400 0.736535i \(-0.263539\pi\)
0.676400 + 0.736535i \(0.263539\pi\)
\(168\) 21.3390 1.64634
\(169\) −5.38928 −0.414560
\(170\) −7.50503 −0.575610
\(171\) 19.7995 1.51411
\(172\) 24.9669 1.90371
\(173\) −24.0918 −1.83166 −0.915831 0.401564i \(-0.868467\pi\)
−0.915831 + 0.401564i \(0.868467\pi\)
\(174\) −29.9482 −2.27037
\(175\) −1.35002 −0.102052
\(176\) 43.3605 3.26842
\(177\) 20.8048 1.56379
\(178\) 15.6789 1.17518
\(179\) −20.0774 −1.50066 −0.750329 0.661065i \(-0.770105\pi\)
−0.750329 + 0.661065i \(0.770105\pi\)
\(180\) −63.4319 −4.72794
\(181\) 4.12601 0.306684 0.153342 0.988173i \(-0.450996\pi\)
0.153342 + 0.988173i \(0.450996\pi\)
\(182\) 7.08656 0.525291
\(183\) −14.7972 −1.09384
\(184\) 57.4791 4.23742
\(185\) −9.31653 −0.684965
\(186\) −55.0912 −4.03949
\(187\) −8.34177 −0.610011
\(188\) 46.1414 3.36521
\(189\) −13.4914 −0.981358
\(190\) 13.4578 0.976334
\(191\) −0.642613 −0.0464979 −0.0232489 0.999730i \(-0.507401\pi\)
−0.0232489 + 0.999730i \(0.507401\pi\)
\(192\) −7.23102 −0.521854
\(193\) 23.2420 1.67300 0.836499 0.547968i \(-0.184598\pi\)
0.836499 + 0.547968i \(0.184598\pi\)
\(194\) 19.8217 1.42312
\(195\) −16.8495 −1.20662
\(196\) 4.59849 0.328464
\(197\) −20.1155 −1.43317 −0.716584 0.697500i \(-0.754296\pi\)
−0.716584 + 0.697500i \(0.754296\pi\)
\(198\) −101.168 −7.18969
\(199\) 3.99916 0.283493 0.141747 0.989903i \(-0.454728\pi\)
0.141747 + 0.989903i \(0.454728\pi\)
\(200\) 9.01127 0.637193
\(201\) −13.3605 −0.942379
\(202\) −1.16631 −0.0820615
\(203\) −3.64687 −0.255960
\(204\) 22.4817 1.57404
\(205\) −9.88962 −0.690721
\(206\) 19.3704 1.34960
\(207\) −62.1746 −4.32143
\(208\) −21.9298 −1.52056
\(209\) 14.9582 1.03468
\(210\) −15.6890 −1.08265
\(211\) 12.0797 0.831604 0.415802 0.909455i \(-0.363501\pi\)
0.415802 + 0.909455i \(0.363501\pi\)
\(212\) −14.5005 −0.995896
\(213\) 25.5178 1.74845
\(214\) 20.2159 1.38193
\(215\) −10.3728 −0.707417
\(216\) 90.0540 6.12740
\(217\) −6.70859 −0.455409
\(218\) −34.6982 −2.35006
\(219\) −12.3741 −0.836162
\(220\) −47.9219 −3.23089
\(221\) 4.21889 0.283793
\(222\) 40.0461 2.68772
\(223\) 27.5569 1.84535 0.922673 0.385583i \(-0.126000\pi\)
0.922673 + 0.385583i \(0.126000\pi\)
\(224\) −7.06966 −0.472362
\(225\) −9.74740 −0.649827
\(226\) −33.7205 −2.24305
\(227\) −5.03708 −0.334323 −0.167161 0.985930i \(-0.553460\pi\)
−0.167161 + 0.985930i \(0.553460\pi\)
\(228\) −40.3137 −2.66984
\(229\) 24.9859 1.65112 0.825558 0.564318i \(-0.190861\pi\)
0.825558 + 0.564318i \(0.190861\pi\)
\(230\) −42.2604 −2.78657
\(231\) −17.4382 −1.14735
\(232\) 24.3424 1.59816
\(233\) 5.15979 0.338029 0.169014 0.985614i \(-0.445942\pi\)
0.169014 + 0.985614i \(0.445942\pi\)
\(234\) 51.1661 3.34484
\(235\) −19.1699 −1.25051
\(236\) −29.9261 −1.94802
\(237\) −32.8719 −2.13526
\(238\) 3.92833 0.254636
\(239\) 6.30611 0.407908 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(240\) 48.5507 3.13393
\(241\) −20.1600 −1.29862 −0.649309 0.760524i \(-0.724942\pi\)
−0.649309 + 0.760524i \(0.724942\pi\)
\(242\) −48.1745 −3.09678
\(243\) −28.1641 −1.80673
\(244\) 21.2846 1.36261
\(245\) −1.91049 −0.122057
\(246\) 42.5095 2.71031
\(247\) −7.56520 −0.481362
\(248\) 44.7791 2.84348
\(249\) 24.5982 1.55885
\(250\) −31.1633 −1.97094
\(251\) −21.0740 −1.33018 −0.665089 0.746764i \(-0.731607\pi\)
−0.665089 + 0.746764i \(0.731607\pi\)
\(252\) 33.2019 2.09152
\(253\) −46.9720 −2.95310
\(254\) −12.4371 −0.780371
\(255\) −9.34026 −0.584910
\(256\) −25.9192 −1.61995
\(257\) −19.3546 −1.20731 −0.603654 0.797246i \(-0.706289\pi\)
−0.603654 + 0.797246i \(0.706289\pi\)
\(258\) 44.5862 2.77582
\(259\) 4.87651 0.303012
\(260\) 24.2367 1.50310
\(261\) −26.3310 −1.62985
\(262\) 38.6193 2.38591
\(263\) 1.00432 0.0619291 0.0309645 0.999520i \(-0.490142\pi\)
0.0309645 + 0.999520i \(0.490142\pi\)
\(264\) 116.398 7.16382
\(265\) 6.02437 0.370074
\(266\) −7.04417 −0.431906
\(267\) 19.5129 1.19417
\(268\) 19.2181 1.17393
\(269\) −25.1647 −1.53432 −0.767159 0.641457i \(-0.778330\pi\)
−0.767159 + 0.641457i \(0.778330\pi\)
\(270\) −66.2104 −4.02943
\(271\) 11.2076 0.680815 0.340407 0.940278i \(-0.389435\pi\)
0.340407 + 0.940278i \(0.389435\pi\)
\(272\) −12.1564 −0.737093
\(273\) 8.81946 0.533778
\(274\) 47.9814 2.89866
\(275\) −7.36401 −0.444067
\(276\) 126.593 7.62002
\(277\) −8.45410 −0.507958 −0.253979 0.967210i \(-0.581739\pi\)
−0.253979 + 0.967210i \(0.581739\pi\)
\(278\) 4.73556 0.284020
\(279\) −48.4371 −2.89985
\(280\) 12.7523 0.762097
\(281\) 18.3157 1.09262 0.546311 0.837583i \(-0.316032\pi\)
0.546311 + 0.837583i \(0.316032\pi\)
\(282\) 82.3999 4.90684
\(283\) −12.7408 −0.757360 −0.378680 0.925528i \(-0.623622\pi\)
−0.378680 + 0.925528i \(0.623622\pi\)
\(284\) −36.7054 −2.17806
\(285\) 16.7487 0.992109
\(286\) 38.6553 2.28573
\(287\) 5.17648 0.305558
\(288\) −51.0441 −3.00780
\(289\) −14.6613 −0.862431
\(290\) −17.8973 −1.05096
\(291\) 24.6688 1.44611
\(292\) 17.7992 1.04162
\(293\) −4.58838 −0.268056 −0.134028 0.990978i \(-0.542791\pi\)
−0.134028 + 0.990978i \(0.542791\pi\)
\(294\) 8.21205 0.478936
\(295\) 12.4331 0.723884
\(296\) −32.5502 −1.89194
\(297\) −73.5922 −4.27025
\(298\) −58.4473 −3.38576
\(299\) 23.7563 1.37386
\(300\) 19.8466 1.14584
\(301\) 5.42937 0.312944
\(302\) 38.9103 2.23904
\(303\) −1.45151 −0.0833873
\(304\) 21.7986 1.25024
\(305\) −8.84290 −0.506343
\(306\) 28.3632 1.62141
\(307\) −5.64280 −0.322052 −0.161026 0.986950i \(-0.551480\pi\)
−0.161026 + 0.986950i \(0.551480\pi\)
\(308\) 25.0835 1.42927
\(309\) 24.1071 1.37141
\(310\) −32.9229 −1.86990
\(311\) 16.3065 0.924656 0.462328 0.886709i \(-0.347014\pi\)
0.462328 + 0.886709i \(0.347014\pi\)
\(312\) −58.8690 −3.33280
\(313\) −27.4240 −1.55010 −0.775049 0.631901i \(-0.782275\pi\)
−0.775049 + 0.631901i \(0.782275\pi\)
\(314\) 9.56812 0.539960
\(315\) −13.7941 −0.777207
\(316\) 47.2837 2.65992
\(317\) 9.00618 0.505838 0.252919 0.967488i \(-0.418609\pi\)
0.252919 + 0.967488i \(0.418609\pi\)
\(318\) −25.8951 −1.45213
\(319\) −19.8927 −1.11378
\(320\) −4.32131 −0.241569
\(321\) 25.1594 1.40426
\(322\) 22.1202 1.23271
\(323\) −4.19366 −0.233341
\(324\) 98.7311 5.48506
\(325\) 3.72438 0.206592
\(326\) −48.5731 −2.69022
\(327\) −43.1831 −2.38803
\(328\) −34.5525 −1.90784
\(329\) 10.0340 0.553194
\(330\) −85.5795 −4.71099
\(331\) −24.5290 −1.34824 −0.674118 0.738624i \(-0.735476\pi\)
−0.674118 + 0.738624i \(0.735476\pi\)
\(332\) −35.3826 −1.94187
\(333\) 35.2092 1.92945
\(334\) −44.9070 −2.45720
\(335\) −7.98435 −0.436232
\(336\) −25.4127 −1.38638
\(337\) 24.7723 1.34943 0.674717 0.738077i \(-0.264266\pi\)
0.674717 + 0.738077i \(0.264266\pi\)
\(338\) 13.8437 0.752999
\(339\) −41.9663 −2.27930
\(340\) 13.4353 0.728629
\(341\) −36.5935 −1.98165
\(342\) −50.8601 −2.75020
\(343\) 1.00000 0.0539949
\(344\) −36.2405 −1.95395
\(345\) −52.5944 −2.83159
\(346\) 61.8858 3.32700
\(347\) −9.62086 −0.516475 −0.258238 0.966081i \(-0.583142\pi\)
−0.258238 + 0.966081i \(0.583142\pi\)
\(348\) 53.6123 2.87392
\(349\) −0.971712 −0.0520146 −0.0260073 0.999662i \(-0.508279\pi\)
−0.0260073 + 0.999662i \(0.508279\pi\)
\(350\) 3.46788 0.185366
\(351\) 37.2196 1.98663
\(352\) −38.5631 −2.05542
\(353\) −3.44080 −0.183135 −0.0915677 0.995799i \(-0.529188\pi\)
−0.0915677 + 0.995799i \(0.529188\pi\)
\(354\) −53.4424 −2.84043
\(355\) 15.2496 0.809366
\(356\) −28.0678 −1.48759
\(357\) 4.88893 0.258750
\(358\) 51.5740 2.72577
\(359\) 36.2705 1.91429 0.957143 0.289616i \(-0.0935275\pi\)
0.957143 + 0.289616i \(0.0935275\pi\)
\(360\) 92.0739 4.85272
\(361\) −11.4800 −0.604213
\(362\) −10.5987 −0.557055
\(363\) −59.9548 −3.14681
\(364\) −12.6861 −0.664933
\(365\) −7.39484 −0.387063
\(366\) 38.0103 1.98683
\(367\) −27.2921 −1.42464 −0.712319 0.701856i \(-0.752355\pi\)
−0.712319 + 0.701856i \(0.752355\pi\)
\(368\) −68.4522 −3.56832
\(369\) 37.3751 1.94567
\(370\) 23.9319 1.24416
\(371\) −3.15331 −0.163712
\(372\) 98.6224 5.11334
\(373\) 9.03245 0.467683 0.233841 0.972275i \(-0.424870\pi\)
0.233841 + 0.972275i \(0.424870\pi\)
\(374\) 21.4280 1.10801
\(375\) −38.7837 −2.00278
\(376\) −66.9761 −3.45403
\(377\) 10.0608 0.518158
\(378\) 34.6562 1.78252
\(379\) −23.5625 −1.21032 −0.605161 0.796103i \(-0.706891\pi\)
−0.605161 + 0.796103i \(0.706891\pi\)
\(380\) −24.0918 −1.23588
\(381\) −15.4783 −0.792980
\(382\) 1.65071 0.0844579
\(383\) 13.8731 0.708880 0.354440 0.935079i \(-0.384672\pi\)
0.354440 + 0.935079i \(0.384672\pi\)
\(384\) −26.6273 −1.35882
\(385\) −10.4212 −0.531114
\(386\) −59.7031 −3.03881
\(387\) 39.2010 1.99270
\(388\) −35.4841 −1.80143
\(389\) −19.1588 −0.971390 −0.485695 0.874128i \(-0.661433\pi\)
−0.485695 + 0.874128i \(0.661433\pi\)
\(390\) 43.2822 2.19168
\(391\) 13.1689 0.665982
\(392\) −6.67489 −0.337133
\(393\) 48.0631 2.42446
\(394\) 51.6717 2.60318
\(395\) −19.6445 −0.988421
\(396\) 181.107 9.10098
\(397\) 2.53541 0.127249 0.0636243 0.997974i \(-0.479734\pi\)
0.0636243 + 0.997974i \(0.479734\pi\)
\(398\) −10.2729 −0.514932
\(399\) −8.76671 −0.438884
\(400\) −10.7316 −0.536578
\(401\) 12.3799 0.618223 0.309111 0.951026i \(-0.399968\pi\)
0.309111 + 0.951026i \(0.399968\pi\)
\(402\) 34.3199 1.71172
\(403\) 18.5073 0.921916
\(404\) 2.08789 0.103877
\(405\) −41.0188 −2.03824
\(406\) 9.36790 0.464921
\(407\) 26.6000 1.31851
\(408\) −32.6331 −1.61558
\(409\) 15.1585 0.749539 0.374770 0.927118i \(-0.377722\pi\)
0.374770 + 0.927118i \(0.377722\pi\)
\(410\) 25.4040 1.25461
\(411\) 59.7145 2.94550
\(412\) −34.6762 −1.70838
\(413\) −6.50781 −0.320228
\(414\) 159.711 7.84938
\(415\) 14.7001 0.721598
\(416\) 19.5035 0.956236
\(417\) 5.89357 0.288609
\(418\) −38.4241 −1.87938
\(419\) 22.0922 1.07927 0.539636 0.841898i \(-0.318562\pi\)
0.539636 + 0.841898i \(0.318562\pi\)
\(420\) 28.0860 1.37046
\(421\) −4.78276 −0.233098 −0.116549 0.993185i \(-0.537183\pi\)
−0.116549 + 0.993185i \(0.537183\pi\)
\(422\) −31.0299 −1.51051
\(423\) 72.4474 3.52251
\(424\) 21.0480 1.02218
\(425\) 2.06456 0.100146
\(426\) −65.5489 −3.17585
\(427\) 4.62860 0.223994
\(428\) −36.1899 −1.74930
\(429\) 48.1077 2.32266
\(430\) 26.6451 1.28494
\(431\) 14.4177 0.694475 0.347237 0.937777i \(-0.387120\pi\)
0.347237 + 0.937777i \(0.387120\pi\)
\(432\) −107.246 −5.15986
\(433\) −14.9463 −0.718272 −0.359136 0.933285i \(-0.616929\pi\)
−0.359136 + 0.933285i \(0.616929\pi\)
\(434\) 17.2327 0.827196
\(435\) −22.2738 −1.06795
\(436\) 62.1155 2.97479
\(437\) −23.6142 −1.12962
\(438\) 31.7859 1.51879
\(439\) −15.6274 −0.745857 −0.372928 0.927860i \(-0.621646\pi\)
−0.372928 + 0.927860i \(0.621646\pi\)
\(440\) 69.5604 3.31616
\(441\) 7.22017 0.343817
\(442\) −10.8373 −0.515477
\(443\) 33.5131 1.59225 0.796127 0.605129i \(-0.206879\pi\)
0.796127 + 0.605129i \(0.206879\pi\)
\(444\) −71.6892 −3.40222
\(445\) 11.6611 0.552787
\(446\) −70.7869 −3.35186
\(447\) −72.7396 −3.44047
\(448\) 2.26189 0.106864
\(449\) 2.68273 0.126606 0.0633029 0.997994i \(-0.479837\pi\)
0.0633029 + 0.997994i \(0.479837\pi\)
\(450\) 25.0387 1.18033
\(451\) 28.2363 1.32960
\(452\) 60.3653 2.83934
\(453\) 48.4252 2.27521
\(454\) 12.9390 0.607258
\(455\) 5.27058 0.247088
\(456\) 58.5169 2.74030
\(457\) 28.4747 1.33199 0.665995 0.745956i \(-0.268007\pi\)
0.665995 + 0.745956i \(0.268007\pi\)
\(458\) −64.1826 −2.99906
\(459\) 20.6321 0.963025
\(460\) 75.6531 3.52734
\(461\) 2.40870 0.112184 0.0560921 0.998426i \(-0.482136\pi\)
0.0560921 + 0.998426i \(0.482136\pi\)
\(462\) 44.7945 2.08403
\(463\) 17.3148 0.804688 0.402344 0.915489i \(-0.368196\pi\)
0.402344 + 0.915489i \(0.368196\pi\)
\(464\) −28.9895 −1.34581
\(465\) −40.9737 −1.90011
\(466\) −13.2542 −0.613990
\(467\) 7.81206 0.361499 0.180749 0.983529i \(-0.442148\pi\)
0.180749 + 0.983529i \(0.442148\pi\)
\(468\) −91.5959 −4.23402
\(469\) 4.17921 0.192978
\(470\) 49.2428 2.27140
\(471\) 11.9078 0.548685
\(472\) 43.4389 1.99944
\(473\) 29.6157 1.36173
\(474\) 84.4398 3.87845
\(475\) −3.70211 −0.169864
\(476\) −7.03236 −0.322328
\(477\) −22.7674 −1.04245
\(478\) −16.1988 −0.740917
\(479\) −11.9759 −0.547192 −0.273596 0.961845i \(-0.588213\pi\)
−0.273596 + 0.961845i \(0.588213\pi\)
\(480\) −43.1790 −1.97084
\(481\) −13.4531 −0.613408
\(482\) 51.7860 2.35879
\(483\) 27.5293 1.25263
\(484\) 86.2404 3.92002
\(485\) 14.7422 0.669411
\(486\) 72.3465 3.28170
\(487\) 19.5404 0.885461 0.442731 0.896655i \(-0.354010\pi\)
0.442731 + 0.896655i \(0.354010\pi\)
\(488\) −30.8954 −1.39857
\(489\) −60.4508 −2.73368
\(490\) 4.90758 0.221702
\(491\) 18.6232 0.840453 0.420226 0.907419i \(-0.361951\pi\)
0.420226 + 0.907419i \(0.361951\pi\)
\(492\) −76.0991 −3.43081
\(493\) 5.57705 0.251178
\(494\) 19.4331 0.874339
\(495\) −75.2429 −3.38191
\(496\) −53.3277 −2.39448
\(497\) −7.98204 −0.358043
\(498\) −63.1867 −2.83146
\(499\) −22.0268 −0.986053 −0.493026 0.870014i \(-0.664109\pi\)
−0.493026 + 0.870014i \(0.664109\pi\)
\(500\) 55.7874 2.49489
\(501\) −55.8883 −2.49690
\(502\) 54.1339 2.41611
\(503\) 34.5399 1.54006 0.770030 0.638008i \(-0.220241\pi\)
0.770030 + 0.638008i \(0.220241\pi\)
\(504\) −48.1938 −2.14672
\(505\) −0.867436 −0.0386004
\(506\) 120.659 5.36397
\(507\) 17.2290 0.765166
\(508\) 22.2644 0.987823
\(509\) −32.5629 −1.44332 −0.721661 0.692246i \(-0.756621\pi\)
−0.721661 + 0.692246i \(0.756621\pi\)
\(510\) 23.9928 1.06242
\(511\) 3.87065 0.171227
\(512\) 49.9218 2.20625
\(513\) −36.9970 −1.63346
\(514\) 49.7173 2.19293
\(515\) 14.4066 0.634830
\(516\) −79.8168 −3.51374
\(517\) 54.7329 2.40715
\(518\) −12.5266 −0.550385
\(519\) 77.0189 3.38076
\(520\) −35.1805 −1.54277
\(521\) −26.2070 −1.14815 −0.574075 0.818803i \(-0.694638\pi\)
−0.574075 + 0.818803i \(0.694638\pi\)
\(522\) 67.6378 2.96043
\(523\) −3.44571 −0.150671 −0.0753353 0.997158i \(-0.524003\pi\)
−0.0753353 + 0.997158i \(0.524003\pi\)
\(524\) −69.1350 −3.02018
\(525\) 4.31589 0.188361
\(526\) −2.57985 −0.112487
\(527\) 10.2593 0.446901
\(528\) −138.619 −6.03263
\(529\) 51.1535 2.22406
\(530\) −15.4751 −0.672196
\(531\) −46.9875 −2.03908
\(532\) 12.6102 0.546723
\(533\) −14.2806 −0.618563
\(534\) −50.1238 −2.16907
\(535\) 15.0354 0.650039
\(536\) −27.8958 −1.20491
\(537\) 64.1855 2.76981
\(538\) 64.6418 2.78691
\(539\) 5.45473 0.234952
\(540\) 118.528 5.10061
\(541\) −0.978042 −0.0420493 −0.0210247 0.999779i \(-0.506693\pi\)
−0.0210247 + 0.999779i \(0.506693\pi\)
\(542\) −28.7896 −1.23662
\(543\) −13.1904 −0.566055
\(544\) 10.8114 0.463537
\(545\) −25.8065 −1.10543
\(546\) −22.6550 −0.969545
\(547\) 1.89014 0.0808167 0.0404084 0.999183i \(-0.487134\pi\)
0.0404084 + 0.999183i \(0.487134\pi\)
\(548\) −85.8947 −3.66924
\(549\) 33.4193 1.42630
\(550\) 18.9163 0.806595
\(551\) −10.0006 −0.426041
\(552\) −183.755 −7.82113
\(553\) 10.2824 0.437253
\(554\) 21.7165 0.922646
\(555\) 29.7840 1.26426
\(556\) −8.47744 −0.359524
\(557\) −30.7042 −1.30098 −0.650489 0.759516i \(-0.725436\pi\)
−0.650489 + 0.759516i \(0.725436\pi\)
\(558\) 124.423 5.26725
\(559\) −14.9783 −0.633514
\(560\) −15.1868 −0.641760
\(561\) 26.6678 1.12592
\(562\) −47.0485 −1.98462
\(563\) −8.17735 −0.344634 −0.172317 0.985042i \(-0.555125\pi\)
−0.172317 + 0.985042i \(0.555125\pi\)
\(564\) −147.510 −6.21127
\(565\) −25.0794 −1.05510
\(566\) 32.7279 1.37566
\(567\) 21.4703 0.901668
\(568\) 53.2793 2.23555
\(569\) −37.3294 −1.56493 −0.782464 0.622696i \(-0.786037\pi\)
−0.782464 + 0.622696i \(0.786037\pi\)
\(570\) −43.0233 −1.80205
\(571\) 27.2548 1.14058 0.570289 0.821444i \(-0.306831\pi\)
0.570289 + 0.821444i \(0.306831\pi\)
\(572\) −69.1993 −2.89337
\(573\) 2.05437 0.0858225
\(574\) −13.2971 −0.555011
\(575\) 11.6254 0.484812
\(576\) 16.3312 0.680467
\(577\) −32.2780 −1.34375 −0.671875 0.740665i \(-0.734511\pi\)
−0.671875 + 0.740665i \(0.734511\pi\)
\(578\) 37.6613 1.56650
\(579\) −74.3025 −3.08790
\(580\) 32.0391 1.33035
\(581\) −7.69439 −0.319217
\(582\) −63.3680 −2.62669
\(583\) −17.2004 −0.712369
\(584\) −25.8362 −1.06911
\(585\) 38.0544 1.57336
\(586\) 11.7864 0.486893
\(587\) −16.5558 −0.683329 −0.341665 0.939822i \(-0.610991\pi\)
−0.341665 + 0.939822i \(0.610991\pi\)
\(588\) −14.7009 −0.606256
\(589\) −18.3966 −0.758021
\(590\) −31.9376 −1.31485
\(591\) 64.3072 2.64524
\(592\) 38.7642 1.59320
\(593\) 24.0201 0.986387 0.493194 0.869920i \(-0.335829\pi\)
0.493194 + 0.869920i \(0.335829\pi\)
\(594\) 189.040 7.75641
\(595\) 2.92166 0.119777
\(596\) 104.630 4.28583
\(597\) −12.7849 −0.523252
\(598\) −61.0241 −2.49546
\(599\) −2.68332 −0.109637 −0.0548187 0.998496i \(-0.517458\pi\)
−0.0548187 + 0.998496i \(0.517458\pi\)
\(600\) −28.8081 −1.17609
\(601\) −12.0529 −0.491647 −0.245824 0.969315i \(-0.579058\pi\)
−0.245824 + 0.969315i \(0.579058\pi\)
\(602\) −13.9467 −0.568426
\(603\) 30.1746 1.22881
\(604\) −69.6559 −2.83426
\(605\) −35.8294 −1.45667
\(606\) 3.72858 0.151463
\(607\) 20.7008 0.840220 0.420110 0.907473i \(-0.361991\pi\)
0.420110 + 0.907473i \(0.361991\pi\)
\(608\) −19.3868 −0.786239
\(609\) 11.6587 0.472433
\(610\) 22.7152 0.919713
\(611\) −27.6814 −1.11987
\(612\) −50.7748 −2.05245
\(613\) −7.26437 −0.293405 −0.146702 0.989181i \(-0.546866\pi\)
−0.146702 + 0.989181i \(0.546866\pi\)
\(614\) 14.4950 0.584969
\(615\) 31.6161 1.27489
\(616\) −36.4097 −1.46699
\(617\) 45.1295 1.81684 0.908422 0.418055i \(-0.137288\pi\)
0.908422 + 0.418055i \(0.137288\pi\)
\(618\) −61.9252 −2.49100
\(619\) 7.39544 0.297248 0.148624 0.988894i \(-0.452516\pi\)
0.148624 + 0.988894i \(0.452516\pi\)
\(620\) 58.9375 2.36699
\(621\) 116.178 4.66207
\(622\) −41.8873 −1.67953
\(623\) −6.10370 −0.244539
\(624\) 70.1073 2.80654
\(625\) −16.4273 −0.657093
\(626\) 70.4456 2.81557
\(627\) −47.8200 −1.90975
\(628\) −17.1285 −0.683503
\(629\) −7.45752 −0.297351
\(630\) 35.4335 1.41171
\(631\) −27.0224 −1.07574 −0.537872 0.843027i \(-0.680771\pi\)
−0.537872 + 0.843027i \(0.680771\pi\)
\(632\) −68.6341 −2.73012
\(633\) −38.6177 −1.53492
\(634\) −23.1347 −0.918795
\(635\) −9.24997 −0.367074
\(636\) 46.3565 1.83816
\(637\) −2.75875 −0.109306
\(638\) 51.0993 2.02304
\(639\) −57.6317 −2.27987
\(640\) −15.9127 −0.629003
\(641\) −49.4139 −1.95173 −0.975865 0.218375i \(-0.929924\pi\)
−0.975865 + 0.218375i \(0.929924\pi\)
\(642\) −64.6283 −2.55067
\(643\) 16.5617 0.653128 0.326564 0.945175i \(-0.394109\pi\)
0.326564 + 0.945175i \(0.394109\pi\)
\(644\) −39.5987 −1.56041
\(645\) 33.1607 1.30570
\(646\) 10.7725 0.423837
\(647\) 19.8062 0.778661 0.389331 0.921098i \(-0.372706\pi\)
0.389331 + 0.921098i \(0.372706\pi\)
\(648\) −143.312 −5.62983
\(649\) −35.4983 −1.39343
\(650\) −9.56703 −0.375250
\(651\) 21.4467 0.840562
\(652\) 86.9539 3.40538
\(653\) −18.8671 −0.738326 −0.369163 0.929365i \(-0.620356\pi\)
−0.369163 + 0.929365i \(0.620356\pi\)
\(654\) 110.927 4.33757
\(655\) 28.7228 1.12229
\(656\) 41.1487 1.60659
\(657\) 27.9467 1.09031
\(658\) −25.7749 −1.00481
\(659\) 14.9081 0.580739 0.290370 0.956915i \(-0.406222\pi\)
0.290370 + 0.956915i \(0.406222\pi\)
\(660\) 153.201 5.96336
\(661\) −27.6019 −1.07359 −0.536795 0.843713i \(-0.680365\pi\)
−0.536795 + 0.843713i \(0.680365\pi\)
\(662\) 63.0090 2.44891
\(663\) −13.4874 −0.523806
\(664\) 51.3593 1.99313
\(665\) −5.23905 −0.203162
\(666\) −90.4438 −3.50463
\(667\) 31.4040 1.21597
\(668\) 80.3910 3.11042
\(669\) −88.0966 −3.40601
\(670\) 20.5098 0.792364
\(671\) 25.2478 0.974679
\(672\) 22.6010 0.871852
\(673\) −26.3053 −1.01399 −0.506997 0.861948i \(-0.669245\pi\)
−0.506997 + 0.861948i \(0.669245\pi\)
\(674\) −63.6339 −2.45109
\(675\) 18.2138 0.701049
\(676\) −24.7826 −0.953175
\(677\) −14.3770 −0.552551 −0.276276 0.961078i \(-0.589100\pi\)
−0.276276 + 0.961078i \(0.589100\pi\)
\(678\) 107.801 4.14007
\(679\) −7.71647 −0.296131
\(680\) −19.5018 −0.747859
\(681\) 16.1030 0.617070
\(682\) 93.9997 3.59944
\(683\) −10.7321 −0.410652 −0.205326 0.978694i \(-0.565825\pi\)
−0.205326 + 0.978694i \(0.565825\pi\)
\(684\) 91.0480 3.48131
\(685\) 35.6858 1.36348
\(686\) −2.56875 −0.0980755
\(687\) −79.8774 −3.04751
\(688\) 43.1590 1.64542
\(689\) 8.69920 0.331413
\(690\) 135.102 5.14325
\(691\) −5.04768 −0.192023 −0.0960113 0.995380i \(-0.530609\pi\)
−0.0960113 + 0.995380i \(0.530609\pi\)
\(692\) −110.786 −4.21144
\(693\) 39.3840 1.49608
\(694\) 24.7136 0.938116
\(695\) 3.52204 0.133599
\(696\) −77.8203 −2.94977
\(697\) −7.91626 −0.299850
\(698\) 2.49609 0.0944784
\(699\) −16.4953 −0.623910
\(700\) −6.20808 −0.234643
\(701\) −15.7907 −0.596406 −0.298203 0.954503i \(-0.596387\pi\)
−0.298203 + 0.954503i \(0.596387\pi\)
\(702\) −95.6079 −3.60849
\(703\) 13.3726 0.504358
\(704\) 12.3380 0.465005
\(705\) 61.2843 2.30810
\(706\) 8.83857 0.332644
\(707\) 0.454038 0.0170759
\(708\) 95.6708 3.59553
\(709\) −30.7089 −1.15330 −0.576649 0.816992i \(-0.695640\pi\)
−0.576649 + 0.816992i \(0.695640\pi\)
\(710\) −39.1725 −1.47012
\(711\) 74.2408 2.78425
\(712\) 40.7415 1.52685
\(713\) 57.7693 2.16348
\(714\) −12.5585 −0.469989
\(715\) 28.7496 1.07517
\(716\) −92.3260 −3.45038
\(717\) −20.1600 −0.752888
\(718\) −93.1701 −3.47708
\(719\) 40.5149 1.51095 0.755475 0.655178i \(-0.227406\pi\)
0.755475 + 0.655178i \(0.227406\pi\)
\(720\) −109.651 −4.08646
\(721\) −7.54078 −0.280833
\(722\) 29.4894 1.09748
\(723\) 64.4495 2.39690
\(724\) 18.9734 0.705141
\(725\) 4.92336 0.182849
\(726\) 154.009 5.71582
\(727\) 34.3785 1.27503 0.637514 0.770438i \(-0.279963\pi\)
0.637514 + 0.770438i \(0.279963\pi\)
\(728\) 18.4144 0.682483
\(729\) 25.6268 0.949139
\(730\) 18.9955 0.703055
\(731\) −8.30299 −0.307097
\(732\) −68.0447 −2.51501
\(733\) 13.7131 0.506504 0.253252 0.967400i \(-0.418500\pi\)
0.253252 + 0.967400i \(0.418500\pi\)
\(734\) 70.1067 2.58769
\(735\) 6.10765 0.225284
\(736\) 60.8786 2.24401
\(737\) 22.7965 0.839719
\(738\) −96.0073 −3.53408
\(739\) 52.7242 1.93949 0.969745 0.244120i \(-0.0784991\pi\)
0.969745 + 0.244120i \(0.0784991\pi\)
\(740\) −42.8420 −1.57490
\(741\) 24.1852 0.888465
\(742\) 8.10007 0.297363
\(743\) 33.1565 1.21639 0.608197 0.793786i \(-0.291893\pi\)
0.608197 + 0.793786i \(0.291893\pi\)
\(744\) −143.154 −5.24829
\(745\) −43.4697 −1.59261
\(746\) −23.2021 −0.849491
\(747\) −55.5548 −2.03264
\(748\) −38.3596 −1.40257
\(749\) −7.86993 −0.287561
\(750\) 99.6258 3.63782
\(751\) 49.9148 1.82142 0.910709 0.413049i \(-0.135536\pi\)
0.910709 + 0.413049i \(0.135536\pi\)
\(752\) 79.7621 2.90863
\(753\) 67.3714 2.45515
\(754\) −25.8437 −0.941173
\(755\) 28.9393 1.05321
\(756\) −62.0404 −2.25639
\(757\) 4.92985 0.179178 0.0895892 0.995979i \(-0.471445\pi\)
0.0895892 + 0.995979i \(0.471445\pi\)
\(758\) 60.5262 2.19841
\(759\) 150.165 5.45063
\(760\) 34.9701 1.26850
\(761\) 7.91919 0.287071 0.143535 0.989645i \(-0.454153\pi\)
0.143535 + 0.989645i \(0.454153\pi\)
\(762\) 39.7600 1.44035
\(763\) 13.5078 0.489015
\(764\) −2.95505 −0.106910
\(765\) 21.0949 0.762688
\(766\) −35.6365 −1.28760
\(767\) 17.9534 0.648261
\(768\) 82.8610 2.98999
\(769\) 53.3536 1.92398 0.961990 0.273084i \(-0.0880437\pi\)
0.961990 + 0.273084i \(0.0880437\pi\)
\(770\) 26.7695 0.964706
\(771\) 61.8748 2.22837
\(772\) 106.878 3.84664
\(773\) 25.4336 0.914783 0.457392 0.889265i \(-0.348784\pi\)
0.457392 + 0.889265i \(0.348784\pi\)
\(774\) −100.698 −3.61950
\(775\) 9.05675 0.325328
\(776\) 51.5066 1.84898
\(777\) −15.5897 −0.559278
\(778\) 49.2143 1.76442
\(779\) 14.1952 0.508597
\(780\) −77.4823 −2.77431
\(781\) −43.5399 −1.55798
\(782\) −33.8278 −1.20968
\(783\) 49.2015 1.75832
\(784\) 7.94917 0.283899
\(785\) 7.11622 0.253989
\(786\) −123.462 −4.40375
\(787\) −21.0090 −0.748890 −0.374445 0.927249i \(-0.622167\pi\)
−0.374445 + 0.927249i \(0.622167\pi\)
\(788\) −92.5009 −3.29521
\(789\) −3.21071 −0.114304
\(790\) 50.4618 1.79535
\(791\) 13.1272 0.466749
\(792\) −262.884 −9.34119
\(793\) −12.7692 −0.453447
\(794\) −6.51285 −0.231132
\(795\) −19.2593 −0.683057
\(796\) 18.3901 0.651821
\(797\) −12.3246 −0.436560 −0.218280 0.975886i \(-0.570045\pi\)
−0.218280 + 0.975886i \(0.570045\pi\)
\(798\) 22.5195 0.797182
\(799\) −15.3448 −0.542859
\(800\) 9.54421 0.337439
\(801\) −44.0697 −1.55713
\(802\) −31.8009 −1.12293
\(803\) 21.1133 0.745073
\(804\) −61.4383 −2.16676
\(805\) 16.4517 0.579846
\(806\) −47.5408 −1.67455
\(807\) 80.4489 2.83194
\(808\) −3.03066 −0.106618
\(809\) 18.3583 0.645443 0.322722 0.946494i \(-0.395402\pi\)
0.322722 + 0.946494i \(0.395402\pi\)
\(810\) 105.367 3.70223
\(811\) −33.1118 −1.16271 −0.581356 0.813649i \(-0.697478\pi\)
−0.581356 + 0.813649i \(0.697478\pi\)
\(812\) −16.7701 −0.588515
\(813\) −35.8296 −1.25660
\(814\) −68.3289 −2.39493
\(815\) −36.1259 −1.26543
\(816\) 38.8629 1.36048
\(817\) 14.8887 0.520890
\(818\) −38.9384 −1.36145
\(819\) −19.9187 −0.696014
\(820\) −45.4774 −1.58814
\(821\) 44.5159 1.55361 0.776807 0.629739i \(-0.216838\pi\)
0.776807 + 0.629739i \(0.216838\pi\)
\(822\) −153.392 −5.35015
\(823\) 49.9970 1.74278 0.871392 0.490587i \(-0.163218\pi\)
0.871392 + 0.490587i \(0.163218\pi\)
\(824\) 50.3339 1.75346
\(825\) 23.5420 0.819628
\(826\) 16.7170 0.581657
\(827\) −35.1271 −1.22149 −0.610744 0.791828i \(-0.709130\pi\)
−0.610744 + 0.791828i \(0.709130\pi\)
\(828\) −285.910 −9.93604
\(829\) −39.1375 −1.35930 −0.679650 0.733536i \(-0.737869\pi\)
−0.679650 + 0.733536i \(0.737869\pi\)
\(830\) −37.7609 −1.31070
\(831\) 27.0269 0.937553
\(832\) −6.23999 −0.216333
\(833\) −1.52927 −0.0529862
\(834\) −15.1391 −0.524225
\(835\) −33.3992 −1.15583
\(836\) 68.7854 2.37899
\(837\) 90.5085 3.12843
\(838\) −56.7493 −1.96037
\(839\) 23.3994 0.807838 0.403919 0.914795i \(-0.367648\pi\)
0.403919 + 0.914795i \(0.367648\pi\)
\(840\) −40.7679 −1.40663
\(841\) −15.7004 −0.541392
\(842\) 12.2857 0.423394
\(843\) −58.5534 −2.01669
\(844\) 55.5486 1.91206
\(845\) 10.2962 0.354199
\(846\) −186.099 −6.39823
\(847\) 18.7541 0.644397
\(848\) −25.0662 −0.860776
\(849\) 40.7309 1.39788
\(850\) −5.30334 −0.181903
\(851\) −41.9928 −1.43949
\(852\) 117.343 4.02012
\(853\) −0.274564 −0.00940088 −0.00470044 0.999989i \(-0.501496\pi\)
−0.00470044 + 0.999989i \(0.501496\pi\)
\(854\) −11.8897 −0.406858
\(855\) −37.8268 −1.29365
\(856\) 52.5310 1.79547
\(857\) 18.4628 0.630679 0.315339 0.948979i \(-0.397882\pi\)
0.315339 + 0.948979i \(0.397882\pi\)
\(858\) −123.577 −4.21885
\(859\) −5.05933 −0.172622 −0.0863111 0.996268i \(-0.527508\pi\)
−0.0863111 + 0.996268i \(0.527508\pi\)
\(860\) −47.6991 −1.62653
\(861\) −16.5487 −0.563978
\(862\) −37.0355 −1.26143
\(863\) −1.00000 −0.0340404
\(864\) 95.3800 3.24489
\(865\) 46.0271 1.56497
\(866\) 38.3933 1.30466
\(867\) 46.8708 1.59181
\(868\) −30.8494 −1.04710
\(869\) 56.0878 1.90265
\(870\) 57.2158 1.93980
\(871\) −11.5294 −0.390660
\(872\) −90.1631 −3.05331
\(873\) −55.7142 −1.88564
\(874\) 60.6591 2.05182
\(875\) 12.1317 0.410125
\(876\) −56.9021 −1.92254
\(877\) 1.82136 0.0615030 0.0307515 0.999527i \(-0.490210\pi\)
0.0307515 + 0.999527i \(0.490210\pi\)
\(878\) 40.1430 1.35476
\(879\) 14.6686 0.494760
\(880\) −82.8399 −2.79253
\(881\) −22.2482 −0.749560 −0.374780 0.927114i \(-0.622282\pi\)
−0.374780 + 0.927114i \(0.622282\pi\)
\(882\) −18.5468 −0.624504
\(883\) −10.7783 −0.362720 −0.181360 0.983417i \(-0.558050\pi\)
−0.181360 + 0.983417i \(0.558050\pi\)
\(884\) 19.4005 0.652511
\(885\) −39.7474 −1.33609
\(886\) −86.0868 −2.89214
\(887\) −53.5965 −1.79959 −0.899797 0.436308i \(-0.856286\pi\)
−0.899797 + 0.436308i \(0.856286\pi\)
\(888\) 104.060 3.49201
\(889\) 4.84167 0.162385
\(890\) −29.9544 −1.00407
\(891\) 117.115 3.92349
\(892\) 126.720 4.24291
\(893\) 27.5159 0.920783
\(894\) 186.850 6.24920
\(895\) 38.3578 1.28216
\(896\) 8.32909 0.278255
\(897\) −75.9465 −2.53578
\(898\) −6.89127 −0.229965
\(899\) 24.4653 0.815964
\(900\) −44.8234 −1.49411
\(901\) 4.82227 0.160653
\(902\) −72.5321 −2.41505
\(903\) −17.3572 −0.577610
\(904\) −87.6225 −2.91428
\(905\) −7.88270 −0.262030
\(906\) −124.392 −4.13266
\(907\) −49.6902 −1.64994 −0.824968 0.565179i \(-0.808807\pi\)
−0.824968 + 0.565179i \(0.808807\pi\)
\(908\) −23.1630 −0.768691
\(909\) 3.27823 0.108732
\(910\) −13.5388 −0.448807
\(911\) −25.5240 −0.845647 −0.422823 0.906212i \(-0.638961\pi\)
−0.422823 + 0.906212i \(0.638961\pi\)
\(912\) −69.6880 −2.30760
\(913\) −41.9708 −1.38903
\(914\) −73.1445 −2.41940
\(915\) 28.2699 0.934573
\(916\) 114.898 3.79632
\(917\) −15.0343 −0.496475
\(918\) −52.9988 −1.74922
\(919\) −2.50207 −0.0825358 −0.0412679 0.999148i \(-0.513140\pi\)
−0.0412679 + 0.999148i \(0.513140\pi\)
\(920\) −109.813 −3.62044
\(921\) 18.0395 0.594421
\(922\) −6.18735 −0.203770
\(923\) 22.0205 0.724813
\(924\) −80.1895 −2.63804
\(925\) −6.58341 −0.216461
\(926\) −44.4775 −1.46162
\(927\) −54.4457 −1.78823
\(928\) 25.7821 0.846339
\(929\) 44.1712 1.44921 0.724606 0.689164i \(-0.242022\pi\)
0.724606 + 0.689164i \(0.242022\pi\)
\(930\) 105.251 3.45133
\(931\) 2.74225 0.0898737
\(932\) 23.7273 0.777212
\(933\) −52.1302 −1.70667
\(934\) −20.0672 −0.656620
\(935\) 15.9369 0.521192
\(936\) 132.955 4.34577
\(937\) 46.7473 1.52717 0.763584 0.645708i \(-0.223438\pi\)
0.763584 + 0.645708i \(0.223438\pi\)
\(938\) −10.7354 −0.350522
\(939\) 87.6719 2.86106
\(940\) −88.1528 −2.87523
\(941\) 13.1809 0.429687 0.214843 0.976649i \(-0.431076\pi\)
0.214843 + 0.976649i \(0.431076\pi\)
\(942\) −30.5883 −0.996622
\(943\) −44.5759 −1.45159
\(944\) −51.7317 −1.68372
\(945\) 25.7753 0.838470
\(946\) −76.0755 −2.47343
\(947\) 40.6263 1.32018 0.660088 0.751188i \(-0.270519\pi\)
0.660088 + 0.751188i \(0.270519\pi\)
\(948\) −151.161 −4.90949
\(949\) −10.6782 −0.346628
\(950\) 9.50980 0.308539
\(951\) −28.7919 −0.933640
\(952\) 10.2077 0.330835
\(953\) 24.5735 0.796012 0.398006 0.917383i \(-0.369702\pi\)
0.398006 + 0.917383i \(0.369702\pi\)
\(954\) 58.4839 1.89348
\(955\) 1.22771 0.0397277
\(956\) 28.9986 0.937882
\(957\) 63.5948 2.05573
\(958\) 30.7631 0.993911
\(959\) −18.6789 −0.603172
\(960\) 13.8148 0.445871
\(961\) 14.0051 0.451779
\(962\) 34.5577 1.11418
\(963\) −56.8222 −1.83107
\(964\) −92.7056 −2.98585
\(965\) −44.4037 −1.42941
\(966\) −70.7159 −2.27525
\(967\) 36.7244 1.18098 0.590488 0.807046i \(-0.298935\pi\)
0.590488 + 0.807046i \(0.298935\pi\)
\(968\) −125.181 −4.02348
\(969\) 13.4067 0.430685
\(970\) −37.8692 −1.21591
\(971\) −32.5720 −1.04529 −0.522643 0.852552i \(-0.675054\pi\)
−0.522643 + 0.852552i \(0.675054\pi\)
\(972\) −129.512 −4.15411
\(973\) −1.84353 −0.0591007
\(974\) −50.1945 −1.60834
\(975\) −11.9065 −0.381313
\(976\) 36.7935 1.17773
\(977\) −58.0328 −1.85663 −0.928317 0.371789i \(-0.878745\pi\)
−0.928317 + 0.371789i \(0.878745\pi\)
\(978\) 155.283 4.96541
\(979\) −33.2940 −1.06408
\(980\) −8.78538 −0.280639
\(981\) 97.5285 3.11385
\(982\) −47.8384 −1.52658
\(983\) 12.3076 0.392551 0.196275 0.980549i \(-0.437115\pi\)
0.196275 + 0.980549i \(0.437115\pi\)
\(984\) 110.461 3.52136
\(985\) 38.4304 1.22450
\(986\) −14.3261 −0.456235
\(987\) −32.0778 −1.02105
\(988\) −34.7886 −1.10677
\(989\) −46.7536 −1.48668
\(990\) 193.280 6.14285
\(991\) 14.2905 0.453951 0.226976 0.973900i \(-0.427116\pi\)
0.226976 + 0.973900i \(0.427116\pi\)
\(992\) 47.4274 1.50582
\(993\) 78.4168 2.48848
\(994\) 20.5039 0.650344
\(995\) −7.64036 −0.242216
\(996\) 113.115 3.58418
\(997\) 16.1716 0.512159 0.256079 0.966656i \(-0.417569\pi\)
0.256079 + 0.966656i \(0.417569\pi\)
\(998\) 56.5813 1.79105
\(999\) −65.7912 −2.08154
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 \(a_p\))