Properties

Label 6025.2.a.h.1.1
Level 6025
Weight 2
Character 6025.1
Self dual Yes
Analytic conductor 48.110
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6025.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1098672178\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
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 1.1
Root \(2.70063\)
Character \(\chi\) = 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.70063 q^{2}\) \(+2.50808 q^{3}\) \(+5.29342 q^{4}\) \(-6.77340 q^{6}\) \(-0.354992 q^{7}\) \(-8.89432 q^{8}\) \(+3.29045 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.70063 q^{2}\) \(+2.50808 q^{3}\) \(+5.29342 q^{4}\) \(-6.77340 q^{6}\) \(-0.354992 q^{7}\) \(-8.89432 q^{8}\) \(+3.29045 q^{9}\) \(+4.18781 q^{11}\) \(+13.2763 q^{12}\) \(+3.72447 q^{13}\) \(+0.958703 q^{14}\) \(+13.4334 q^{16}\) \(+6.46259 q^{17}\) \(-8.88631 q^{18}\) \(-1.31002 q^{19}\) \(-0.890347 q^{21}\) \(-11.3097 q^{22}\) \(+4.10799 q^{23}\) \(-22.3076 q^{24}\) \(-10.0584 q^{26}\) \(+0.728479 q^{27}\) \(-1.87912 q^{28}\) \(-8.85227 q^{29}\) \(+5.11371 q^{31}\) \(-18.4902 q^{32}\) \(+10.5034 q^{33}\) \(-17.4531 q^{34}\) \(+17.4177 q^{36}\) \(-5.41403 q^{37}\) \(+3.53789 q^{38}\) \(+9.34127 q^{39}\) \(+11.8244 q^{41}\) \(+2.40450 q^{42}\) \(-0.673253 q^{43}\) \(+22.1678 q^{44}\) \(-11.0942 q^{46}\) \(-5.22965 q^{47}\) \(+33.6921 q^{48}\) \(-6.87398 q^{49}\) \(+16.2087 q^{51}\) \(+19.7152 q^{52}\) \(+9.92404 q^{53}\) \(-1.96735 q^{54}\) \(+3.15741 q^{56}\) \(-3.28564 q^{57}\) \(+23.9067 q^{58}\) \(-1.23315 q^{59}\) \(+4.04837 q^{61}\) \(-13.8102 q^{62}\) \(-1.16808 q^{63}\) \(+23.0683 q^{64}\) \(-28.3657 q^{66}\) \(+14.0522 q^{67}\) \(+34.2092 q^{68}\) \(+10.3032 q^{69}\) \(+13.0525 q^{71}\) \(-29.2663 q^{72}\) \(-7.76916 q^{73}\) \(+14.6213 q^{74}\) \(-6.93450 q^{76}\) \(-1.48664 q^{77}\) \(-25.2273 q^{78}\) \(-1.17673 q^{79}\) \(-8.04428 q^{81}\) \(-31.9333 q^{82}\) \(-6.25297 q^{83}\) \(-4.71298 q^{84}\) \(+1.81821 q^{86}\) \(-22.2022 q^{87}\) \(-37.2477 q^{88}\) \(+3.80839 q^{89}\) \(-1.32216 q^{91}\) \(+21.7453 q^{92}\) \(+12.8256 q^{93}\) \(+14.1234 q^{94}\) \(-46.3748 q^{96}\) \(+9.91591 q^{97}\) \(+18.5641 q^{98}\) \(+13.7798 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut 22q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 15q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut -\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 5q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut -\mathstrut 8q^{36} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut +\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 49q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 42q^{44} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 34q^{47} \) \(\mathstrut +\mathstrut 49q^{48} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 41q^{52} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut -\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut q^{56} \) \(\mathstrut +\mathstrut 22q^{57} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 26q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 17q^{62} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 13q^{64} \) \(\mathstrut -\mathstrut 2q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 35q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut 94q^{71} \) \(\mathstrut -\mathstrut 17q^{72} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 26q^{74} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 7q^{77} \) \(\mathstrut -\mathstrut 54q^{78} \) \(\mathstrut +\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 8q^{83} \) \(\mathstrut +\mathstrut 2q^{84} \) \(\mathstrut +\mathstrut 9q^{86} \) \(\mathstrut -\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut -\mathstrut 3q^{89} \) \(\mathstrut -\mathstrut 20q^{91} \) \(\mathstrut -\mathstrut 36q^{92} \) \(\mathstrut -\mathstrut 12q^{93} \) \(\mathstrut +\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 23q^{96} \) \(\mathstrut +\mathstrut 29q^{97} \) \(\mathstrut -\mathstrut 28q^{98} \) \(\mathstrut +\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70063 −1.90964 −0.954818 0.297191i \(-0.903950\pi\)
−0.954818 + 0.297191i \(0.903950\pi\)
\(3\) 2.50808 1.44804 0.724020 0.689779i \(-0.242292\pi\)
0.724020 + 0.689779i \(0.242292\pi\)
\(4\) 5.29342 2.64671
\(5\) 0 0
\(6\) −6.77340 −2.76523
\(7\) −0.354992 −0.134174 −0.0670872 0.997747i \(-0.521371\pi\)
−0.0670872 + 0.997747i \(0.521371\pi\)
\(8\) −8.89432 −3.14462
\(9\) 3.29045 1.09682
\(10\) 0 0
\(11\) 4.18781 1.26267 0.631336 0.775509i \(-0.282507\pi\)
0.631336 + 0.775509i \(0.282507\pi\)
\(12\) 13.2763 3.83254
\(13\) 3.72447 1.03298 0.516492 0.856292i \(-0.327238\pi\)
0.516492 + 0.856292i \(0.327238\pi\)
\(14\) 0.958703 0.256224
\(15\) 0 0
\(16\) 13.4334 3.35836
\(17\) 6.46259 1.56741 0.783704 0.621134i \(-0.213328\pi\)
0.783704 + 0.621134i \(0.213328\pi\)
\(18\) −8.88631 −2.09452
\(19\) −1.31002 −0.300540 −0.150270 0.988645i \(-0.548014\pi\)
−0.150270 + 0.988645i \(0.548014\pi\)
\(20\) 0 0
\(21\) −0.890347 −0.194290
\(22\) −11.3097 −2.41124
\(23\) 4.10799 0.856576 0.428288 0.903642i \(-0.359117\pi\)
0.428288 + 0.903642i \(0.359117\pi\)
\(24\) −22.3076 −4.55353
\(25\) 0 0
\(26\) −10.0584 −1.97262
\(27\) 0.728479 0.140196
\(28\) −1.87912 −0.355121
\(29\) −8.85227 −1.64382 −0.821912 0.569614i \(-0.807093\pi\)
−0.821912 + 0.569614i \(0.807093\pi\)
\(30\) 0 0
\(31\) 5.11371 0.918449 0.459225 0.888320i \(-0.348127\pi\)
0.459225 + 0.888320i \(0.348127\pi\)
\(32\) −18.4902 −3.26863
\(33\) 10.5034 1.82840
\(34\) −17.4531 −2.99318
\(35\) 0 0
\(36\) 17.4177 2.90296
\(37\) −5.41403 −0.890061 −0.445030 0.895515i \(-0.646807\pi\)
−0.445030 + 0.895515i \(0.646807\pi\)
\(38\) 3.53789 0.573922
\(39\) 9.34127 1.49580
\(40\) 0 0
\(41\) 11.8244 1.84665 0.923327 0.384014i \(-0.125459\pi\)
0.923327 + 0.384014i \(0.125459\pi\)
\(42\) 2.40450 0.371023
\(43\) −0.673253 −0.102670 −0.0513350 0.998681i \(-0.516348\pi\)
−0.0513350 + 0.998681i \(0.516348\pi\)
\(44\) 22.1678 3.34193
\(45\) 0 0
\(46\) −11.0942 −1.63575
\(47\) −5.22965 −0.762823 −0.381412 0.924405i \(-0.624562\pi\)
−0.381412 + 0.924405i \(0.624562\pi\)
\(48\) 33.6921 4.86304
\(49\) −6.87398 −0.981997
\(50\) 0 0
\(51\) 16.2087 2.26967
\(52\) 19.7152 2.73401
\(53\) 9.92404 1.36317 0.681586 0.731738i \(-0.261291\pi\)
0.681586 + 0.731738i \(0.261291\pi\)
\(54\) −1.96735 −0.267723
\(55\) 0 0
\(56\) 3.15741 0.421927
\(57\) −3.28564 −0.435194
\(58\) 23.9067 3.13911
\(59\) −1.23315 −0.160542 −0.0802710 0.996773i \(-0.525579\pi\)
−0.0802710 + 0.996773i \(0.525579\pi\)
\(60\) 0 0
\(61\) 4.04837 0.518341 0.259170 0.965832i \(-0.416551\pi\)
0.259170 + 0.965832i \(0.416551\pi\)
\(62\) −13.8102 −1.75390
\(63\) −1.16808 −0.147165
\(64\) 23.0683 2.88354
\(65\) 0 0
\(66\) −28.3657 −3.49158
\(67\) 14.0522 1.71675 0.858375 0.513022i \(-0.171474\pi\)
0.858375 + 0.513022i \(0.171474\pi\)
\(68\) 34.2092 4.14847
\(69\) 10.3032 1.24036
\(70\) 0 0
\(71\) 13.0525 1.54905 0.774526 0.632542i \(-0.217989\pi\)
0.774526 + 0.632542i \(0.217989\pi\)
\(72\) −29.2663 −3.44907
\(73\) −7.76916 −0.909312 −0.454656 0.890667i \(-0.650238\pi\)
−0.454656 + 0.890667i \(0.650238\pi\)
\(74\) 14.6213 1.69969
\(75\) 0 0
\(76\) −6.93450 −0.795442
\(77\) −1.48664 −0.169418
\(78\) −25.2273 −2.85643
\(79\) −1.17673 −0.132393 −0.0661963 0.997807i \(-0.521086\pi\)
−0.0661963 + 0.997807i \(0.521086\pi\)
\(80\) 0 0
\(81\) −8.04428 −0.893809
\(82\) −31.9333 −3.52644
\(83\) −6.25297 −0.686353 −0.343176 0.939271i \(-0.611503\pi\)
−0.343176 + 0.939271i \(0.611503\pi\)
\(84\) −4.71298 −0.514228
\(85\) 0 0
\(86\) 1.81821 0.196062
\(87\) −22.2022 −2.38032
\(88\) −37.2477 −3.97062
\(89\) 3.80839 0.403688 0.201844 0.979418i \(-0.435307\pi\)
0.201844 + 0.979418i \(0.435307\pi\)
\(90\) 0 0
\(91\) −1.32216 −0.138600
\(92\) 21.7453 2.26711
\(93\) 12.8256 1.32995
\(94\) 14.1234 1.45671
\(95\) 0 0
\(96\) −46.3748 −4.73311
\(97\) 9.91591 1.00681 0.503404 0.864051i \(-0.332081\pi\)
0.503404 + 0.864051i \(0.332081\pi\)
\(98\) 18.5641 1.87526
\(99\) 13.7798 1.38492
\(100\) 0 0
\(101\) 7.46224 0.742521 0.371260 0.928529i \(-0.378926\pi\)
0.371260 + 0.928529i \(0.378926\pi\)
\(102\) −43.7737 −4.33424
\(103\) −7.83988 −0.772486 −0.386243 0.922397i \(-0.626227\pi\)
−0.386243 + 0.922397i \(0.626227\pi\)
\(104\) −33.1267 −3.24834
\(105\) 0 0
\(106\) −26.8012 −2.60316
\(107\) 0.890206 0.0860595 0.0430297 0.999074i \(-0.486299\pi\)
0.0430297 + 0.999074i \(0.486299\pi\)
\(108\) 3.85614 0.371058
\(109\) 3.92555 0.375999 0.188000 0.982169i \(-0.439800\pi\)
0.188000 + 0.982169i \(0.439800\pi\)
\(110\) 0 0
\(111\) −13.5788 −1.28884
\(112\) −4.76877 −0.450606
\(113\) −17.3995 −1.63681 −0.818404 0.574643i \(-0.805141\pi\)
−0.818404 + 0.574643i \(0.805141\pi\)
\(114\) 8.87331 0.831061
\(115\) 0 0
\(116\) −46.8588 −4.35073
\(117\) 12.2552 1.13299
\(118\) 3.33028 0.306577
\(119\) −2.29417 −0.210306
\(120\) 0 0
\(121\) 6.53776 0.594342
\(122\) −10.9332 −0.989842
\(123\) 29.6564 2.67403
\(124\) 27.0690 2.43087
\(125\) 0 0
\(126\) 3.15457 0.281031
\(127\) −18.7331 −1.66230 −0.831148 0.556052i \(-0.812316\pi\)
−0.831148 + 0.556052i \(0.812316\pi\)
\(128\) −25.3187 −2.23787
\(129\) −1.68857 −0.148670
\(130\) 0 0
\(131\) −1.40627 −0.122867 −0.0614333 0.998111i \(-0.519567\pi\)
−0.0614333 + 0.998111i \(0.519567\pi\)
\(132\) 55.5987 4.83924
\(133\) 0.465048 0.0403247
\(134\) −37.9499 −3.27837
\(135\) 0 0
\(136\) −57.4803 −4.92890
\(137\) −5.54974 −0.474146 −0.237073 0.971492i \(-0.576188\pi\)
−0.237073 + 0.971492i \(0.576188\pi\)
\(138\) −27.8251 −2.36863
\(139\) −11.1540 −0.946072 −0.473036 0.881043i \(-0.656842\pi\)
−0.473036 + 0.881043i \(0.656842\pi\)
\(140\) 0 0
\(141\) −13.1164 −1.10460
\(142\) −35.2501 −2.95812
\(143\) 15.5974 1.30432
\(144\) 44.2021 3.68351
\(145\) 0 0
\(146\) 20.9817 1.73645
\(147\) −17.2405 −1.42197
\(148\) −28.6587 −2.35573
\(149\) 8.27009 0.677512 0.338756 0.940874i \(-0.389994\pi\)
0.338756 + 0.940874i \(0.389994\pi\)
\(150\) 0 0
\(151\) −11.8990 −0.968323 −0.484162 0.874979i \(-0.660875\pi\)
−0.484162 + 0.874979i \(0.660875\pi\)
\(152\) 11.6518 0.945083
\(153\) 21.2648 1.71916
\(154\) 4.01487 0.323527
\(155\) 0 0
\(156\) 49.4473 3.95895
\(157\) 5.88156 0.469399 0.234700 0.972068i \(-0.424589\pi\)
0.234700 + 0.972068i \(0.424589\pi\)
\(158\) 3.17792 0.252822
\(159\) 24.8903 1.97393
\(160\) 0 0
\(161\) −1.45830 −0.114930
\(162\) 21.7246 1.70685
\(163\) 3.21033 0.251452 0.125726 0.992065i \(-0.459874\pi\)
0.125726 + 0.992065i \(0.459874\pi\)
\(164\) 62.5913 4.88756
\(165\) 0 0
\(166\) 16.8870 1.31068
\(167\) 9.62511 0.744813 0.372407 0.928070i \(-0.378533\pi\)
0.372407 + 0.928070i \(0.378533\pi\)
\(168\) 7.91903 0.610967
\(169\) 0.871711 0.0670547
\(170\) 0 0
\(171\) −4.31057 −0.329637
\(172\) −3.56381 −0.271738
\(173\) 11.7677 0.894682 0.447341 0.894364i \(-0.352371\pi\)
0.447341 + 0.894364i \(0.352371\pi\)
\(174\) 59.9599 4.54555
\(175\) 0 0
\(176\) 56.2567 4.24051
\(177\) −3.09283 −0.232471
\(178\) −10.2851 −0.770898
\(179\) −4.74606 −0.354737 −0.177369 0.984144i \(-0.556759\pi\)
−0.177369 + 0.984144i \(0.556759\pi\)
\(180\) 0 0
\(181\) −9.56167 −0.710713 −0.355357 0.934731i \(-0.615641\pi\)
−0.355357 + 0.934731i \(0.615641\pi\)
\(182\) 3.57066 0.264675
\(183\) 10.1536 0.750578
\(184\) −36.5378 −2.69360
\(185\) 0 0
\(186\) −34.6372 −2.53972
\(187\) 27.0641 1.97912
\(188\) −27.6827 −2.01897
\(189\) −0.258604 −0.0188107
\(190\) 0 0
\(191\) 23.1412 1.67444 0.837218 0.546870i \(-0.184181\pi\)
0.837218 + 0.546870i \(0.184181\pi\)
\(192\) 57.8571 4.17548
\(193\) −9.15643 −0.659095 −0.329547 0.944139i \(-0.606896\pi\)
−0.329547 + 0.944139i \(0.606896\pi\)
\(194\) −26.7792 −1.92264
\(195\) 0 0
\(196\) −36.3869 −2.59906
\(197\) 6.75045 0.480950 0.240475 0.970655i \(-0.422697\pi\)
0.240475 + 0.970655i \(0.422697\pi\)
\(198\) −37.2142 −2.64470
\(199\) 3.26300 0.231308 0.115654 0.993290i \(-0.463104\pi\)
0.115654 + 0.993290i \(0.463104\pi\)
\(200\) 0 0
\(201\) 35.2440 2.48592
\(202\) −20.1528 −1.41794
\(203\) 3.14248 0.220559
\(204\) 85.7993 6.00715
\(205\) 0 0
\(206\) 21.1726 1.47517
\(207\) 13.5172 0.939507
\(208\) 50.0325 3.46913
\(209\) −5.48613 −0.379483
\(210\) 0 0
\(211\) −23.1474 −1.59354 −0.796768 0.604285i \(-0.793459\pi\)
−0.796768 + 0.604285i \(0.793459\pi\)
\(212\) 52.5321 3.60792
\(213\) 32.7368 2.24309
\(214\) −2.40412 −0.164342
\(215\) 0 0
\(216\) −6.47932 −0.440862
\(217\) −1.81532 −0.123232
\(218\) −10.6015 −0.718022
\(219\) −19.4857 −1.31672
\(220\) 0 0
\(221\) 24.0698 1.61911
\(222\) 36.6714 2.46122
\(223\) 18.2948 1.22511 0.612557 0.790427i \(-0.290141\pi\)
0.612557 + 0.790427i \(0.290141\pi\)
\(224\) 6.56387 0.438567
\(225\) 0 0
\(226\) 46.9897 3.12571
\(227\) −10.4809 −0.695642 −0.347821 0.937561i \(-0.613078\pi\)
−0.347821 + 0.937561i \(0.613078\pi\)
\(228\) −17.3923 −1.15183
\(229\) −5.51626 −0.364524 −0.182262 0.983250i \(-0.558342\pi\)
−0.182262 + 0.983250i \(0.558342\pi\)
\(230\) 0 0
\(231\) −3.72861 −0.245324
\(232\) 78.7349 5.16920
\(233\) −27.7343 −1.81693 −0.908466 0.417959i \(-0.862746\pi\)
−0.908466 + 0.417959i \(0.862746\pi\)
\(234\) −33.0968 −2.16361
\(235\) 0 0
\(236\) −6.52756 −0.424908
\(237\) −2.95133 −0.191710
\(238\) 6.19570 0.401608
\(239\) 6.60568 0.427286 0.213643 0.976912i \(-0.431467\pi\)
0.213643 + 0.976912i \(0.431467\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) −17.6561 −1.13498
\(243\) −22.3611 −1.43447
\(244\) 21.4297 1.37190
\(245\) 0 0
\(246\) −80.0911 −5.10642
\(247\) −4.87915 −0.310453
\(248\) −45.4829 −2.88817
\(249\) −15.6829 −0.993865
\(250\) 0 0
\(251\) 21.2628 1.34210 0.671049 0.741413i \(-0.265844\pi\)
0.671049 + 0.741413i \(0.265844\pi\)
\(252\) −6.18316 −0.389502
\(253\) 17.2035 1.08157
\(254\) 50.5913 3.17438
\(255\) 0 0
\(256\) 22.2398 1.38999
\(257\) −7.33227 −0.457374 −0.228687 0.973500i \(-0.573443\pi\)
−0.228687 + 0.973500i \(0.573443\pi\)
\(258\) 4.56021 0.283906
\(259\) 1.92194 0.119423
\(260\) 0 0
\(261\) −29.1280 −1.80298
\(262\) 3.79782 0.234630
\(263\) −20.6204 −1.27151 −0.635753 0.771892i \(-0.719310\pi\)
−0.635753 + 0.771892i \(0.719310\pi\)
\(264\) −93.4202 −5.74961
\(265\) 0 0
\(266\) −1.25592 −0.0770056
\(267\) 9.55173 0.584557
\(268\) 74.3842 4.54374
\(269\) −0.178772 −0.0108999 −0.00544997 0.999985i \(-0.501735\pi\)
−0.00544997 + 0.999985i \(0.501735\pi\)
\(270\) 0 0
\(271\) −17.9311 −1.08923 −0.544617 0.838685i \(-0.683325\pi\)
−0.544617 + 0.838685i \(0.683325\pi\)
\(272\) 86.8149 5.26392
\(273\) −3.31608 −0.200698
\(274\) 14.9878 0.905446
\(275\) 0 0
\(276\) 54.5390 3.28286
\(277\) −2.56354 −0.154028 −0.0770140 0.997030i \(-0.524539\pi\)
−0.0770140 + 0.997030i \(0.524539\pi\)
\(278\) 30.1229 1.80665
\(279\) 16.8264 1.00737
\(280\) 0 0
\(281\) −22.4531 −1.33944 −0.669720 0.742614i \(-0.733586\pi\)
−0.669720 + 0.742614i \(0.733586\pi\)
\(282\) 35.4225 2.10938
\(283\) −13.1240 −0.780141 −0.390070 0.920785i \(-0.627549\pi\)
−0.390070 + 0.920785i \(0.627549\pi\)
\(284\) 69.0926 4.09989
\(285\) 0 0
\(286\) −42.1228 −2.49078
\(287\) −4.19755 −0.247774
\(288\) −60.8411 −3.58509
\(289\) 24.7651 1.45677
\(290\) 0 0
\(291\) 24.8699 1.45790
\(292\) −41.1254 −2.40668
\(293\) 32.3935 1.89245 0.946225 0.323509i \(-0.104863\pi\)
0.946225 + 0.323509i \(0.104863\pi\)
\(294\) 46.5602 2.71545
\(295\) 0 0
\(296\) 48.1541 2.79890
\(297\) 3.05073 0.177021
\(298\) −22.3345 −1.29380
\(299\) 15.3001 0.884829
\(300\) 0 0
\(301\) 0.238999 0.0137757
\(302\) 32.1347 1.84914
\(303\) 18.7159 1.07520
\(304\) −17.5981 −1.00932
\(305\) 0 0
\(306\) −57.4286 −3.28297
\(307\) −12.6847 −0.723952 −0.361976 0.932187i \(-0.617898\pi\)
−0.361976 + 0.932187i \(0.617898\pi\)
\(308\) −7.86940 −0.448401
\(309\) −19.6630 −1.11859
\(310\) 0 0
\(311\) 22.1050 1.25346 0.626730 0.779236i \(-0.284393\pi\)
0.626730 + 0.779236i \(0.284393\pi\)
\(312\) −83.0842 −4.70372
\(313\) −10.8859 −0.615305 −0.307653 0.951499i \(-0.599543\pi\)
−0.307653 + 0.951499i \(0.599543\pi\)
\(314\) −15.8839 −0.896382
\(315\) 0 0
\(316\) −6.22893 −0.350405
\(317\) 7.76634 0.436201 0.218101 0.975926i \(-0.430014\pi\)
0.218101 + 0.975926i \(0.430014\pi\)
\(318\) −67.2195 −3.76948
\(319\) −37.0716 −2.07561
\(320\) 0 0
\(321\) 2.23271 0.124618
\(322\) 3.93835 0.219475
\(323\) −8.46614 −0.471069
\(324\) −42.5817 −2.36565
\(325\) 0 0
\(326\) −8.66992 −0.480182
\(327\) 9.84558 0.544462
\(328\) −105.170 −5.80702
\(329\) 1.85648 0.102351
\(330\) 0 0
\(331\) 0.317941 0.0174756 0.00873781 0.999962i \(-0.497219\pi\)
0.00873781 + 0.999962i \(0.497219\pi\)
\(332\) −33.0996 −1.81658
\(333\) −17.8146 −0.976235
\(334\) −25.9939 −1.42232
\(335\) 0 0
\(336\) −11.9604 −0.652495
\(337\) 10.0901 0.549641 0.274821 0.961496i \(-0.411382\pi\)
0.274821 + 0.961496i \(0.411382\pi\)
\(338\) −2.35417 −0.128050
\(339\) −43.6393 −2.37016
\(340\) 0 0
\(341\) 21.4152 1.15970
\(342\) 11.6413 0.629488
\(343\) 4.92515 0.265933
\(344\) 5.98812 0.322858
\(345\) 0 0
\(346\) −31.7802 −1.70852
\(347\) 12.2330 0.656700 0.328350 0.944556i \(-0.393508\pi\)
0.328350 + 0.944556i \(0.393508\pi\)
\(348\) −117.525 −6.30002
\(349\) 0.0471917 0.00252612 0.00126306 0.999999i \(-0.499598\pi\)
0.00126306 + 0.999999i \(0.499598\pi\)
\(350\) 0 0
\(351\) 2.71320 0.144820
\(352\) −77.4334 −4.12721
\(353\) −9.38275 −0.499393 −0.249697 0.968324i \(-0.580331\pi\)
−0.249697 + 0.968324i \(0.580331\pi\)
\(354\) 8.35259 0.443935
\(355\) 0 0
\(356\) 20.1594 1.06845
\(357\) −5.75395 −0.304531
\(358\) 12.8174 0.677419
\(359\) 4.83057 0.254948 0.127474 0.991842i \(-0.459313\pi\)
0.127474 + 0.991842i \(0.459313\pi\)
\(360\) 0 0
\(361\) −17.2838 −0.909676
\(362\) 25.8226 1.35720
\(363\) 16.3972 0.860630
\(364\) −6.99874 −0.366834
\(365\) 0 0
\(366\) −27.4212 −1.43333
\(367\) 26.6792 1.39264 0.696322 0.717730i \(-0.254819\pi\)
0.696322 + 0.717730i \(0.254819\pi\)
\(368\) 55.1845 2.87669
\(369\) 38.9075 2.02544
\(370\) 0 0
\(371\) −3.52295 −0.182903
\(372\) 67.8911 3.51999
\(373\) 1.30441 0.0675400 0.0337700 0.999430i \(-0.489249\pi\)
0.0337700 + 0.999430i \(0.489249\pi\)
\(374\) −73.0902 −3.77940
\(375\) 0 0
\(376\) 46.5142 2.39879
\(377\) −32.9700 −1.69804
\(378\) 0.698395 0.0359216
\(379\) −3.62474 −0.186191 −0.0930953 0.995657i \(-0.529676\pi\)
−0.0930953 + 0.995657i \(0.529676\pi\)
\(380\) 0 0
\(381\) −46.9841 −2.40707
\(382\) −62.4958 −3.19756
\(383\) 28.5501 1.45884 0.729420 0.684066i \(-0.239790\pi\)
0.729420 + 0.684066i \(0.239790\pi\)
\(384\) −63.5011 −3.24053
\(385\) 0 0
\(386\) 24.7282 1.25863
\(387\) −2.21531 −0.112610
\(388\) 52.4891 2.66473
\(389\) 29.3393 1.48756 0.743780 0.668424i \(-0.233031\pi\)
0.743780 + 0.668424i \(0.233031\pi\)
\(390\) 0 0
\(391\) 26.5483 1.34260
\(392\) 61.1394 3.08800
\(393\) −3.52704 −0.177916
\(394\) −18.2305 −0.918439
\(395\) 0 0
\(396\) 72.9422 3.66548
\(397\) −3.94029 −0.197758 −0.0988788 0.995099i \(-0.531526\pi\)
−0.0988788 + 0.995099i \(0.531526\pi\)
\(398\) −8.81218 −0.441715
\(399\) 1.16638 0.0583918
\(400\) 0 0
\(401\) 0.0336542 0.00168061 0.000840304 1.00000i \(-0.499733\pi\)
0.000840304 1.00000i \(0.499733\pi\)
\(402\) −95.1812 −4.74721
\(403\) 19.0459 0.948743
\(404\) 39.5008 1.96524
\(405\) 0 0
\(406\) −8.48669 −0.421188
\(407\) −22.6729 −1.12386
\(408\) −144.165 −7.13724
\(409\) −8.89629 −0.439893 −0.219947 0.975512i \(-0.570588\pi\)
−0.219947 + 0.975512i \(0.570588\pi\)
\(410\) 0 0
\(411\) −13.9192 −0.686582
\(412\) −41.4998 −2.04455
\(413\) 0.437757 0.0215406
\(414\) −36.5049 −1.79412
\(415\) 0 0
\(416\) −68.8662 −3.37644
\(417\) −27.9752 −1.36995
\(418\) 14.8160 0.724675
\(419\) −29.8619 −1.45885 −0.729425 0.684061i \(-0.760212\pi\)
−0.729425 + 0.684061i \(0.760212\pi\)
\(420\) 0 0
\(421\) 15.9683 0.778247 0.389124 0.921186i \(-0.372778\pi\)
0.389124 + 0.921186i \(0.372778\pi\)
\(422\) 62.5128 3.04307
\(423\) −17.2079 −0.836678
\(424\) −88.2676 −4.28665
\(425\) 0 0
\(426\) −88.4100 −4.28348
\(427\) −1.43714 −0.0695480
\(428\) 4.71223 0.227774
\(429\) 39.1195 1.88871
\(430\) 0 0
\(431\) 24.8345 1.19624 0.598118 0.801408i \(-0.295915\pi\)
0.598118 + 0.801408i \(0.295915\pi\)
\(432\) 9.78598 0.470828
\(433\) 31.1730 1.49808 0.749040 0.662524i \(-0.230515\pi\)
0.749040 + 0.662524i \(0.230515\pi\)
\(434\) 4.90253 0.235329
\(435\) 0 0
\(436\) 20.7796 0.995161
\(437\) −5.38157 −0.257435
\(438\) 52.6236 2.51445
\(439\) −0.959384 −0.0457889 −0.0228944 0.999738i \(-0.507288\pi\)
−0.0228944 + 0.999738i \(0.507288\pi\)
\(440\) 0 0
\(441\) −22.6185 −1.07707
\(442\) −65.0036 −3.09190
\(443\) −6.52446 −0.309986 −0.154993 0.987916i \(-0.549536\pi\)
−0.154993 + 0.987916i \(0.549536\pi\)
\(444\) −71.8783 −3.41119
\(445\) 0 0
\(446\) −49.4077 −2.33952
\(447\) 20.7420 0.981065
\(448\) −8.18906 −0.386897
\(449\) −9.39811 −0.443524 −0.221762 0.975101i \(-0.571181\pi\)
−0.221762 + 0.975101i \(0.571181\pi\)
\(450\) 0 0
\(451\) 49.5182 2.33172
\(452\) −92.1029 −4.33216
\(453\) −29.8435 −1.40217
\(454\) 28.3051 1.32842
\(455\) 0 0
\(456\) 29.2235 1.36852
\(457\) 27.0904 1.26724 0.633618 0.773646i \(-0.281569\pi\)
0.633618 + 0.773646i \(0.281569\pi\)
\(458\) 14.8974 0.696109
\(459\) 4.70786 0.219744
\(460\) 0 0
\(461\) −32.1068 −1.49536 −0.747682 0.664057i \(-0.768833\pi\)
−0.747682 + 0.664057i \(0.768833\pi\)
\(462\) 10.0696 0.468480
\(463\) −17.5754 −0.816797 −0.408399 0.912804i \(-0.633913\pi\)
−0.408399 + 0.912804i \(0.633913\pi\)
\(464\) −118.916 −5.52056
\(465\) 0 0
\(466\) 74.9001 3.46968
\(467\) −12.9732 −0.600329 −0.300164 0.953887i \(-0.597042\pi\)
−0.300164 + 0.953887i \(0.597042\pi\)
\(468\) 64.8720 2.99871
\(469\) −4.98842 −0.230344
\(470\) 0 0
\(471\) 14.7514 0.679708
\(472\) 10.9680 0.504843
\(473\) −2.81945 −0.129639
\(474\) 7.97046 0.366096
\(475\) 0 0
\(476\) −12.1440 −0.556619
\(477\) 32.6546 1.49515
\(478\) −17.8395 −0.815960
\(479\) −6.68222 −0.305319 −0.152659 0.988279i \(-0.548784\pi\)
−0.152659 + 0.988279i \(0.548784\pi\)
\(480\) 0 0
\(481\) −20.1644 −0.919418
\(482\) −2.70063 −0.123010
\(483\) −3.65754 −0.166424
\(484\) 34.6071 1.57305
\(485\) 0 0
\(486\) 60.3892 2.73931
\(487\) −19.6021 −0.888256 −0.444128 0.895963i \(-0.646486\pi\)
−0.444128 + 0.895963i \(0.646486\pi\)
\(488\) −36.0075 −1.62998
\(489\) 8.05175 0.364113
\(490\) 0 0
\(491\) −6.61946 −0.298732 −0.149366 0.988782i \(-0.547723\pi\)
−0.149366 + 0.988782i \(0.547723\pi\)
\(492\) 156.984 7.07738
\(493\) −57.2086 −2.57654
\(494\) 13.1768 0.592852
\(495\) 0 0
\(496\) 68.6947 3.08448
\(497\) −4.63355 −0.207843
\(498\) 42.3538 1.89792
\(499\) 39.6828 1.77645 0.888223 0.459413i \(-0.151940\pi\)
0.888223 + 0.459413i \(0.151940\pi\)
\(500\) 0 0
\(501\) 24.1405 1.07852
\(502\) −57.4231 −2.56292
\(503\) 13.9042 0.619960 0.309980 0.950743i \(-0.399678\pi\)
0.309980 + 0.950743i \(0.399678\pi\)
\(504\) 10.3893 0.462777
\(505\) 0 0
\(506\) −46.4603 −2.06541
\(507\) 2.18632 0.0970979
\(508\) −99.1622 −4.39961
\(509\) 33.7260 1.49488 0.747439 0.664331i \(-0.231283\pi\)
0.747439 + 0.664331i \(0.231283\pi\)
\(510\) 0 0
\(511\) 2.75799 0.122006
\(512\) −9.42420 −0.416495
\(513\) −0.954324 −0.0421344
\(514\) 19.8018 0.873418
\(515\) 0 0
\(516\) −8.93831 −0.393487
\(517\) −21.9008 −0.963196
\(518\) −5.19045 −0.228055
\(519\) 29.5143 1.29553
\(520\) 0 0
\(521\) −37.2520 −1.63204 −0.816020 0.578023i \(-0.803824\pi\)
−0.816020 + 0.578023i \(0.803824\pi\)
\(522\) 78.6639 3.44303
\(523\) 14.7673 0.645730 0.322865 0.946445i \(-0.395354\pi\)
0.322865 + 0.946445i \(0.395354\pi\)
\(524\) −7.44399 −0.325192
\(525\) 0 0
\(526\) 55.6880 2.42811
\(527\) 33.0478 1.43958
\(528\) 141.096 6.14043
\(529\) −6.12439 −0.266278
\(530\) 0 0
\(531\) −4.05761 −0.176085
\(532\) 2.46169 0.106728
\(533\) 44.0395 1.90756
\(534\) −25.7957 −1.11629
\(535\) 0 0
\(536\) −124.985 −5.39852
\(537\) −11.9035 −0.513674
\(538\) 0.482799 0.0208149
\(539\) −28.7869 −1.23994
\(540\) 0 0
\(541\) 0.345044 0.0148346 0.00741730 0.999972i \(-0.497639\pi\)
0.00741730 + 0.999972i \(0.497639\pi\)
\(542\) 48.4252 2.08004
\(543\) −23.9814 −1.02914
\(544\) −119.494 −5.12328
\(545\) 0 0
\(546\) 8.95550 0.383260
\(547\) 6.16271 0.263498 0.131749 0.991283i \(-0.457941\pi\)
0.131749 + 0.991283i \(0.457941\pi\)
\(548\) −29.3771 −1.25493
\(549\) 13.3210 0.568525
\(550\) 0 0
\(551\) 11.5967 0.494035
\(552\) −91.6396 −3.90044
\(553\) 0.417730 0.0177637
\(554\) 6.92318 0.294138
\(555\) 0 0
\(556\) −59.0429 −2.50398
\(557\) −7.45145 −0.315728 −0.157864 0.987461i \(-0.550461\pi\)
−0.157864 + 0.987461i \(0.550461\pi\)
\(558\) −45.4420 −1.92371
\(559\) −2.50751 −0.106056
\(560\) 0 0
\(561\) 67.8789 2.86585
\(562\) 60.6376 2.55784
\(563\) 14.5393 0.612760 0.306380 0.951909i \(-0.400882\pi\)
0.306380 + 0.951909i \(0.400882\pi\)
\(564\) −69.4305 −2.92355
\(565\) 0 0
\(566\) 35.4431 1.48978
\(567\) 2.85565 0.119926
\(568\) −116.093 −4.87117
\(569\) 12.1696 0.510175 0.255088 0.966918i \(-0.417896\pi\)
0.255088 + 0.966918i \(0.417896\pi\)
\(570\) 0 0
\(571\) −16.0026 −0.669687 −0.334843 0.942274i \(-0.608683\pi\)
−0.334843 + 0.942274i \(0.608683\pi\)
\(572\) 82.5635 3.45216
\(573\) 58.0398 2.42465
\(574\) 11.3360 0.473157
\(575\) 0 0
\(576\) 75.9052 3.16271
\(577\) −0.0727829 −0.00302999 −0.00151500 0.999999i \(-0.500482\pi\)
−0.00151500 + 0.999999i \(0.500482\pi\)
\(578\) −66.8814 −2.78190
\(579\) −22.9650 −0.954395
\(580\) 0 0
\(581\) 2.21975 0.0920909
\(582\) −67.1644 −2.78405
\(583\) 41.5600 1.72124
\(584\) 69.1014 2.85944
\(585\) 0 0
\(586\) −87.4830 −3.61389
\(587\) −0.902377 −0.0372451 −0.0186225 0.999827i \(-0.505928\pi\)
−0.0186225 + 0.999827i \(0.505928\pi\)
\(588\) −91.2611 −3.76354
\(589\) −6.69907 −0.276031
\(590\) 0 0
\(591\) 16.9307 0.696434
\(592\) −72.7291 −2.98915
\(593\) 23.7787 0.976476 0.488238 0.872711i \(-0.337640\pi\)
0.488238 + 0.872711i \(0.337640\pi\)
\(594\) −8.23891 −0.338046
\(595\) 0 0
\(596\) 43.7771 1.79318
\(597\) 8.18387 0.334943
\(598\) −41.3200 −1.68970
\(599\) 48.7217 1.99072 0.995358 0.0962439i \(-0.0306829\pi\)
0.995358 + 0.0962439i \(0.0306829\pi\)
\(600\) 0 0
\(601\) −3.90565 −0.159315 −0.0796573 0.996822i \(-0.525383\pi\)
−0.0796573 + 0.996822i \(0.525383\pi\)
\(602\) −0.645449 −0.0263066
\(603\) 46.2381 1.88296
\(604\) −62.9862 −2.56287
\(605\) 0 0
\(606\) −50.5447 −2.05324
\(607\) 15.1915 0.616605 0.308302 0.951288i \(-0.400239\pi\)
0.308302 + 0.951288i \(0.400239\pi\)
\(608\) 24.2226 0.982355
\(609\) 7.88159 0.319378
\(610\) 0 0
\(611\) −19.4777 −0.787984
\(612\) 112.564 4.55012
\(613\) 29.1406 1.17698 0.588490 0.808505i \(-0.299723\pi\)
0.588490 + 0.808505i \(0.299723\pi\)
\(614\) 34.2566 1.38248
\(615\) 0 0
\(616\) 13.2226 0.532755
\(617\) 31.1143 1.25261 0.626307 0.779576i \(-0.284565\pi\)
0.626307 + 0.779576i \(0.284565\pi\)
\(618\) 53.1026 2.13610
\(619\) 40.3950 1.62361 0.811806 0.583927i \(-0.198484\pi\)
0.811806 + 0.583927i \(0.198484\pi\)
\(620\) 0 0
\(621\) 2.99259 0.120088
\(622\) −59.6976 −2.39365
\(623\) −1.35195 −0.0541646
\(624\) 125.485 5.02344
\(625\) 0 0
\(626\) 29.3987 1.17501
\(627\) −13.7596 −0.549507
\(628\) 31.1335 1.24236
\(629\) −34.9886 −1.39509
\(630\) 0 0
\(631\) 7.99234 0.318170 0.159085 0.987265i \(-0.449146\pi\)
0.159085 + 0.987265i \(0.449146\pi\)
\(632\) 10.4662 0.416324
\(633\) −58.0556 −2.30750
\(634\) −20.9740 −0.832986
\(635\) 0 0
\(636\) 131.755 5.22441
\(637\) −25.6020 −1.01439
\(638\) 100.117 3.96366
\(639\) 42.9488 1.69903
\(640\) 0 0
\(641\) −25.0212 −0.988277 −0.494139 0.869383i \(-0.664516\pi\)
−0.494139 + 0.869383i \(0.664516\pi\)
\(642\) −6.02972 −0.237974
\(643\) 9.88861 0.389969 0.194984 0.980806i \(-0.437534\pi\)
0.194984 + 0.980806i \(0.437534\pi\)
\(644\) −7.71942 −0.304188
\(645\) 0 0
\(646\) 22.8639 0.899570
\(647\) −43.3237 −1.70323 −0.851615 0.524168i \(-0.824376\pi\)
−0.851615 + 0.524168i \(0.824376\pi\)
\(648\) 71.5484 2.81068
\(649\) −5.16419 −0.202712
\(650\) 0 0
\(651\) −4.55298 −0.178445
\(652\) 16.9936 0.665521
\(653\) 13.6441 0.533936 0.266968 0.963705i \(-0.413978\pi\)
0.266968 + 0.963705i \(0.413978\pi\)
\(654\) −26.5893 −1.03972
\(655\) 0 0
\(656\) 158.842 6.20173
\(657\) −25.5641 −0.997349
\(658\) −5.01368 −0.195454
\(659\) −18.6052 −0.724756 −0.362378 0.932031i \(-0.618035\pi\)
−0.362378 + 0.932031i \(0.618035\pi\)
\(660\) 0 0
\(661\) −39.9082 −1.55225 −0.776124 0.630580i \(-0.782817\pi\)
−0.776124 + 0.630580i \(0.782817\pi\)
\(662\) −0.858643 −0.0333721
\(663\) 60.3688 2.34453
\(664\) 55.6159 2.15832
\(665\) 0 0
\(666\) 48.1107 1.86425
\(667\) −36.3650 −1.40806
\(668\) 50.9497 1.97130
\(669\) 45.8849 1.77401
\(670\) 0 0
\(671\) 16.9538 0.654494
\(672\) 16.4627 0.635062
\(673\) 0.931169 0.0358939 0.0179470 0.999839i \(-0.494287\pi\)
0.0179470 + 0.999839i \(0.494287\pi\)
\(674\) −27.2496 −1.04961
\(675\) 0 0
\(676\) 4.61433 0.177474
\(677\) −35.1023 −1.34909 −0.674546 0.738233i \(-0.735661\pi\)
−0.674546 + 0.738233i \(0.735661\pi\)
\(678\) 117.854 4.52615
\(679\) −3.52007 −0.135088
\(680\) 0 0
\(681\) −26.2869 −1.00732
\(682\) −57.8347 −2.21461
\(683\) 17.5204 0.670399 0.335199 0.942147i \(-0.391196\pi\)
0.335199 + 0.942147i \(0.391196\pi\)
\(684\) −22.8177 −0.872455
\(685\) 0 0
\(686\) −13.3010 −0.507836
\(687\) −13.8352 −0.527846
\(688\) −9.04410 −0.344803
\(689\) 36.9618 1.40813
\(690\) 0 0
\(691\) 33.6421 1.27981 0.639903 0.768455i \(-0.278974\pi\)
0.639903 + 0.768455i \(0.278974\pi\)
\(692\) 62.2914 2.36796
\(693\) −4.89172 −0.185821
\(694\) −33.0367 −1.25406
\(695\) 0 0
\(696\) 197.473 7.48520
\(697\) 76.4160 2.89446
\(698\) −0.127448 −0.00482396
\(699\) −69.5597 −2.63099
\(700\) 0 0
\(701\) −20.5783 −0.777232 −0.388616 0.921400i \(-0.627047\pi\)
−0.388616 + 0.921400i \(0.627047\pi\)
\(702\) −7.32736 −0.276553
\(703\) 7.09250 0.267499
\(704\) 96.6057 3.64096
\(705\) 0 0
\(706\) 25.3394 0.953660
\(707\) −2.64904 −0.0996272
\(708\) −16.3716 −0.615284
\(709\) −16.3548 −0.614216 −0.307108 0.951675i \(-0.599361\pi\)
−0.307108 + 0.951675i \(0.599361\pi\)
\(710\) 0 0
\(711\) −3.87198 −0.145210
\(712\) −33.8730 −1.26944
\(713\) 21.0071 0.786721
\(714\) 15.5393 0.581544
\(715\) 0 0
\(716\) −25.1229 −0.938887
\(717\) 16.5675 0.618726
\(718\) −13.0456 −0.486858
\(719\) 21.1731 0.789624 0.394812 0.918762i \(-0.370810\pi\)
0.394812 + 0.918762i \(0.370810\pi\)
\(720\) 0 0
\(721\) 2.78309 0.103648
\(722\) 46.6773 1.73715
\(723\) 2.50808 0.0932764
\(724\) −50.6139 −1.88105
\(725\) 0 0
\(726\) −44.2828 −1.64349
\(727\) 15.8288 0.587059 0.293530 0.955950i \(-0.405170\pi\)
0.293530 + 0.955950i \(0.405170\pi\)
\(728\) 11.7597 0.435843
\(729\) −31.9506 −1.18335
\(730\) 0 0
\(731\) −4.35096 −0.160926
\(732\) 53.7474 1.98656
\(733\) 8.66500 0.320049 0.160025 0.987113i \(-0.448843\pi\)
0.160025 + 0.987113i \(0.448843\pi\)
\(734\) −72.0507 −2.65944
\(735\) 0 0
\(736\) −75.9575 −2.79983
\(737\) 58.8480 2.16769
\(738\) −105.075 −3.86786
\(739\) −51.3157 −1.88768 −0.943840 0.330403i \(-0.892815\pi\)
−0.943840 + 0.330403i \(0.892815\pi\)
\(740\) 0 0
\(741\) −12.2373 −0.449548
\(742\) 9.51421 0.349278
\(743\) −19.9955 −0.733563 −0.366781 0.930307i \(-0.619540\pi\)
−0.366781 + 0.930307i \(0.619540\pi\)
\(744\) −114.075 −4.18218
\(745\) 0 0
\(746\) −3.52274 −0.128977
\(747\) −20.5751 −0.752804
\(748\) 143.262 5.23816
\(749\) −0.316016 −0.0115470
\(750\) 0 0
\(751\) −30.4912 −1.11264 −0.556320 0.830968i \(-0.687787\pi\)
−0.556320 + 0.830968i \(0.687787\pi\)
\(752\) −70.2523 −2.56184
\(753\) 53.3288 1.94341
\(754\) 89.0400 3.24264
\(755\) 0 0
\(756\) −1.36890 −0.0497864
\(757\) −10.7919 −0.392238 −0.196119 0.980580i \(-0.562834\pi\)
−0.196119 + 0.980580i \(0.562834\pi\)
\(758\) 9.78910 0.355556
\(759\) 43.1477 1.56616
\(760\) 0 0
\(761\) 14.3354 0.519657 0.259828 0.965655i \(-0.416334\pi\)
0.259828 + 0.965655i \(0.416334\pi\)
\(762\) 126.887 4.59662
\(763\) −1.39354 −0.0504495
\(764\) 122.496 4.43174
\(765\) 0 0
\(766\) −77.1032 −2.78585
\(767\) −4.59282 −0.165837
\(768\) 55.7791 2.01276
\(769\) 20.7301 0.747547 0.373773 0.927520i \(-0.378064\pi\)
0.373773 + 0.927520i \(0.378064\pi\)
\(770\) 0 0
\(771\) −18.3899 −0.662296
\(772\) −48.4688 −1.74443
\(773\) −40.3752 −1.45220 −0.726098 0.687591i \(-0.758668\pi\)
−0.726098 + 0.687591i \(0.758668\pi\)
\(774\) 5.98273 0.215045
\(775\) 0 0
\(776\) −88.1952 −3.16602
\(777\) 4.82037 0.172930
\(778\) −79.2346 −2.84070
\(779\) −15.4902 −0.554993
\(780\) 0 0
\(781\) 54.6616 1.95594
\(782\) −71.6971 −2.56388
\(783\) −6.44869 −0.230457
\(784\) −92.3413 −3.29790
\(785\) 0 0
\(786\) 9.52524 0.339754
\(787\) 18.3264 0.653266 0.326633 0.945151i \(-0.394086\pi\)
0.326633 + 0.945151i \(0.394086\pi\)
\(788\) 35.7330 1.27293
\(789\) −51.7175 −1.84119
\(790\) 0 0
\(791\) 6.17668 0.219618
\(792\) −122.562 −4.35505
\(793\) 15.0780 0.535437
\(794\) 10.6413 0.377645
\(795\) 0 0
\(796\) 17.2725 0.612206
\(797\) 36.1893 1.28189 0.640945 0.767587i \(-0.278543\pi\)
0.640945 + 0.767587i \(0.278543\pi\)
\(798\) −3.14995 −0.111507
\(799\) −33.7971 −1.19566
\(800\) 0 0
\(801\) 12.5313 0.442773
\(802\) −0.0908875 −0.00320935
\(803\) −32.5358 −1.14816
\(804\) 186.561 6.57952
\(805\) 0 0
\(806\) −51.4359 −1.81175
\(807\) −0.448375 −0.0157835
\(808\) −66.3715 −2.33494
\(809\) −0.129006 −0.00453561 −0.00226781 0.999997i \(-0.500722\pi\)
−0.00226781 + 0.999997i \(0.500722\pi\)
\(810\) 0 0
\(811\) −22.3392 −0.784434 −0.392217 0.919873i \(-0.628292\pi\)
−0.392217 + 0.919873i \(0.628292\pi\)
\(812\) 16.6345 0.583756
\(813\) −44.9725 −1.57725
\(814\) 61.2313 2.14615
\(815\) 0 0
\(816\) 217.738 7.62237
\(817\) 0.881977 0.0308565
\(818\) 24.0256 0.840036
\(819\) −4.35050 −0.152019
\(820\) 0 0
\(821\) 27.9841 0.976653 0.488327 0.872661i \(-0.337607\pi\)
0.488327 + 0.872661i \(0.337607\pi\)
\(822\) 37.5906 1.31112
\(823\) −4.52041 −0.157572 −0.0787859 0.996892i \(-0.525104\pi\)
−0.0787859 + 0.996892i \(0.525104\pi\)
\(824\) 69.7303 2.42917
\(825\) 0 0
\(826\) −1.18222 −0.0411347
\(827\) 10.2432 0.356189 0.178095 0.984013i \(-0.443007\pi\)
0.178095 + 0.984013i \(0.443007\pi\)
\(828\) 71.5520 2.48660
\(829\) 15.8251 0.549630 0.274815 0.961497i \(-0.411383\pi\)
0.274815 + 0.961497i \(0.411383\pi\)
\(830\) 0 0
\(831\) −6.42955 −0.223039
\(832\) 85.9173 2.97865
\(833\) −44.4237 −1.53919
\(834\) 75.5506 2.61610
\(835\) 0 0
\(836\) −29.0404 −1.00438
\(837\) 3.72523 0.128763
\(838\) 80.6461 2.78587
\(839\) 33.9655 1.17262 0.586309 0.810087i \(-0.300580\pi\)
0.586309 + 0.810087i \(0.300580\pi\)
\(840\) 0 0
\(841\) 49.3626 1.70216
\(842\) −43.1245 −1.48617
\(843\) −56.3141 −1.93956
\(844\) −122.529 −4.21763
\(845\) 0 0
\(846\) 46.4723 1.59775
\(847\) −2.32085 −0.0797454
\(848\) 133.314 4.57802
\(849\) −32.9160 −1.12967
\(850\) 0 0
\(851\) −22.2408 −0.762405
\(852\) 173.290 5.93680
\(853\) −51.3501 −1.75819 −0.879097 0.476643i \(-0.841853\pi\)
−0.879097 + 0.476643i \(0.841853\pi\)
\(854\) 3.88118 0.132811
\(855\) 0 0
\(856\) −7.91778 −0.270624
\(857\) 27.2848 0.932030 0.466015 0.884777i \(-0.345689\pi\)
0.466015 + 0.884777i \(0.345689\pi\)
\(858\) −105.647 −3.60674
\(859\) −6.65604 −0.227101 −0.113551 0.993532i \(-0.536222\pi\)
−0.113551 + 0.993532i \(0.536222\pi\)
\(860\) 0 0
\(861\) −10.5278 −0.358786
\(862\) −67.0689 −2.28438
\(863\) −43.1149 −1.46765 −0.733824 0.679340i \(-0.762266\pi\)
−0.733824 + 0.679340i \(0.762266\pi\)
\(864\) −13.4697 −0.458249
\(865\) 0 0
\(866\) −84.1870 −2.86079
\(867\) 62.1127 2.10946
\(868\) −9.60928 −0.326160
\(869\) −4.92793 −0.167168
\(870\) 0 0
\(871\) 52.3371 1.77338
\(872\) −34.9151 −1.18237
\(873\) 32.6278 1.10429
\(874\) 14.5336 0.491607
\(875\) 0 0
\(876\) −103.146 −3.48497
\(877\) −30.7736 −1.03915 −0.519575 0.854425i \(-0.673910\pi\)
−0.519575 + 0.854425i \(0.673910\pi\)
\(878\) 2.59094 0.0874401
\(879\) 81.2455 2.74034
\(880\) 0 0
\(881\) −35.5730 −1.19849 −0.599243 0.800567i \(-0.704532\pi\)
−0.599243 + 0.800567i \(0.704532\pi\)
\(882\) 61.0843 2.05682
\(883\) 39.0447 1.31396 0.656979 0.753909i \(-0.271834\pi\)
0.656979 + 0.753909i \(0.271834\pi\)
\(884\) 127.411 4.28531
\(885\) 0 0
\(886\) 17.6202 0.591961
\(887\) 35.4372 1.18987 0.594933 0.803775i \(-0.297179\pi\)
0.594933 + 0.803775i \(0.297179\pi\)
\(888\) 120.774 4.05292
\(889\) 6.65010 0.223037
\(890\) 0 0
\(891\) −33.6879 −1.12859
\(892\) 96.8423 3.24252
\(893\) 6.85097 0.229259
\(894\) −56.0166 −1.87348
\(895\) 0 0
\(896\) 8.98792 0.300265
\(897\) 38.3739 1.28127
\(898\) 25.3808 0.846970
\(899\) −45.2679 −1.50977
\(900\) 0 0
\(901\) 64.1350 2.13665
\(902\) −133.730 −4.45274
\(903\) 0.599429 0.0199477
\(904\) 154.757 5.14713
\(905\) 0 0
\(906\) 80.5964 2.67763
\(907\) 6.19074 0.205560 0.102780 0.994704i \(-0.467226\pi\)
0.102780 + 0.994704i \(0.467226\pi\)
\(908\) −55.4798 −1.84116
\(909\) 24.5542 0.814410
\(910\) 0 0
\(911\) 0.700721 0.0232159 0.0116080 0.999933i \(-0.496305\pi\)
0.0116080 + 0.999933i \(0.496305\pi\)
\(912\) −44.1375 −1.46154
\(913\) −26.1863 −0.866638
\(914\) −73.1612 −2.41996
\(915\) 0 0
\(916\) −29.1999 −0.964790
\(917\) 0.499215 0.0164855
\(918\) −12.7142 −0.419631
\(919\) −29.3520 −0.968233 −0.484117 0.875004i \(-0.660859\pi\)
−0.484117 + 0.875004i \(0.660859\pi\)
\(920\) 0 0
\(921\) −31.8141 −1.04831
\(922\) 86.7088 2.85560
\(923\) 48.6139 1.60014
\(924\) −19.7371 −0.649302
\(925\) 0 0
\(926\) 47.4646 1.55978
\(927\) −25.7967 −0.847276
\(928\) 163.680 5.37306
\(929\) 52.4498 1.72082 0.860411 0.509601i \(-0.170207\pi\)
0.860411 + 0.509601i \(0.170207\pi\)
\(930\) 0 0
\(931\) 9.00507 0.295129
\(932\) −146.809 −4.80889
\(933\) 55.4411 1.81506
\(934\) 35.0359 1.14641
\(935\) 0 0
\(936\) −109.002 −3.56283
\(937\) 25.6384 0.837569 0.418784 0.908086i \(-0.362456\pi\)
0.418784 + 0.908086i \(0.362456\pi\)
\(938\) 13.4719 0.439873
\(939\) −27.3026 −0.890986
\(940\) 0 0
\(941\) −12.3906 −0.403921 −0.201960 0.979394i \(-0.564731\pi\)
−0.201960 + 0.979394i \(0.564731\pi\)
\(942\) −39.8381 −1.29800
\(943\) 48.5744 1.58180
\(944\) −16.5654 −0.539158
\(945\) 0 0
\(946\) 7.61431 0.247563
\(947\) 7.84757 0.255012 0.127506 0.991838i \(-0.459303\pi\)
0.127506 + 0.991838i \(0.459303\pi\)
\(948\) −15.6226 −0.507400
\(949\) −28.9361 −0.939304
\(950\) 0 0
\(951\) 19.4786 0.631637
\(952\) 20.4051 0.661331
\(953\) 31.9352 1.03448 0.517242 0.855839i \(-0.326959\pi\)
0.517242 + 0.855839i \(0.326959\pi\)
\(954\) −88.1881 −2.85519
\(955\) 0 0
\(956\) 34.9666 1.13090
\(957\) −92.9785 −3.00557
\(958\) 18.0462 0.583047
\(959\) 1.97011 0.0636182
\(960\) 0 0
\(961\) −4.84999 −0.156451
\(962\) 54.4567 1.75575
\(963\) 2.92918 0.0943916
\(964\) 5.29342 0.170490
\(965\) 0 0
\(966\) 9.87767 0.317809
\(967\) −8.42368 −0.270887 −0.135444 0.990785i \(-0.543246\pi\)
−0.135444 + 0.990785i \(0.543246\pi\)
\(968\) −58.1489 −1.86898
\(969\) −21.2337 −0.682126
\(970\) 0 0
\(971\) −44.1565 −1.41705 −0.708525 0.705686i \(-0.750639\pi\)
−0.708525 + 0.705686i \(0.750639\pi\)
\(972\) −118.367 −3.79661
\(973\) 3.95959 0.126939
\(974\) 52.9381 1.69625
\(975\) 0 0
\(976\) 54.3836 1.74078
\(977\) 5.28247 0.169001 0.0845006 0.996423i \(-0.473071\pi\)
0.0845006 + 0.996423i \(0.473071\pi\)
\(978\) −21.7448 −0.695323
\(979\) 15.9488 0.509726
\(980\) 0 0
\(981\) 12.9168 0.412403
\(982\) 17.8767 0.570469
\(983\) 3.33673 0.106425 0.0532125 0.998583i \(-0.483054\pi\)
0.0532125 + 0.998583i \(0.483054\pi\)
\(984\) −263.773 −8.40879
\(985\) 0 0
\(986\) 154.499 4.92026
\(987\) 4.65621 0.148209
\(988\) −25.8274 −0.821678
\(989\) −2.76572 −0.0879447
\(990\) 0 0
\(991\) −21.6985 −0.689274 −0.344637 0.938736i \(-0.611998\pi\)
−0.344637 + 0.938736i \(0.611998\pi\)
\(992\) −94.5534 −3.00207
\(993\) 0.797421 0.0253054
\(994\) 12.5135 0.396904
\(995\) 0 0
\(996\) −83.0163 −2.63047
\(997\) 10.6834 0.338347 0.169174 0.985586i \(-0.445890\pi\)
0.169174 + 0.985586i \(0.445890\pi\)
\(998\) −107.169 −3.39236
\(999\) −3.94401 −0.124783
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 \(a_p\))