Properties

Label 6025.2.a.h.1.4
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 1.4
Root \(1.63125\)
Character \(\chi\) = 6025.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.63125 q^{2}\) \(+1.16790 q^{3}\) \(+0.660992 q^{4}\) \(-1.90514 q^{6}\) \(-5.06139 q^{7}\) \(+2.18426 q^{8}\) \(-1.63601 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.63125 q^{2}\) \(+1.16790 q^{3}\) \(+0.660992 q^{4}\) \(-1.90514 q^{6}\) \(-5.06139 q^{7}\) \(+2.18426 q^{8}\) \(-1.63601 q^{9}\) \(+1.08118 q^{11}\) \(+0.771973 q^{12}\) \(-3.01110 q^{13}\) \(+8.25641 q^{14}\) \(-4.88507 q^{16}\) \(-2.47710 q^{17}\) \(+2.66875 q^{18}\) \(-7.12459 q^{19}\) \(-5.91119 q^{21}\) \(-1.76369 q^{22}\) \(-5.33139 q^{23}\) \(+2.55100 q^{24}\) \(+4.91187 q^{26}\) \(-5.41439 q^{27}\) \(-3.34554 q^{28}\) \(-6.80248 q^{29}\) \(-8.37871 q^{31}\) \(+3.60028 q^{32}\) \(+1.26271 q^{33}\) \(+4.04078 q^{34}\) \(-1.08139 q^{36}\) \(+2.09398 q^{37}\) \(+11.6220 q^{38}\) \(-3.51666 q^{39}\) \(-10.6564 q^{41}\) \(+9.64266 q^{42}\) \(+5.49791 q^{43}\) \(+0.714654 q^{44}\) \(+8.69686 q^{46}\) \(-4.90386 q^{47}\) \(-5.70528 q^{48}\) \(+18.6176 q^{49}\) \(-2.89301 q^{51}\) \(-1.99032 q^{52}\) \(+4.04410 q^{53}\) \(+8.83226 q^{54}\) \(-11.0554 q^{56}\) \(-8.32081 q^{57}\) \(+11.0966 q^{58}\) \(+5.64831 q^{59}\) \(-2.03784 q^{61}\) \(+13.6678 q^{62}\) \(+8.28048 q^{63}\) \(+3.89718 q^{64}\) \(-2.05981 q^{66}\) \(-7.65097 q^{67}\) \(-1.63735 q^{68}\) \(-6.22653 q^{69}\) \(+12.2631 q^{71}\) \(-3.57348 q^{72}\) \(-0.733715 q^{73}\) \(-3.41582 q^{74}\) \(-4.70930 q^{76}\) \(-5.47229 q^{77}\) \(+5.73657 q^{78}\) \(+6.86216 q^{79}\) \(-1.41544 q^{81}\) \(+17.3833 q^{82}\) \(-5.58812 q^{83}\) \(-3.90725 q^{84}\) \(-8.96849 q^{86}\) \(-7.94461 q^{87}\) \(+2.36159 q^{88}\) \(+9.62798 q^{89}\) \(+15.2403 q^{91}\) \(-3.52401 q^{92}\) \(-9.78549 q^{93}\) \(+7.99945 q^{94}\) \(+4.20476 q^{96}\) \(+10.9185 q^{97}\) \(-30.3701 q^{98}\) \(-1.76883 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 13q^{4} \) \(\mathstrut -\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut 22q^{11} \) \(\mathstrut +\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 15q^{16} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut -\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut -\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 5q^{27} \) \(\mathstrut +\mathstrut 11q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut -\mathstrut 8q^{36} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut +\mathstrut 31q^{39} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 49q^{42} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut +\mathstrut 42q^{44} \) \(\mathstrut -\mathstrut 25q^{46} \) \(\mathstrut -\mathstrut 34q^{47} \) \(\mathstrut +\mathstrut 49q^{48} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 41q^{52} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut -\mathstrut 40q^{54} \) \(\mathstrut +\mathstrut q^{56} \) \(\mathstrut +\mathstrut 22q^{57} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 26q^{59} \) \(\mathstrut -\mathstrut 26q^{61} \) \(\mathstrut +\mathstrut 17q^{62} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 13q^{64} \) \(\mathstrut -\mathstrut 2q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 35q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut +\mathstrut 94q^{71} \) \(\mathstrut -\mathstrut 17q^{72} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 26q^{74} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 7q^{77} \) \(\mathstrut -\mathstrut 54q^{78} \) \(\mathstrut +\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 15q^{82} \) \(\mathstrut +\mathstrut 8q^{83} \) \(\mathstrut +\mathstrut 2q^{84} \) \(\mathstrut +\mathstrut 9q^{86} \) \(\mathstrut -\mathstrut 4q^{87} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut -\mathstrut 3q^{89} \) \(\mathstrut -\mathstrut 20q^{91} \) \(\mathstrut -\mathstrut 36q^{92} \) \(\mathstrut -\mathstrut 12q^{93} \) \(\mathstrut +\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 23q^{96} \) \(\mathstrut +\mathstrut 29q^{97} \) \(\mathstrut -\mathstrut 28q^{98} \) \(\mathstrut +\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.63125 −1.15347 −0.576736 0.816931i \(-0.695674\pi\)
−0.576736 + 0.816931i \(0.695674\pi\)
\(3\) 1.16790 0.674287 0.337144 0.941453i \(-0.390539\pi\)
0.337144 + 0.941453i \(0.390539\pi\)
\(4\) 0.660992 0.330496
\(5\) 0 0
\(6\) −1.90514 −0.777771
\(7\) −5.06139 −1.91302 −0.956512 0.291693i \(-0.905782\pi\)
−0.956512 + 0.291693i \(0.905782\pi\)
\(8\) 2.18426 0.772253
\(9\) −1.63601 −0.545337
\(10\) 0 0
\(11\) 1.08118 0.325989 0.162995 0.986627i \(-0.447885\pi\)
0.162995 + 0.986627i \(0.447885\pi\)
\(12\) 0.771973 0.222849
\(13\) −3.01110 −0.835129 −0.417565 0.908647i \(-0.637116\pi\)
−0.417565 + 0.908647i \(0.637116\pi\)
\(14\) 8.25641 2.20662
\(15\) 0 0
\(16\) −4.88507 −1.22127
\(17\) −2.47710 −0.600785 −0.300393 0.953816i \(-0.597118\pi\)
−0.300393 + 0.953816i \(0.597118\pi\)
\(18\) 2.66875 0.629030
\(19\) −7.12459 −1.63449 −0.817247 0.576287i \(-0.804501\pi\)
−0.817247 + 0.576287i \(0.804501\pi\)
\(20\) 0 0
\(21\) −5.91119 −1.28993
\(22\) −1.76369 −0.376019
\(23\) −5.33139 −1.11167 −0.555836 0.831292i \(-0.687602\pi\)
−0.555836 + 0.831292i \(0.687602\pi\)
\(24\) 2.55100 0.520721
\(25\) 0 0
\(26\) 4.91187 0.963298
\(27\) −5.41439 −1.04200
\(28\) −3.34554 −0.632247
\(29\) −6.80248 −1.26319 −0.631595 0.775299i \(-0.717599\pi\)
−0.631595 + 0.775299i \(0.717599\pi\)
\(30\) 0 0
\(31\) −8.37871 −1.50486 −0.752430 0.658672i \(-0.771119\pi\)
−0.752430 + 0.658672i \(0.771119\pi\)
\(32\) 3.60028 0.636445
\(33\) 1.26271 0.219810
\(34\) 4.04078 0.692989
\(35\) 0 0
\(36\) −1.08139 −0.180232
\(37\) 2.09398 0.344249 0.172124 0.985075i \(-0.444937\pi\)
0.172124 + 0.985075i \(0.444937\pi\)
\(38\) 11.6220 1.88534
\(39\) −3.51666 −0.563117
\(40\) 0 0
\(41\) −10.6564 −1.66425 −0.832124 0.554589i \(-0.812875\pi\)
−0.832124 + 0.554589i \(0.812875\pi\)
\(42\) 9.64266 1.48789
\(43\) 5.49791 0.838423 0.419211 0.907889i \(-0.362307\pi\)
0.419211 + 0.907889i \(0.362307\pi\)
\(44\) 0.714654 0.107738
\(45\) 0 0
\(46\) 8.69686 1.28228
\(47\) −4.90386 −0.715302 −0.357651 0.933855i \(-0.616422\pi\)
−0.357651 + 0.933855i \(0.616422\pi\)
\(48\) −5.70528 −0.823486
\(49\) 18.6176 2.65966
\(50\) 0 0
\(51\) −2.89301 −0.405102
\(52\) −1.99032 −0.276007
\(53\) 4.04410 0.555500 0.277750 0.960653i \(-0.410411\pi\)
0.277750 + 0.960653i \(0.410411\pi\)
\(54\) 8.83226 1.20192
\(55\) 0 0
\(56\) −11.0554 −1.47734
\(57\) −8.32081 −1.10212
\(58\) 11.0966 1.45705
\(59\) 5.64831 0.735347 0.367673 0.929955i \(-0.380154\pi\)
0.367673 + 0.929955i \(0.380154\pi\)
\(60\) 0 0
\(61\) −2.03784 −0.260919 −0.130459 0.991454i \(-0.541645\pi\)
−0.130459 + 0.991454i \(0.541645\pi\)
\(62\) 13.6678 1.73581
\(63\) 8.28048 1.04324
\(64\) 3.89718 0.487148
\(65\) 0 0
\(66\) −2.05981 −0.253545
\(67\) −7.65097 −0.934715 −0.467358 0.884068i \(-0.654794\pi\)
−0.467358 + 0.884068i \(0.654794\pi\)
\(68\) −1.63735 −0.198557
\(69\) −6.22653 −0.749586
\(70\) 0 0
\(71\) 12.2631 1.45536 0.727682 0.685915i \(-0.240598\pi\)
0.727682 + 0.685915i \(0.240598\pi\)
\(72\) −3.57348 −0.421138
\(73\) −0.733715 −0.0858748 −0.0429374 0.999078i \(-0.513672\pi\)
−0.0429374 + 0.999078i \(0.513672\pi\)
\(74\) −3.41582 −0.397081
\(75\) 0 0
\(76\) −4.70930 −0.540194
\(77\) −5.47229 −0.623625
\(78\) 5.73657 0.649539
\(79\) 6.86216 0.772053 0.386027 0.922488i \(-0.373847\pi\)
0.386027 + 0.922488i \(0.373847\pi\)
\(80\) 0 0
\(81\) −1.41544 −0.157271
\(82\) 17.3833 1.91966
\(83\) −5.58812 −0.613376 −0.306688 0.951810i \(-0.599221\pi\)
−0.306688 + 0.951810i \(0.599221\pi\)
\(84\) −3.90725 −0.426316
\(85\) 0 0
\(86\) −8.96849 −0.967097
\(87\) −7.94461 −0.851752
\(88\) 2.36159 0.251746
\(89\) 9.62798 1.02056 0.510282 0.860007i \(-0.329541\pi\)
0.510282 + 0.860007i \(0.329541\pi\)
\(90\) 0 0
\(91\) 15.2403 1.59762
\(92\) −3.52401 −0.367403
\(93\) −9.78549 −1.01471
\(94\) 7.99945 0.825080
\(95\) 0 0
\(96\) 4.20476 0.429147
\(97\) 10.9185 1.10861 0.554303 0.832315i \(-0.312985\pi\)
0.554303 + 0.832315i \(0.312985\pi\)
\(98\) −30.3701 −3.06784
\(99\) −1.76883 −0.177774
\(100\) 0 0
\(101\) −13.9401 −1.38709 −0.693545 0.720413i \(-0.743952\pi\)
−0.693545 + 0.720413i \(0.743952\pi\)
\(102\) 4.71923 0.467273
\(103\) 7.14621 0.704137 0.352068 0.935974i \(-0.385478\pi\)
0.352068 + 0.935974i \(0.385478\pi\)
\(104\) −6.57703 −0.644931
\(105\) 0 0
\(106\) −6.59695 −0.640753
\(107\) −17.8929 −1.72977 −0.864886 0.501968i \(-0.832610\pi\)
−0.864886 + 0.501968i \(0.832610\pi\)
\(108\) −3.57887 −0.344377
\(109\) −14.9297 −1.43001 −0.715004 0.699120i \(-0.753575\pi\)
−0.715004 + 0.699120i \(0.753575\pi\)
\(110\) 0 0
\(111\) 2.44556 0.232123
\(112\) 24.7252 2.33632
\(113\) −0.859306 −0.0808367 −0.0404184 0.999183i \(-0.512869\pi\)
−0.0404184 + 0.999183i \(0.512869\pi\)
\(114\) 13.5734 1.27126
\(115\) 0 0
\(116\) −4.49639 −0.417479
\(117\) 4.92619 0.455427
\(118\) −9.21383 −0.848201
\(119\) 12.5376 1.14932
\(120\) 0 0
\(121\) −9.83104 −0.893731
\(122\) 3.32424 0.300962
\(123\) −12.4456 −1.12218
\(124\) −5.53826 −0.497351
\(125\) 0 0
\(126\) −13.5076 −1.20335
\(127\) 3.01886 0.267880 0.133940 0.990989i \(-0.457237\pi\)
0.133940 + 0.990989i \(0.457237\pi\)
\(128\) −13.5578 −1.19836
\(129\) 6.42100 0.565338
\(130\) 0 0
\(131\) −2.17519 −0.190047 −0.0950234 0.995475i \(-0.530293\pi\)
−0.0950234 + 0.995475i \(0.530293\pi\)
\(132\) 0.834644 0.0726464
\(133\) 36.0603 3.12683
\(134\) 12.4807 1.07817
\(135\) 0 0
\(136\) −5.41064 −0.463958
\(137\) −15.9150 −1.35971 −0.679854 0.733347i \(-0.737957\pi\)
−0.679854 + 0.733347i \(0.737957\pi\)
\(138\) 10.1571 0.864626
\(139\) −15.0721 −1.27840 −0.639201 0.769040i \(-0.720735\pi\)
−0.639201 + 0.769040i \(0.720735\pi\)
\(140\) 0 0
\(141\) −5.72722 −0.482319
\(142\) −20.0043 −1.67872
\(143\) −3.25555 −0.272243
\(144\) 7.99203 0.666003
\(145\) 0 0
\(146\) 1.19688 0.0990542
\(147\) 21.7435 1.79338
\(148\) 1.38411 0.113773
\(149\) −1.36774 −0.112050 −0.0560250 0.998429i \(-0.517843\pi\)
−0.0560250 + 0.998429i \(0.517843\pi\)
\(150\) 0 0
\(151\) 17.1854 1.39853 0.699264 0.714864i \(-0.253511\pi\)
0.699264 + 0.714864i \(0.253511\pi\)
\(152\) −15.5620 −1.26224
\(153\) 4.05256 0.327630
\(154\) 8.92669 0.719334
\(155\) 0 0
\(156\) −2.32449 −0.186108
\(157\) −12.1279 −0.967909 −0.483955 0.875093i \(-0.660800\pi\)
−0.483955 + 0.875093i \(0.660800\pi\)
\(158\) −11.1939 −0.890541
\(159\) 4.72310 0.374566
\(160\) 0 0
\(161\) 26.9842 2.12665
\(162\) 2.30894 0.181407
\(163\) −10.7083 −0.838737 −0.419369 0.907816i \(-0.637749\pi\)
−0.419369 + 0.907816i \(0.637749\pi\)
\(164\) −7.04379 −0.550028
\(165\) 0 0
\(166\) 9.11564 0.707511
\(167\) 10.5539 0.816684 0.408342 0.912829i \(-0.366107\pi\)
0.408342 + 0.912829i \(0.366107\pi\)
\(168\) −12.9116 −0.996151
\(169\) −3.93327 −0.302559
\(170\) 0 0
\(171\) 11.6559 0.891350
\(172\) 3.63407 0.277096
\(173\) 2.07621 0.157851 0.0789255 0.996881i \(-0.474851\pi\)
0.0789255 + 0.996881i \(0.474851\pi\)
\(174\) 12.9597 0.982472
\(175\) 0 0
\(176\) −5.28166 −0.398120
\(177\) 6.59665 0.495835
\(178\) −15.7057 −1.17719
\(179\) −3.06922 −0.229405 −0.114702 0.993400i \(-0.536591\pi\)
−0.114702 + 0.993400i \(0.536591\pi\)
\(180\) 0 0
\(181\) −0.391403 −0.0290927 −0.0145464 0.999894i \(-0.504630\pi\)
−0.0145464 + 0.999894i \(0.504630\pi\)
\(182\) −24.8609 −1.84281
\(183\) −2.37999 −0.175934
\(184\) −11.6452 −0.858492
\(185\) 0 0
\(186\) 15.9626 1.17044
\(187\) −2.67820 −0.195849
\(188\) −3.24142 −0.236405
\(189\) 27.4043 1.99337
\(190\) 0 0
\(191\) 4.99018 0.361077 0.180538 0.983568i \(-0.442216\pi\)
0.180538 + 0.983568i \(0.442216\pi\)
\(192\) 4.55152 0.328477
\(193\) −13.5209 −0.973254 −0.486627 0.873610i \(-0.661773\pi\)
−0.486627 + 0.873610i \(0.661773\pi\)
\(194\) −17.8109 −1.27874
\(195\) 0 0
\(196\) 12.3061 0.879008
\(197\) −5.86751 −0.418043 −0.209021 0.977911i \(-0.567028\pi\)
−0.209021 + 0.977911i \(0.567028\pi\)
\(198\) 2.88541 0.205057
\(199\) 12.5774 0.891585 0.445792 0.895136i \(-0.352922\pi\)
0.445792 + 0.895136i \(0.352922\pi\)
\(200\) 0 0
\(201\) −8.93557 −0.630266
\(202\) 22.7398 1.59997
\(203\) 34.4300 2.41651
\(204\) −1.91225 −0.133885
\(205\) 0 0
\(206\) −11.6573 −0.812201
\(207\) 8.72221 0.606236
\(208\) 14.7095 1.01992
\(209\) −7.70299 −0.532827
\(210\) 0 0
\(211\) 6.00657 0.413509 0.206755 0.978393i \(-0.433710\pi\)
0.206755 + 0.978393i \(0.433710\pi\)
\(212\) 2.67312 0.183591
\(213\) 14.3221 0.981333
\(214\) 29.1879 1.99524
\(215\) 0 0
\(216\) −11.8265 −0.804689
\(217\) 42.4079 2.87884
\(218\) 24.3542 1.64947
\(219\) −0.856905 −0.0579043
\(220\) 0 0
\(221\) 7.45880 0.501733
\(222\) −3.98934 −0.267747
\(223\) 25.7624 1.72518 0.862590 0.505904i \(-0.168841\pi\)
0.862590 + 0.505904i \(0.168841\pi\)
\(224\) −18.2224 −1.21753
\(225\) 0 0
\(226\) 1.40175 0.0932429
\(227\) −5.03720 −0.334331 −0.167165 0.985929i \(-0.553461\pi\)
−0.167165 + 0.985929i \(0.553461\pi\)
\(228\) −5.49999 −0.364246
\(229\) 21.1245 1.39594 0.697972 0.716125i \(-0.254086\pi\)
0.697972 + 0.716125i \(0.254086\pi\)
\(230\) 0 0
\(231\) −6.39108 −0.420502
\(232\) −14.8584 −0.975502
\(233\) −20.9468 −1.37227 −0.686135 0.727474i \(-0.740694\pi\)
−0.686135 + 0.727474i \(0.740694\pi\)
\(234\) −8.03588 −0.525322
\(235\) 0 0
\(236\) 3.73349 0.243029
\(237\) 8.01431 0.520586
\(238\) −20.4520 −1.32570
\(239\) −7.83541 −0.506831 −0.253415 0.967358i \(-0.581554\pi\)
−0.253415 + 0.967358i \(0.581554\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) 16.0369 1.03089
\(243\) 14.5901 0.935955
\(244\) −1.34700 −0.0862326
\(245\) 0 0
\(246\) 20.3019 1.29440
\(247\) 21.4529 1.36501
\(248\) −18.3013 −1.16213
\(249\) −6.52636 −0.413591
\(250\) 0 0
\(251\) −7.01648 −0.442876 −0.221438 0.975174i \(-0.571075\pi\)
−0.221438 + 0.975174i \(0.571075\pi\)
\(252\) 5.47334 0.344788
\(253\) −5.76421 −0.362393
\(254\) −4.92453 −0.308992
\(255\) 0 0
\(256\) 14.3219 0.895121
\(257\) −11.3057 −0.705229 −0.352615 0.935769i \(-0.614707\pi\)
−0.352615 + 0.935769i \(0.614707\pi\)
\(258\) −10.4743 −0.652101
\(259\) −10.5985 −0.658556
\(260\) 0 0
\(261\) 11.1289 0.688864
\(262\) 3.54828 0.219214
\(263\) −19.8667 −1.22503 −0.612516 0.790458i \(-0.709842\pi\)
−0.612516 + 0.790458i \(0.709842\pi\)
\(264\) 2.75810 0.169749
\(265\) 0 0
\(266\) −58.8236 −3.60671
\(267\) 11.2445 0.688153
\(268\) −5.05724 −0.308920
\(269\) −20.2533 −1.23486 −0.617431 0.786625i \(-0.711827\pi\)
−0.617431 + 0.786625i \(0.711827\pi\)
\(270\) 0 0
\(271\) −4.23892 −0.257496 −0.128748 0.991677i \(-0.541096\pi\)
−0.128748 + 0.991677i \(0.541096\pi\)
\(272\) 12.1008 0.733720
\(273\) 17.7992 1.07726
\(274\) 25.9614 1.56839
\(275\) 0 0
\(276\) −4.11569 −0.247735
\(277\) 0.369469 0.0221992 0.0110996 0.999938i \(-0.496467\pi\)
0.0110996 + 0.999938i \(0.496467\pi\)
\(278\) 24.5865 1.47460
\(279\) 13.7077 0.820656
\(280\) 0 0
\(281\) 24.6918 1.47299 0.736494 0.676444i \(-0.236480\pi\)
0.736494 + 0.676444i \(0.236480\pi\)
\(282\) 9.34255 0.556341
\(283\) −0.0696775 −0.00414190 −0.00207095 0.999998i \(-0.500659\pi\)
−0.00207095 + 0.999998i \(0.500659\pi\)
\(284\) 8.10583 0.480992
\(285\) 0 0
\(286\) 5.31064 0.314024
\(287\) 53.9361 3.18375
\(288\) −5.89009 −0.347077
\(289\) −10.8640 −0.639057
\(290\) 0 0
\(291\) 12.7517 0.747518
\(292\) −0.484980 −0.0283813
\(293\) 7.59140 0.443494 0.221747 0.975104i \(-0.428824\pi\)
0.221747 + 0.975104i \(0.428824\pi\)
\(294\) −35.4692 −2.06861
\(295\) 0 0
\(296\) 4.57381 0.265847
\(297\) −5.85395 −0.339681
\(298\) 2.23114 0.129246
\(299\) 16.0534 0.928389
\(300\) 0 0
\(301\) −27.8270 −1.60392
\(302\) −28.0338 −1.61316
\(303\) −16.2806 −0.935297
\(304\) 34.8042 1.99616
\(305\) 0 0
\(306\) −6.61076 −0.377912
\(307\) 20.6437 1.17820 0.589100 0.808060i \(-0.299482\pi\)
0.589100 + 0.808060i \(0.299482\pi\)
\(308\) −3.61714 −0.206106
\(309\) 8.34605 0.474790
\(310\) 0 0
\(311\) 24.0882 1.36592 0.682959 0.730456i \(-0.260693\pi\)
0.682959 + 0.730456i \(0.260693\pi\)
\(312\) −7.68132 −0.434869
\(313\) −16.3804 −0.925876 −0.462938 0.886391i \(-0.653205\pi\)
−0.462938 + 0.886391i \(0.653205\pi\)
\(314\) 19.7836 1.11646
\(315\) 0 0
\(316\) 4.53584 0.255161
\(317\) 1.59833 0.0897714 0.0448857 0.998992i \(-0.485708\pi\)
0.0448857 + 0.998992i \(0.485708\pi\)
\(318\) −7.70458 −0.432051
\(319\) −7.35473 −0.411786
\(320\) 0 0
\(321\) −20.8971 −1.16636
\(322\) −44.0181 −2.45304
\(323\) 17.6483 0.981980
\(324\) −0.935593 −0.0519774
\(325\) 0 0
\(326\) 17.4679 0.967460
\(327\) −17.4364 −0.964236
\(328\) −23.2764 −1.28522
\(329\) 24.8203 1.36839
\(330\) 0 0
\(331\) −26.9070 −1.47894 −0.739472 0.673188i \(-0.764925\pi\)
−0.739472 + 0.673188i \(0.764925\pi\)
\(332\) −3.69370 −0.202718
\(333\) −3.42578 −0.187732
\(334\) −17.2161 −0.942022
\(335\) 0 0
\(336\) 28.8766 1.57535
\(337\) 10.8794 0.592640 0.296320 0.955089i \(-0.404240\pi\)
0.296320 + 0.955089i \(0.404240\pi\)
\(338\) 6.41617 0.348994
\(339\) −1.00358 −0.0545072
\(340\) 0 0
\(341\) −9.05892 −0.490568
\(342\) −19.0138 −1.02815
\(343\) −58.8013 −3.17497
\(344\) 12.0089 0.647475
\(345\) 0 0
\(346\) −3.38682 −0.182077
\(347\) −12.9007 −0.692546 −0.346273 0.938134i \(-0.612553\pi\)
−0.346273 + 0.938134i \(0.612553\pi\)
\(348\) −5.25133 −0.281501
\(349\) −10.7803 −0.577058 −0.288529 0.957471i \(-0.593166\pi\)
−0.288529 + 0.957471i \(0.593166\pi\)
\(350\) 0 0
\(351\) 16.3033 0.870205
\(352\) 3.89256 0.207474
\(353\) −6.56859 −0.349611 −0.174805 0.984603i \(-0.555930\pi\)
−0.174805 + 0.984603i \(0.555930\pi\)
\(354\) −10.7608 −0.571931
\(355\) 0 0
\(356\) 6.36402 0.337292
\(357\) 14.6426 0.774970
\(358\) 5.00669 0.264612
\(359\) 15.8305 0.835504 0.417752 0.908561i \(-0.362818\pi\)
0.417752 + 0.908561i \(0.362818\pi\)
\(360\) 0 0
\(361\) 31.7598 1.67157
\(362\) 0.638477 0.0335576
\(363\) −11.4817 −0.602631
\(364\) 10.0738 0.528008
\(365\) 0 0
\(366\) 3.88237 0.202935
\(367\) 5.63657 0.294226 0.147113 0.989120i \(-0.453002\pi\)
0.147113 + 0.989120i \(0.453002\pi\)
\(368\) 26.0442 1.35765
\(369\) 17.4340 0.907576
\(370\) 0 0
\(371\) −20.4687 −1.06268
\(372\) −6.46814 −0.335357
\(373\) −1.29504 −0.0670548 −0.0335274 0.999438i \(-0.510674\pi\)
−0.0335274 + 0.999438i \(0.510674\pi\)
\(374\) 4.36883 0.225907
\(375\) 0 0
\(376\) −10.7113 −0.552394
\(377\) 20.4830 1.05493
\(378\) −44.7035 −2.29930
\(379\) −13.8155 −0.709656 −0.354828 0.934932i \(-0.615461\pi\)
−0.354828 + 0.934932i \(0.615461\pi\)
\(380\) 0 0
\(381\) 3.52572 0.180628
\(382\) −8.14026 −0.416492
\(383\) −12.0143 −0.613900 −0.306950 0.951726i \(-0.599308\pi\)
−0.306950 + 0.951726i \(0.599308\pi\)
\(384\) −15.8342 −0.808036
\(385\) 0 0
\(386\) 22.0560 1.12262
\(387\) −8.99463 −0.457223
\(388\) 7.21704 0.366390
\(389\) 4.86222 0.246524 0.123262 0.992374i \(-0.460664\pi\)
0.123262 + 0.992374i \(0.460664\pi\)
\(390\) 0 0
\(391\) 13.2064 0.667876
\(392\) 40.6658 2.05393
\(393\) −2.54040 −0.128146
\(394\) 9.57141 0.482201
\(395\) 0 0
\(396\) −1.16918 −0.0587536
\(397\) −9.17854 −0.460658 −0.230329 0.973113i \(-0.573980\pi\)
−0.230329 + 0.973113i \(0.573980\pi\)
\(398\) −20.5169 −1.02842
\(399\) 42.1148 2.10838
\(400\) 0 0
\(401\) −28.0569 −1.40109 −0.700547 0.713607i \(-0.747060\pi\)
−0.700547 + 0.713607i \(0.747060\pi\)
\(402\) 14.5762 0.726994
\(403\) 25.2291 1.25675
\(404\) −9.21429 −0.458428
\(405\) 0 0
\(406\) −56.1641 −2.78738
\(407\) 2.26398 0.112221
\(408\) −6.31908 −0.312841
\(409\) −11.6170 −0.574422 −0.287211 0.957867i \(-0.592728\pi\)
−0.287211 + 0.957867i \(0.592728\pi\)
\(410\) 0 0
\(411\) −18.5871 −0.916834
\(412\) 4.72359 0.232714
\(413\) −28.5883 −1.40674
\(414\) −14.2281 −0.699275
\(415\) 0 0
\(416\) −10.8408 −0.531514
\(417\) −17.6027 −0.862010
\(418\) 12.5655 0.614601
\(419\) 15.5789 0.761080 0.380540 0.924765i \(-0.375738\pi\)
0.380540 + 0.924765i \(0.375738\pi\)
\(420\) 0 0
\(421\) 7.53596 0.367280 0.183640 0.982994i \(-0.441212\pi\)
0.183640 + 0.982994i \(0.441212\pi\)
\(422\) −9.79824 −0.476971
\(423\) 8.02277 0.390081
\(424\) 8.83337 0.428986
\(425\) 0 0
\(426\) −23.3630 −1.13194
\(427\) 10.3143 0.499144
\(428\) −11.8271 −0.571683
\(429\) −3.80216 −0.183570
\(430\) 0 0
\(431\) 24.2144 1.16636 0.583182 0.812341i \(-0.301807\pi\)
0.583182 + 0.812341i \(0.301807\pi\)
\(432\) 26.4497 1.27256
\(433\) −1.90821 −0.0917025 −0.0458512 0.998948i \(-0.514600\pi\)
−0.0458512 + 0.998948i \(0.514600\pi\)
\(434\) −69.1781 −3.32065
\(435\) 0 0
\(436\) −9.86844 −0.472612
\(437\) 37.9840 1.81702
\(438\) 1.39783 0.0667910
\(439\) −14.9135 −0.711784 −0.355892 0.934527i \(-0.615823\pi\)
−0.355892 + 0.934527i \(0.615823\pi\)
\(440\) 0 0
\(441\) −30.4586 −1.45041
\(442\) −12.1672 −0.578735
\(443\) 23.0698 1.09608 0.548039 0.836453i \(-0.315375\pi\)
0.548039 + 0.836453i \(0.315375\pi\)
\(444\) 1.61650 0.0767156
\(445\) 0 0
\(446\) −42.0251 −1.98995
\(447\) −1.59739 −0.0755539
\(448\) −19.7251 −0.931925
\(449\) 14.5420 0.686277 0.343139 0.939285i \(-0.388510\pi\)
0.343139 + 0.939285i \(0.388510\pi\)
\(450\) 0 0
\(451\) −11.5215 −0.542527
\(452\) −0.567995 −0.0267162
\(453\) 20.0708 0.943009
\(454\) 8.21696 0.385641
\(455\) 0 0
\(456\) −18.1748 −0.851115
\(457\) −11.8002 −0.551991 −0.275995 0.961159i \(-0.589007\pi\)
−0.275995 + 0.961159i \(0.589007\pi\)
\(458\) −34.4594 −1.61018
\(459\) 13.4120 0.626019
\(460\) 0 0
\(461\) 15.0722 0.701985 0.350992 0.936378i \(-0.385844\pi\)
0.350992 + 0.936378i \(0.385844\pi\)
\(462\) 10.4255 0.485037
\(463\) −24.3295 −1.13069 −0.565344 0.824855i \(-0.691257\pi\)
−0.565344 + 0.824855i \(0.691257\pi\)
\(464\) 33.2306 1.54269
\(465\) 0 0
\(466\) 34.1695 1.58287
\(467\) −29.7743 −1.37779 −0.688895 0.724862i \(-0.741904\pi\)
−0.688895 + 0.724862i \(0.741904\pi\)
\(468\) 3.25618 0.150517
\(469\) 38.7245 1.78813
\(470\) 0 0
\(471\) −14.1641 −0.652649
\(472\) 12.3374 0.567874
\(473\) 5.94424 0.273317
\(474\) −13.0734 −0.600481
\(475\) 0 0
\(476\) 8.28724 0.379845
\(477\) −6.61619 −0.302934
\(478\) 12.7816 0.584615
\(479\) −10.1987 −0.465991 −0.232996 0.972478i \(-0.574853\pi\)
−0.232996 + 0.972478i \(0.574853\pi\)
\(480\) 0 0
\(481\) −6.30520 −0.287492
\(482\) −1.63125 −0.0743016
\(483\) 31.5149 1.43398
\(484\) −6.49825 −0.295375
\(485\) 0 0
\(486\) −23.8002 −1.07960
\(487\) 24.9246 1.12944 0.564720 0.825282i \(-0.308984\pi\)
0.564720 + 0.825282i \(0.308984\pi\)
\(488\) −4.45118 −0.201495
\(489\) −12.5062 −0.565550
\(490\) 0 0
\(491\) −26.8710 −1.21267 −0.606335 0.795209i \(-0.707361\pi\)
−0.606335 + 0.795209i \(0.707361\pi\)
\(492\) −8.22644 −0.370877
\(493\) 16.8504 0.758905
\(494\) −34.9951 −1.57450
\(495\) 0 0
\(496\) 40.9306 1.83784
\(497\) −62.0684 −2.78415
\(498\) 10.6462 0.477066
\(499\) −37.6147 −1.68387 −0.841933 0.539582i \(-0.818582\pi\)
−0.841933 + 0.539582i \(0.818582\pi\)
\(500\) 0 0
\(501\) 12.3259 0.550680
\(502\) 11.4457 0.510845
\(503\) 38.0897 1.69834 0.849168 0.528123i \(-0.177104\pi\)
0.849168 + 0.528123i \(0.177104\pi\)
\(504\) 18.0867 0.805648
\(505\) 0 0
\(506\) 9.40290 0.418010
\(507\) −4.59367 −0.204012
\(508\) 1.99544 0.0885334
\(509\) −37.4493 −1.65991 −0.829954 0.557831i \(-0.811634\pi\)
−0.829954 + 0.557831i \(0.811634\pi\)
\(510\) 0 0
\(511\) 3.71362 0.164281
\(512\) 3.75296 0.165859
\(513\) 38.5754 1.70314
\(514\) 18.4424 0.813462
\(515\) 0 0
\(516\) 4.24423 0.186842
\(517\) −5.30198 −0.233181
\(518\) 17.2888 0.759626
\(519\) 2.42480 0.106437
\(520\) 0 0
\(521\) 14.8226 0.649391 0.324695 0.945819i \(-0.394738\pi\)
0.324695 + 0.945819i \(0.394738\pi\)
\(522\) −18.1541 −0.794584
\(523\) −23.8624 −1.04343 −0.521715 0.853120i \(-0.674708\pi\)
−0.521715 + 0.853120i \(0.674708\pi\)
\(524\) −1.43778 −0.0628098
\(525\) 0 0
\(526\) 32.4076 1.41304
\(527\) 20.7549 0.904098
\(528\) −6.16845 −0.268447
\(529\) 5.42372 0.235814
\(530\) 0 0
\(531\) −9.24069 −0.401012
\(532\) 23.8356 1.03340
\(533\) 32.0875 1.38986
\(534\) −18.3427 −0.793765
\(535\) 0 0
\(536\) −16.7117 −0.721837
\(537\) −3.58454 −0.154685
\(538\) 33.0382 1.42438
\(539\) 20.1291 0.867021
\(540\) 0 0
\(541\) −12.9272 −0.555782 −0.277891 0.960613i \(-0.589635\pi\)
−0.277891 + 0.960613i \(0.589635\pi\)
\(542\) 6.91477 0.297015
\(543\) −0.457119 −0.0196168
\(544\) −8.91825 −0.382367
\(545\) 0 0
\(546\) −29.0350 −1.24258
\(547\) 9.03128 0.386150 0.193075 0.981184i \(-0.438154\pi\)
0.193075 + 0.981184i \(0.438154\pi\)
\(548\) −10.5197 −0.449379
\(549\) 3.33393 0.142289
\(550\) 0 0
\(551\) 48.4649 2.06467
\(552\) −13.6004 −0.578870
\(553\) −34.7320 −1.47696
\(554\) −0.602698 −0.0256062
\(555\) 0 0
\(556\) −9.96256 −0.422507
\(557\) 4.33616 0.183729 0.0918644 0.995772i \(-0.470717\pi\)
0.0918644 + 0.995772i \(0.470717\pi\)
\(558\) −22.3607 −0.946603
\(559\) −16.5547 −0.700191
\(560\) 0 0
\(561\) −3.12787 −0.132059
\(562\) −40.2786 −1.69905
\(563\) −6.56701 −0.276767 −0.138383 0.990379i \(-0.544191\pi\)
−0.138383 + 0.990379i \(0.544191\pi\)
\(564\) −3.78565 −0.159405
\(565\) 0 0
\(566\) 0.113662 0.00477756
\(567\) 7.16407 0.300863
\(568\) 26.7859 1.12391
\(569\) 18.1137 0.759366 0.379683 0.925117i \(-0.376033\pi\)
0.379683 + 0.925117i \(0.376033\pi\)
\(570\) 0 0
\(571\) 6.26298 0.262098 0.131049 0.991376i \(-0.458166\pi\)
0.131049 + 0.991376i \(0.458166\pi\)
\(572\) −2.15190 −0.0899753
\(573\) 5.82803 0.243470
\(574\) −87.9835 −3.67236
\(575\) 0 0
\(576\) −6.37583 −0.265660
\(577\) 1.76988 0.0736810 0.0368405 0.999321i \(-0.488271\pi\)
0.0368405 + 0.999321i \(0.488271\pi\)
\(578\) 17.7219 0.737134
\(579\) −15.7910 −0.656253
\(580\) 0 0
\(581\) 28.2836 1.17340
\(582\) −20.8013 −0.862241
\(583\) 4.37241 0.181087
\(584\) −1.60263 −0.0663171
\(585\) 0 0
\(586\) −12.3835 −0.511558
\(587\) −11.9082 −0.491502 −0.245751 0.969333i \(-0.579035\pi\)
−0.245751 + 0.969333i \(0.579035\pi\)
\(588\) 14.3723 0.592704
\(589\) 59.6949 2.45969
\(590\) 0 0
\(591\) −6.85266 −0.281881
\(592\) −10.2293 −0.420420
\(593\) 34.2932 1.40825 0.704126 0.710075i \(-0.251339\pi\)
0.704126 + 0.710075i \(0.251339\pi\)
\(594\) 9.54929 0.391812
\(595\) 0 0
\(596\) −0.904069 −0.0370321
\(597\) 14.6891 0.601184
\(598\) −26.1871 −1.07087
\(599\) −18.2245 −0.744632 −0.372316 0.928106i \(-0.621436\pi\)
−0.372316 + 0.928106i \(0.621436\pi\)
\(600\) 0 0
\(601\) −19.2591 −0.785595 −0.392797 0.919625i \(-0.628493\pi\)
−0.392797 + 0.919625i \(0.628493\pi\)
\(602\) 45.3930 1.85008
\(603\) 12.5171 0.509735
\(604\) 11.3594 0.462208
\(605\) 0 0
\(606\) 26.5578 1.07884
\(607\) −39.9799 −1.62273 −0.811367 0.584536i \(-0.801276\pi\)
−0.811367 + 0.584536i \(0.801276\pi\)
\(608\) −25.6505 −1.04027
\(609\) 40.2108 1.62942
\(610\) 0 0
\(611\) 14.7660 0.597369
\(612\) 2.67871 0.108281
\(613\) 18.3233 0.740070 0.370035 0.929018i \(-0.379346\pi\)
0.370035 + 0.929018i \(0.379346\pi\)
\(614\) −33.6752 −1.35902
\(615\) 0 0
\(616\) −11.9529 −0.481597
\(617\) −12.3769 −0.498273 −0.249137 0.968468i \(-0.580147\pi\)
−0.249137 + 0.968468i \(0.580147\pi\)
\(618\) −13.6145 −0.547657
\(619\) −8.87878 −0.356868 −0.178434 0.983952i \(-0.557103\pi\)
−0.178434 + 0.983952i \(0.557103\pi\)
\(620\) 0 0
\(621\) 28.8662 1.15836
\(622\) −39.2941 −1.57555
\(623\) −48.7309 −1.95236
\(624\) 17.1792 0.687717
\(625\) 0 0
\(626\) 26.7206 1.06797
\(627\) −8.99632 −0.359278
\(628\) −8.01643 −0.319890
\(629\) −5.18701 −0.206820
\(630\) 0 0
\(631\) 34.5564 1.37567 0.687835 0.725867i \(-0.258561\pi\)
0.687835 + 0.725867i \(0.258561\pi\)
\(632\) 14.9888 0.596221
\(633\) 7.01507 0.278824
\(634\) −2.60729 −0.103549
\(635\) 0 0
\(636\) 3.12193 0.123793
\(637\) −56.0596 −2.22116
\(638\) 11.9974 0.474983
\(639\) −20.0626 −0.793664
\(640\) 0 0
\(641\) −1.70265 −0.0672505 −0.0336253 0.999435i \(-0.510705\pi\)
−0.0336253 + 0.999435i \(0.510705\pi\)
\(642\) 34.0885 1.34537
\(643\) −40.7018 −1.60512 −0.802561 0.596571i \(-0.796530\pi\)
−0.802561 + 0.596571i \(0.796530\pi\)
\(644\) 17.8364 0.702851
\(645\) 0 0
\(646\) −28.7889 −1.13269
\(647\) 30.3915 1.19481 0.597406 0.801939i \(-0.296198\pi\)
0.597406 + 0.801939i \(0.296198\pi\)
\(648\) −3.09169 −0.121453
\(649\) 6.10685 0.239715
\(650\) 0 0
\(651\) 49.5282 1.94116
\(652\) −7.07809 −0.277200
\(653\) −6.95225 −0.272062 −0.136031 0.990705i \(-0.543435\pi\)
−0.136031 + 0.990705i \(0.543435\pi\)
\(654\) 28.4432 1.11222
\(655\) 0 0
\(656\) 52.0573 2.03249
\(657\) 1.20037 0.0468307
\(658\) −40.4883 −1.57840
\(659\) −38.2304 −1.48924 −0.744622 0.667486i \(-0.767370\pi\)
−0.744622 + 0.667486i \(0.767370\pi\)
\(660\) 0 0
\(661\) 35.0225 1.36222 0.681109 0.732182i \(-0.261498\pi\)
0.681109 + 0.732182i \(0.261498\pi\)
\(662\) 43.8922 1.70592
\(663\) 8.71113 0.338312
\(664\) −12.2059 −0.473681
\(665\) 0 0
\(666\) 5.58832 0.216543
\(667\) 36.2667 1.40425
\(668\) 6.97604 0.269911
\(669\) 30.0879 1.16327
\(670\) 0 0
\(671\) −2.20328 −0.0850566
\(672\) −21.2819 −0.820968
\(673\) 19.3765 0.746909 0.373454 0.927649i \(-0.378173\pi\)
0.373454 + 0.927649i \(0.378173\pi\)
\(674\) −17.7471 −0.683594
\(675\) 0 0
\(676\) −2.59986 −0.0999947
\(677\) 3.01738 0.115967 0.0579837 0.998318i \(-0.481533\pi\)
0.0579837 + 0.998318i \(0.481533\pi\)
\(678\) 1.63710 0.0628725
\(679\) −55.2627 −2.12079
\(680\) 0 0
\(681\) −5.88294 −0.225435
\(682\) 14.7774 0.565856
\(683\) 5.60316 0.214399 0.107199 0.994238i \(-0.465812\pi\)
0.107199 + 0.994238i \(0.465812\pi\)
\(684\) 7.70447 0.294588
\(685\) 0 0
\(686\) 95.9200 3.66224
\(687\) 24.6713 0.941267
\(688\) −26.8577 −1.02394
\(689\) −12.1772 −0.463914
\(690\) 0 0
\(691\) 49.0976 1.86776 0.933881 0.357583i \(-0.116399\pi\)
0.933881 + 0.357583i \(0.116399\pi\)
\(692\) 1.37236 0.0521691
\(693\) 8.95272 0.340086
\(694\) 21.0443 0.798832
\(695\) 0 0
\(696\) −17.3531 −0.657768
\(697\) 26.3970 0.999856
\(698\) 17.5855 0.665619
\(699\) −24.4637 −0.925304
\(700\) 0 0
\(701\) 14.0248 0.529709 0.264855 0.964288i \(-0.414676\pi\)
0.264855 + 0.964288i \(0.414676\pi\)
\(702\) −26.5948 −1.00376
\(703\) −14.9188 −0.562673
\(704\) 4.21357 0.158805
\(705\) 0 0
\(706\) 10.7150 0.403266
\(707\) 70.5561 2.65354
\(708\) 4.36034 0.163872
\(709\) −10.0074 −0.375835 −0.187918 0.982185i \(-0.560174\pi\)
−0.187918 + 0.982185i \(0.560174\pi\)
\(710\) 0 0
\(711\) −11.2266 −0.421029
\(712\) 21.0300 0.788134
\(713\) 44.6702 1.67291
\(714\) −23.8858 −0.893905
\(715\) 0 0
\(716\) −2.02873 −0.0758173
\(717\) −9.15098 −0.341749
\(718\) −25.8236 −0.963730
\(719\) 32.3086 1.20491 0.602454 0.798154i \(-0.294190\pi\)
0.602454 + 0.798154i \(0.294190\pi\)
\(720\) 0 0
\(721\) −36.1697 −1.34703
\(722\) −51.8084 −1.92811
\(723\) 1.16790 0.0434347
\(724\) −0.258714 −0.00961504
\(725\) 0 0
\(726\) 18.7295 0.695118
\(727\) −14.7153 −0.545762 −0.272881 0.962048i \(-0.587977\pi\)
−0.272881 + 0.962048i \(0.587977\pi\)
\(728\) 33.2889 1.23377
\(729\) 21.2861 0.788373
\(730\) 0 0
\(731\) −13.6189 −0.503712
\(732\) −1.57316 −0.0581455
\(733\) −28.2634 −1.04393 −0.521966 0.852966i \(-0.674801\pi\)
−0.521966 + 0.852966i \(0.674801\pi\)
\(734\) −9.19468 −0.339382
\(735\) 0 0
\(736\) −19.1945 −0.707518
\(737\) −8.27210 −0.304707
\(738\) −28.4392 −1.04686
\(739\) −34.0536 −1.25268 −0.626340 0.779550i \(-0.715448\pi\)
−0.626340 + 0.779550i \(0.715448\pi\)
\(740\) 0 0
\(741\) 25.0548 0.920411
\(742\) 33.3897 1.22578
\(743\) 47.2361 1.73293 0.866463 0.499241i \(-0.166388\pi\)
0.866463 + 0.499241i \(0.166388\pi\)
\(744\) −21.3741 −0.783612
\(745\) 0 0
\(746\) 2.11255 0.0773458
\(747\) 9.14222 0.334496
\(748\) −1.77027 −0.0647275
\(749\) 90.5629 3.30910
\(750\) 0 0
\(751\) 36.7588 1.34135 0.670674 0.741752i \(-0.266005\pi\)
0.670674 + 0.741752i \(0.266005\pi\)
\(752\) 23.9557 0.873576
\(753\) −8.19454 −0.298626
\(754\) −33.4129 −1.21683
\(755\) 0 0
\(756\) 18.1141 0.658802
\(757\) −7.43315 −0.270162 −0.135081 0.990835i \(-0.543130\pi\)
−0.135081 + 0.990835i \(0.543130\pi\)
\(758\) 22.5367 0.818568
\(759\) −6.73202 −0.244357
\(760\) 0 0
\(761\) 1.06982 0.0387809 0.0193905 0.999812i \(-0.493827\pi\)
0.0193905 + 0.999812i \(0.493827\pi\)
\(762\) −5.75135 −0.208350
\(763\) 75.5651 2.73564
\(764\) 3.29847 0.119335
\(765\) 0 0
\(766\) 19.5983 0.708116
\(767\) −17.0076 −0.614109
\(768\) 16.7266 0.603569
\(769\) −26.2212 −0.945562 −0.472781 0.881180i \(-0.656750\pi\)
−0.472781 + 0.881180i \(0.656750\pi\)
\(770\) 0 0
\(771\) −13.2039 −0.475527
\(772\) −8.93720 −0.321657
\(773\) 15.9051 0.572065 0.286033 0.958220i \(-0.407663\pi\)
0.286033 + 0.958220i \(0.407663\pi\)
\(774\) 14.6725 0.527394
\(775\) 0 0
\(776\) 23.8489 0.856124
\(777\) −12.3779 −0.444056
\(778\) −7.93152 −0.284359
\(779\) 75.9225 2.72020
\(780\) 0 0
\(781\) 13.2587 0.474433
\(782\) −21.5430 −0.770376
\(783\) 36.8313 1.31624
\(784\) −90.9485 −3.24816
\(785\) 0 0
\(786\) 4.14404 0.147813
\(787\) 44.7474 1.59507 0.797536 0.603272i \(-0.206137\pi\)
0.797536 + 0.603272i \(0.206137\pi\)
\(788\) −3.87838 −0.138162
\(789\) −23.2023 −0.826023
\(790\) 0 0
\(791\) 4.34928 0.154643
\(792\) −3.86358 −0.137286
\(793\) 6.13614 0.217901
\(794\) 14.9725 0.531356
\(795\) 0 0
\(796\) 8.31354 0.294665
\(797\) 20.2003 0.715530 0.357765 0.933812i \(-0.383539\pi\)
0.357765 + 0.933812i \(0.383539\pi\)
\(798\) −68.7000 −2.43195
\(799\) 12.1474 0.429743
\(800\) 0 0
\(801\) −15.7515 −0.556551
\(802\) 45.7679 1.61612
\(803\) −0.793280 −0.0279943
\(804\) −5.90634 −0.208301
\(805\) 0 0
\(806\) −41.1552 −1.44963
\(807\) −23.6538 −0.832652
\(808\) −30.4488 −1.07118
\(809\) 31.3338 1.10164 0.550818 0.834625i \(-0.314316\pi\)
0.550818 + 0.834625i \(0.314316\pi\)
\(810\) 0 0
\(811\) −28.2192 −0.990909 −0.495454 0.868634i \(-0.664998\pi\)
−0.495454 + 0.868634i \(0.664998\pi\)
\(812\) 22.7580 0.798648
\(813\) −4.95064 −0.173626
\(814\) −3.69313 −0.129444
\(815\) 0 0
\(816\) 14.1325 0.494738
\(817\) −39.1704 −1.37040
\(818\) 18.9502 0.662579
\(819\) −24.9334 −0.871242
\(820\) 0 0
\(821\) −36.8115 −1.28473 −0.642365 0.766399i \(-0.722047\pi\)
−0.642365 + 0.766399i \(0.722047\pi\)
\(822\) 30.3203 1.05754
\(823\) 34.8680 1.21542 0.607711 0.794158i \(-0.292088\pi\)
0.607711 + 0.794158i \(0.292088\pi\)
\(824\) 15.6092 0.543772
\(825\) 0 0
\(826\) 46.6347 1.62263
\(827\) 11.6305 0.404431 0.202216 0.979341i \(-0.435186\pi\)
0.202216 + 0.979341i \(0.435186\pi\)
\(828\) 5.76532 0.200359
\(829\) −45.8232 −1.59150 −0.795752 0.605622i \(-0.792924\pi\)
−0.795752 + 0.605622i \(0.792924\pi\)
\(830\) 0 0
\(831\) 0.431502 0.0149686
\(832\) −11.7348 −0.406831
\(833\) −46.1178 −1.59789
\(834\) 28.7145 0.994303
\(835\) 0 0
\(836\) −5.09162 −0.176097
\(837\) 45.3656 1.56807
\(838\) −25.4132 −0.877884
\(839\) −3.48632 −0.120361 −0.0601806 0.998188i \(-0.519168\pi\)
−0.0601806 + 0.998188i \(0.519168\pi\)
\(840\) 0 0
\(841\) 17.2737 0.595646
\(842\) −12.2931 −0.423647
\(843\) 28.8375 0.993216
\(844\) 3.97030 0.136663
\(845\) 0 0
\(846\) −13.0872 −0.449947
\(847\) 49.7587 1.70973
\(848\) −19.7557 −0.678414
\(849\) −0.0813764 −0.00279283
\(850\) 0 0
\(851\) −11.1638 −0.382692
\(852\) 9.46679 0.324327
\(853\) 44.6130 1.52752 0.763760 0.645500i \(-0.223351\pi\)
0.763760 + 0.645500i \(0.223351\pi\)
\(854\) −16.8252 −0.575748
\(855\) 0 0
\(856\) −39.0828 −1.33582
\(857\) −21.1188 −0.721404 −0.360702 0.932681i \(-0.617463\pi\)
−0.360702 + 0.932681i \(0.617463\pi\)
\(858\) 6.20229 0.211743
\(859\) −36.4020 −1.24202 −0.621011 0.783802i \(-0.713278\pi\)
−0.621011 + 0.783802i \(0.713278\pi\)
\(860\) 0 0
\(861\) 62.9920 2.14676
\(862\) −39.4998 −1.34537
\(863\) 4.01817 0.136780 0.0683900 0.997659i \(-0.478214\pi\)
0.0683900 + 0.997659i \(0.478214\pi\)
\(864\) −19.4933 −0.663176
\(865\) 0 0
\(866\) 3.11277 0.105776
\(867\) −12.6880 −0.430908
\(868\) 28.0313 0.951444
\(869\) 7.41925 0.251681
\(870\) 0 0
\(871\) 23.0379 0.780608
\(872\) −32.6104 −1.10433
\(873\) −17.8628 −0.604563
\(874\) −61.9616 −2.09588
\(875\) 0 0
\(876\) −0.566408 −0.0191372
\(877\) −48.0234 −1.62163 −0.810817 0.585300i \(-0.800977\pi\)
−0.810817 + 0.585300i \(0.800977\pi\)
\(878\) 24.3278 0.821022
\(879\) 8.86599 0.299042
\(880\) 0 0
\(881\) −56.8752 −1.91617 −0.958087 0.286479i \(-0.907515\pi\)
−0.958087 + 0.286479i \(0.907515\pi\)
\(882\) 49.6858 1.67301
\(883\) −44.7065 −1.50449 −0.752246 0.658882i \(-0.771030\pi\)
−0.752246 + 0.658882i \(0.771030\pi\)
\(884\) 4.93021 0.165821
\(885\) 0 0
\(886\) −37.6327 −1.26429
\(887\) −5.64866 −0.189663 −0.0948317 0.995493i \(-0.530231\pi\)
−0.0948317 + 0.995493i \(0.530231\pi\)
\(888\) 5.34175 0.179257
\(889\) −15.2796 −0.512462
\(890\) 0 0
\(891\) −1.53035 −0.0512686
\(892\) 17.0288 0.570165
\(893\) 34.9380 1.16916
\(894\) 2.60575 0.0871492
\(895\) 0 0
\(896\) 68.6215 2.29248
\(897\) 18.7487 0.626001
\(898\) −23.7216 −0.791601
\(899\) 56.9960 1.90092
\(900\) 0 0
\(901\) −10.0176 −0.333736
\(902\) 18.7945 0.625789
\(903\) −32.4992 −1.08150
\(904\) −1.87695 −0.0624265
\(905\) 0 0
\(906\) −32.7406 −1.08773
\(907\) −25.2839 −0.839538 −0.419769 0.907631i \(-0.637889\pi\)
−0.419769 + 0.907631i \(0.637889\pi\)
\(908\) −3.32955 −0.110495
\(909\) 22.8061 0.756431
\(910\) 0 0
\(911\) 27.3571 0.906380 0.453190 0.891414i \(-0.350286\pi\)
0.453190 + 0.891414i \(0.350286\pi\)
\(912\) 40.6478 1.34598
\(913\) −6.04178 −0.199954
\(914\) 19.2492 0.636705
\(915\) 0 0
\(916\) 13.9631 0.461354
\(917\) 11.0095 0.363564
\(918\) −21.8784 −0.722095
\(919\) −44.3463 −1.46285 −0.731424 0.681923i \(-0.761144\pi\)
−0.731424 + 0.681923i \(0.761144\pi\)
\(920\) 0 0
\(921\) 24.1098 0.794445
\(922\) −24.5867 −0.809719
\(923\) −36.9255 −1.21542
\(924\) −4.22446 −0.138974
\(925\) 0 0
\(926\) 39.6876 1.30422
\(927\) −11.6913 −0.383992
\(928\) −24.4908 −0.803950
\(929\) −33.2552 −1.09107 −0.545535 0.838088i \(-0.683673\pi\)
−0.545535 + 0.838088i \(0.683673\pi\)
\(930\) 0 0
\(931\) −132.643 −4.34720
\(932\) −13.8457 −0.453530
\(933\) 28.1326 0.921021
\(934\) 48.5694 1.58924
\(935\) 0 0
\(936\) 10.7601 0.351705
\(937\) 51.9272 1.69639 0.848194 0.529686i \(-0.177690\pi\)
0.848194 + 0.529686i \(0.177690\pi\)
\(938\) −63.1696 −2.06256
\(939\) −19.1307 −0.624306
\(940\) 0 0
\(941\) 21.0604 0.686549 0.343274 0.939235i \(-0.388464\pi\)
0.343274 + 0.939235i \(0.388464\pi\)
\(942\) 23.1053 0.752812
\(943\) 56.8134 1.85010
\(944\) −27.5924 −0.898056
\(945\) 0 0
\(946\) −9.69658 −0.315263
\(947\) 22.4529 0.729621 0.364810 0.931082i \(-0.381134\pi\)
0.364810 + 0.931082i \(0.381134\pi\)
\(948\) 5.29740 0.172052
\(949\) 2.20929 0.0717166
\(950\) 0 0
\(951\) 1.86669 0.0605317
\(952\) 27.3853 0.887564
\(953\) −29.3558 −0.950927 −0.475463 0.879736i \(-0.657720\pi\)
−0.475463 + 0.879736i \(0.657720\pi\)
\(954\) 10.7927 0.349426
\(955\) 0 0
\(956\) −5.17915 −0.167506
\(957\) −8.58958 −0.277662
\(958\) 16.6367 0.537508
\(959\) 80.5519 2.60116
\(960\) 0 0
\(961\) 39.2028 1.26461
\(962\) 10.2854 0.331614
\(963\) 29.2730 0.943309
\(964\) 0.660992 0.0212891
\(965\) 0 0
\(966\) −51.4088 −1.65405
\(967\) −26.9397 −0.866324 −0.433162 0.901316i \(-0.642602\pi\)
−0.433162 + 0.901316i \(0.642602\pi\)
\(968\) −21.4736 −0.690187
\(969\) 20.6115 0.662136
\(970\) 0 0
\(971\) −38.3427 −1.23047 −0.615237 0.788342i \(-0.710940\pi\)
−0.615237 + 0.788342i \(0.710940\pi\)
\(972\) 9.64394 0.309330
\(973\) 76.2859 2.44561
\(974\) −40.6583 −1.30278
\(975\) 0 0
\(976\) 9.95500 0.318652
\(977\) 13.7841 0.440991 0.220496 0.975388i \(-0.429233\pi\)
0.220496 + 0.975388i \(0.429233\pi\)
\(978\) 20.4008 0.652346
\(979\) 10.4096 0.332693
\(980\) 0 0
\(981\) 24.4252 0.779836
\(982\) 43.8334 1.39878
\(983\) −14.8201 −0.472688 −0.236344 0.971669i \(-0.575949\pi\)
−0.236344 + 0.971669i \(0.575949\pi\)
\(984\) −27.1844 −0.866608
\(985\) 0 0
\(986\) −27.4874 −0.875376
\(987\) 28.9877 0.922688
\(988\) 14.1802 0.451132
\(989\) −29.3115 −0.932051
\(990\) 0 0
\(991\) −52.3768 −1.66380 −0.831902 0.554923i \(-0.812748\pi\)
−0.831902 + 0.554923i \(0.812748\pi\)
\(992\) −30.1657 −0.957761
\(993\) −31.4247 −0.997233
\(994\) 101.249 3.21143
\(995\) 0 0
\(996\) −4.31387 −0.136690
\(997\) −23.1646 −0.733630 −0.366815 0.930294i \(-0.619552\pi\)
−0.366815 + 0.930294i \(0.619552\pi\)
\(998\) 61.3592 1.94229
\(999\) −11.3377 −0.358708
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 \(a_p\))