Properties

Label 4012.2.a.g.1.1
Level 4012
Weight 2
Character 4012.1
Self dual Yes
Analytic conductor 32.036
Analytic rank 1
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4012.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0359812909\)
Analytic rank: \(1\)
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 \(3.27119\)
Character \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-3.27119 q^{3}\) \(+3.82141 q^{5}\) \(-1.10063 q^{7}\) \(+7.70067 q^{9}\) \(+O(q^{10})\) \(q\)\(-3.27119 q^{3}\) \(+3.82141 q^{5}\) \(-1.10063 q^{7}\) \(+7.70067 q^{9}\) \(+4.05597 q^{11}\) \(+2.22527 q^{13}\) \(-12.5006 q^{15}\) \(-1.00000 q^{17}\) \(-5.58725 q^{19}\) \(+3.60037 q^{21}\) \(-8.79238 q^{23}\) \(+9.60321 q^{25}\) \(-15.3768 q^{27}\) \(-7.67625 q^{29}\) \(+4.75500 q^{31}\) \(-13.2678 q^{33}\) \(-4.20597 q^{35}\) \(+1.29636 q^{37}\) \(-7.27928 q^{39}\) \(-6.85530 q^{41}\) \(-2.65701 q^{43}\) \(+29.4274 q^{45}\) \(-11.7214 q^{47}\) \(-5.78861 q^{49}\) \(+3.27119 q^{51}\) \(-9.59673 q^{53}\) \(+15.4995 q^{55}\) \(+18.2769 q^{57}\) \(+1.00000 q^{59}\) \(-11.2376 q^{61}\) \(-8.47560 q^{63}\) \(+8.50368 q^{65}\) \(+2.30373 q^{67}\) \(+28.7615 q^{69}\) \(+6.69275 q^{71}\) \(+9.58317 q^{73}\) \(-31.4139 q^{75}\) \(-4.46413 q^{77}\) \(+5.58062 q^{79}\) \(+27.1983 q^{81}\) \(-8.10186 q^{83}\) \(-3.82141 q^{85}\) \(+25.1105 q^{87}\) \(+8.45021 q^{89}\) \(-2.44920 q^{91}\) \(-15.5545 q^{93}\) \(-21.3512 q^{95}\) \(-3.32787 q^{97}\) \(+31.2337 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 15q^{19} \) \(\mathstrut +\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 33q^{33} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 30q^{45} \) \(\mathstrut -\mathstrut 60q^{47} \) \(\mathstrut +\mathstrut 10q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 41q^{57} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 23q^{63} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 62q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 13q^{87} \) \(\mathstrut -\mathstrut 29q^{89} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 31q^{93} \) \(\mathstrut -\mathstrut 48q^{95} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 3q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.27119 −1.88862 −0.944310 0.329056i \(-0.893270\pi\)
−0.944310 + 0.329056i \(0.893270\pi\)
\(4\) 0 0
\(5\) 3.82141 1.70899 0.854494 0.519461i \(-0.173867\pi\)
0.854494 + 0.519461i \(0.173867\pi\)
\(6\) 0 0
\(7\) −1.10063 −0.416000 −0.208000 0.978129i \(-0.566695\pi\)
−0.208000 + 0.978129i \(0.566695\pi\)
\(8\) 0 0
\(9\) 7.70067 2.56689
\(10\) 0 0
\(11\) 4.05597 1.22292 0.611461 0.791275i \(-0.290582\pi\)
0.611461 + 0.791275i \(0.290582\pi\)
\(12\) 0 0
\(13\) 2.22527 0.617179 0.308589 0.951195i \(-0.400143\pi\)
0.308589 + 0.951195i \(0.400143\pi\)
\(14\) 0 0
\(15\) −12.5006 −3.22763
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −5.58725 −1.28180 −0.640901 0.767623i \(-0.721439\pi\)
−0.640901 + 0.767623i \(0.721439\pi\)
\(20\) 0 0
\(21\) 3.60037 0.785666
\(22\) 0 0
\(23\) −8.79238 −1.83334 −0.916669 0.399648i \(-0.869132\pi\)
−0.916669 + 0.399648i \(0.869132\pi\)
\(24\) 0 0
\(25\) 9.60321 1.92064
\(26\) 0 0
\(27\) −15.3768 −2.95926
\(28\) 0 0
\(29\) −7.67625 −1.42544 −0.712722 0.701447i \(-0.752538\pi\)
−0.712722 + 0.701447i \(0.752538\pi\)
\(30\) 0 0
\(31\) 4.75500 0.854023 0.427011 0.904246i \(-0.359566\pi\)
0.427011 + 0.904246i \(0.359566\pi\)
\(32\) 0 0
\(33\) −13.2678 −2.30963
\(34\) 0 0
\(35\) −4.20597 −0.710939
\(36\) 0 0
\(37\) 1.29636 0.213120 0.106560 0.994306i \(-0.466016\pi\)
0.106560 + 0.994306i \(0.466016\pi\)
\(38\) 0 0
\(39\) −7.27928 −1.16562
\(40\) 0 0
\(41\) −6.85530 −1.07062 −0.535309 0.844656i \(-0.679805\pi\)
−0.535309 + 0.844656i \(0.679805\pi\)
\(42\) 0 0
\(43\) −2.65701 −0.405191 −0.202595 0.979263i \(-0.564938\pi\)
−0.202595 + 0.979263i \(0.564938\pi\)
\(44\) 0 0
\(45\) 29.4274 4.38678
\(46\) 0 0
\(47\) −11.7214 −1.70974 −0.854871 0.518841i \(-0.826364\pi\)
−0.854871 + 0.518841i \(0.826364\pi\)
\(48\) 0 0
\(49\) −5.78861 −0.826944
\(50\) 0 0
\(51\) 3.27119 0.458058
\(52\) 0 0
\(53\) −9.59673 −1.31821 −0.659106 0.752050i \(-0.729065\pi\)
−0.659106 + 0.752050i \(0.729065\pi\)
\(54\) 0 0
\(55\) 15.4995 2.08996
\(56\) 0 0
\(57\) 18.2769 2.42084
\(58\) 0 0
\(59\) 1.00000 0.130189
\(60\) 0 0
\(61\) −11.2376 −1.43883 −0.719414 0.694582i \(-0.755590\pi\)
−0.719414 + 0.694582i \(0.755590\pi\)
\(62\) 0 0
\(63\) −8.47560 −1.06783
\(64\) 0 0
\(65\) 8.50368 1.05475
\(66\) 0 0
\(67\) 2.30373 0.281445 0.140722 0.990049i \(-0.455057\pi\)
0.140722 + 0.990049i \(0.455057\pi\)
\(68\) 0 0
\(69\) 28.7615 3.46248
\(70\) 0 0
\(71\) 6.69275 0.794284 0.397142 0.917757i \(-0.370002\pi\)
0.397142 + 0.917757i \(0.370002\pi\)
\(72\) 0 0
\(73\) 9.58317 1.12163 0.560813 0.827943i \(-0.310489\pi\)
0.560813 + 0.827943i \(0.310489\pi\)
\(74\) 0 0
\(75\) −31.4139 −3.62736
\(76\) 0 0
\(77\) −4.46413 −0.508735
\(78\) 0 0
\(79\) 5.58062 0.627869 0.313934 0.949445i \(-0.398353\pi\)
0.313934 + 0.949445i \(0.398353\pi\)
\(80\) 0 0
\(81\) 27.1983 3.02203
\(82\) 0 0
\(83\) −8.10186 −0.889295 −0.444648 0.895706i \(-0.646671\pi\)
−0.444648 + 0.895706i \(0.646671\pi\)
\(84\) 0 0
\(85\) −3.82141 −0.414491
\(86\) 0 0
\(87\) 25.1105 2.69212
\(88\) 0 0
\(89\) 8.45021 0.895720 0.447860 0.894104i \(-0.352186\pi\)
0.447860 + 0.894104i \(0.352186\pi\)
\(90\) 0 0
\(91\) −2.44920 −0.256746
\(92\) 0 0
\(93\) −15.5545 −1.61293
\(94\) 0 0
\(95\) −21.3512 −2.19059
\(96\) 0 0
\(97\) −3.32787 −0.337894 −0.168947 0.985625i \(-0.554037\pi\)
−0.168947 + 0.985625i \(0.554037\pi\)
\(98\) 0 0
\(99\) 31.2337 3.13910
\(100\) 0 0
\(101\) 5.24482 0.521879 0.260940 0.965355i \(-0.415968\pi\)
0.260940 + 0.965355i \(0.415968\pi\)
\(102\) 0 0
\(103\) −18.9660 −1.86877 −0.934387 0.356259i \(-0.884052\pi\)
−0.934387 + 0.356259i \(0.884052\pi\)
\(104\) 0 0
\(105\) 13.7585 1.34269
\(106\) 0 0
\(107\) 12.4038 1.19912 0.599558 0.800331i \(-0.295343\pi\)
0.599558 + 0.800331i \(0.295343\pi\)
\(108\) 0 0
\(109\) −1.00930 −0.0966734 −0.0483367 0.998831i \(-0.515392\pi\)
−0.0483367 + 0.998831i \(0.515392\pi\)
\(110\) 0 0
\(111\) −4.24063 −0.402502
\(112\) 0 0
\(113\) −7.76908 −0.730853 −0.365427 0.930840i \(-0.619077\pi\)
−0.365427 + 0.930840i \(0.619077\pi\)
\(114\) 0 0
\(115\) −33.5993 −3.13315
\(116\) 0 0
\(117\) 17.1361 1.58423
\(118\) 0 0
\(119\) 1.10063 0.100895
\(120\) 0 0
\(121\) 5.45090 0.495536
\(122\) 0 0
\(123\) 22.4250 2.02199
\(124\) 0 0
\(125\) 17.5908 1.57337
\(126\) 0 0
\(127\) 3.32657 0.295186 0.147593 0.989048i \(-0.452848\pi\)
0.147593 + 0.989048i \(0.452848\pi\)
\(128\) 0 0
\(129\) 8.69159 0.765252
\(130\) 0 0
\(131\) 7.21932 0.630755 0.315378 0.948966i \(-0.397869\pi\)
0.315378 + 0.948966i \(0.397869\pi\)
\(132\) 0 0
\(133\) 6.14950 0.533230
\(134\) 0 0
\(135\) −58.7610 −5.05734
\(136\) 0 0
\(137\) −15.9196 −1.36010 −0.680050 0.733166i \(-0.738042\pi\)
−0.680050 + 0.733166i \(0.738042\pi\)
\(138\) 0 0
\(139\) −10.5516 −0.894977 −0.447489 0.894290i \(-0.647681\pi\)
−0.447489 + 0.894290i \(0.647681\pi\)
\(140\) 0 0
\(141\) 38.3429 3.22905
\(142\) 0 0
\(143\) 9.02563 0.754761
\(144\) 0 0
\(145\) −29.3341 −2.43607
\(146\) 0 0
\(147\) 18.9356 1.56178
\(148\) 0 0
\(149\) −11.1086 −0.910048 −0.455024 0.890479i \(-0.650369\pi\)
−0.455024 + 0.890479i \(0.650369\pi\)
\(150\) 0 0
\(151\) 12.1732 0.990642 0.495321 0.868710i \(-0.335050\pi\)
0.495321 + 0.868710i \(0.335050\pi\)
\(152\) 0 0
\(153\) −7.70067 −0.622562
\(154\) 0 0
\(155\) 18.1708 1.45952
\(156\) 0 0
\(157\) −5.52818 −0.441197 −0.220598 0.975365i \(-0.570801\pi\)
−0.220598 + 0.975365i \(0.570801\pi\)
\(158\) 0 0
\(159\) 31.3927 2.48960
\(160\) 0 0
\(161\) 9.67717 0.762668
\(162\) 0 0
\(163\) −8.07857 −0.632762 −0.316381 0.948632i \(-0.602468\pi\)
−0.316381 + 0.948632i \(0.602468\pi\)
\(164\) 0 0
\(165\) −50.7019 −3.94714
\(166\) 0 0
\(167\) −6.57513 −0.508799 −0.254399 0.967099i \(-0.581878\pi\)
−0.254399 + 0.967099i \(0.581878\pi\)
\(168\) 0 0
\(169\) −8.04817 −0.619090
\(170\) 0 0
\(171\) −43.0255 −3.29024
\(172\) 0 0
\(173\) 9.85196 0.749031 0.374515 0.927221i \(-0.377809\pi\)
0.374515 + 0.927221i \(0.377809\pi\)
\(174\) 0 0
\(175\) −10.5696 −0.798987
\(176\) 0 0
\(177\) −3.27119 −0.245877
\(178\) 0 0
\(179\) 16.4294 1.22799 0.613997 0.789308i \(-0.289561\pi\)
0.613997 + 0.789308i \(0.289561\pi\)
\(180\) 0 0
\(181\) 1.87598 0.139441 0.0697203 0.997567i \(-0.477789\pi\)
0.0697203 + 0.997567i \(0.477789\pi\)
\(182\) 0 0
\(183\) 36.7603 2.71740
\(184\) 0 0
\(185\) 4.95392 0.364219
\(186\) 0 0
\(187\) −4.05597 −0.296602
\(188\) 0 0
\(189\) 16.9242 1.23105
\(190\) 0 0
\(191\) −12.5411 −0.907439 −0.453719 0.891145i \(-0.649903\pi\)
−0.453719 + 0.891145i \(0.649903\pi\)
\(192\) 0 0
\(193\) −12.2994 −0.885327 −0.442663 0.896688i \(-0.645966\pi\)
−0.442663 + 0.896688i \(0.645966\pi\)
\(194\) 0 0
\(195\) −27.8171 −1.99203
\(196\) 0 0
\(197\) 23.9912 1.70930 0.854652 0.519201i \(-0.173770\pi\)
0.854652 + 0.519201i \(0.173770\pi\)
\(198\) 0 0
\(199\) 19.2957 1.36784 0.683919 0.729558i \(-0.260274\pi\)
0.683919 + 0.729558i \(0.260274\pi\)
\(200\) 0 0
\(201\) −7.53592 −0.531543
\(202\) 0 0
\(203\) 8.44873 0.592985
\(204\) 0 0
\(205\) −26.1970 −1.82967
\(206\) 0 0
\(207\) −67.7072 −4.70597
\(208\) 0 0
\(209\) −22.6617 −1.56754
\(210\) 0 0
\(211\) 5.90494 0.406513 0.203257 0.979126i \(-0.434847\pi\)
0.203257 + 0.979126i \(0.434847\pi\)
\(212\) 0 0
\(213\) −21.8932 −1.50010
\(214\) 0 0
\(215\) −10.1536 −0.692467
\(216\) 0 0
\(217\) −5.23350 −0.355273
\(218\) 0 0
\(219\) −31.3483 −2.11832
\(220\) 0 0
\(221\) −2.22527 −0.149688
\(222\) 0 0
\(223\) 18.0199 1.20670 0.603352 0.797475i \(-0.293831\pi\)
0.603352 + 0.797475i \(0.293831\pi\)
\(224\) 0 0
\(225\) 73.9511 4.93007
\(226\) 0 0
\(227\) −15.8257 −1.05039 −0.525194 0.850983i \(-0.676007\pi\)
−0.525194 + 0.850983i \(0.676007\pi\)
\(228\) 0 0
\(229\) −5.02899 −0.332325 −0.166163 0.986098i \(-0.553138\pi\)
−0.166163 + 0.986098i \(0.553138\pi\)
\(230\) 0 0
\(231\) 14.6030 0.960808
\(232\) 0 0
\(233\) 7.10234 0.465290 0.232645 0.972562i \(-0.425262\pi\)
0.232645 + 0.972562i \(0.425262\pi\)
\(234\) 0 0
\(235\) −44.7923 −2.92193
\(236\) 0 0
\(237\) −18.2552 −1.18581
\(238\) 0 0
\(239\) 5.04925 0.326609 0.163304 0.986576i \(-0.447785\pi\)
0.163304 + 0.986576i \(0.447785\pi\)
\(240\) 0 0
\(241\) −13.8701 −0.893453 −0.446727 0.894671i \(-0.647410\pi\)
−0.446727 + 0.894671i \(0.647410\pi\)
\(242\) 0 0
\(243\) −42.8403 −2.74821
\(244\) 0 0
\(245\) −22.1207 −1.41324
\(246\) 0 0
\(247\) −12.4331 −0.791101
\(248\) 0 0
\(249\) 26.5027 1.67954
\(250\) 0 0
\(251\) −10.5787 −0.667724 −0.333862 0.942622i \(-0.608352\pi\)
−0.333862 + 0.942622i \(0.608352\pi\)
\(252\) 0 0
\(253\) −35.6616 −2.24203
\(254\) 0 0
\(255\) 12.5006 0.782816
\(256\) 0 0
\(257\) 19.2234 1.19913 0.599563 0.800328i \(-0.295341\pi\)
0.599563 + 0.800328i \(0.295341\pi\)
\(258\) 0 0
\(259\) −1.42681 −0.0886578
\(260\) 0 0
\(261\) −59.1123 −3.65896
\(262\) 0 0
\(263\) 3.33295 0.205518 0.102759 0.994706i \(-0.467233\pi\)
0.102759 + 0.994706i \(0.467233\pi\)
\(264\) 0 0
\(265\) −36.6731 −2.25281
\(266\) 0 0
\(267\) −27.6422 −1.69168
\(268\) 0 0
\(269\) −21.6195 −1.31817 −0.659083 0.752071i \(-0.729055\pi\)
−0.659083 + 0.752071i \(0.729055\pi\)
\(270\) 0 0
\(271\) 17.5371 1.06530 0.532651 0.846335i \(-0.321196\pi\)
0.532651 + 0.846335i \(0.321196\pi\)
\(272\) 0 0
\(273\) 8.01181 0.484897
\(274\) 0 0
\(275\) 38.9503 2.34879
\(276\) 0 0
\(277\) −20.4180 −1.22680 −0.613400 0.789773i \(-0.710198\pi\)
−0.613400 + 0.789773i \(0.710198\pi\)
\(278\) 0 0
\(279\) 36.6167 2.19218
\(280\) 0 0
\(281\) −9.57349 −0.571106 −0.285553 0.958363i \(-0.592177\pi\)
−0.285553 + 0.958363i \(0.592177\pi\)
\(282\) 0 0
\(283\) −20.0460 −1.19161 −0.595806 0.803129i \(-0.703167\pi\)
−0.595806 + 0.803129i \(0.703167\pi\)
\(284\) 0 0
\(285\) 69.8437 4.13719
\(286\) 0 0
\(287\) 7.54517 0.445377
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 10.8861 0.638153
\(292\) 0 0
\(293\) −17.7665 −1.03793 −0.518965 0.854795i \(-0.673683\pi\)
−0.518965 + 0.854795i \(0.673683\pi\)
\(294\) 0 0
\(295\) 3.82141 0.222491
\(296\) 0 0
\(297\) −62.3677 −3.61894
\(298\) 0 0
\(299\) −19.5654 −1.13150
\(300\) 0 0
\(301\) 2.92440 0.168559
\(302\) 0 0
\(303\) −17.1568 −0.985632
\(304\) 0 0
\(305\) −42.9435 −2.45894
\(306\) 0 0
\(307\) 12.0091 0.685396 0.342698 0.939446i \(-0.388659\pi\)
0.342698 + 0.939446i \(0.388659\pi\)
\(308\) 0 0
\(309\) 62.0413 3.52941
\(310\) 0 0
\(311\) −20.1162 −1.14068 −0.570342 0.821407i \(-0.693189\pi\)
−0.570342 + 0.821407i \(0.693189\pi\)
\(312\) 0 0
\(313\) 13.4115 0.758062 0.379031 0.925384i \(-0.376257\pi\)
0.379031 + 0.925384i \(0.376257\pi\)
\(314\) 0 0
\(315\) −32.3888 −1.82490
\(316\) 0 0
\(317\) 17.0862 0.959656 0.479828 0.877362i \(-0.340699\pi\)
0.479828 + 0.877362i \(0.340699\pi\)
\(318\) 0 0
\(319\) −31.1347 −1.74321
\(320\) 0 0
\(321\) −40.5750 −2.26468
\(322\) 0 0
\(323\) 5.58725 0.310883
\(324\) 0 0
\(325\) 21.3697 1.18538
\(326\) 0 0
\(327\) 3.30161 0.182579
\(328\) 0 0
\(329\) 12.9009 0.711252
\(330\) 0 0
\(331\) −25.9892 −1.42850 −0.714249 0.699892i \(-0.753232\pi\)
−0.714249 + 0.699892i \(0.753232\pi\)
\(332\) 0 0
\(333\) 9.98281 0.547055
\(334\) 0 0
\(335\) 8.80349 0.480986
\(336\) 0 0
\(337\) −6.10967 −0.332815 −0.166408 0.986057i \(-0.553217\pi\)
−0.166408 + 0.986057i \(0.553217\pi\)
\(338\) 0 0
\(339\) 25.4141 1.38030
\(340\) 0 0
\(341\) 19.2861 1.04440
\(342\) 0 0
\(343\) 14.0756 0.760009
\(344\) 0 0
\(345\) 109.910 5.91734
\(346\) 0 0
\(347\) −16.8679 −0.905517 −0.452758 0.891633i \(-0.649560\pi\)
−0.452758 + 0.891633i \(0.649560\pi\)
\(348\) 0 0
\(349\) 8.48831 0.454369 0.227184 0.973852i \(-0.427048\pi\)
0.227184 + 0.973852i \(0.427048\pi\)
\(350\) 0 0
\(351\) −34.2175 −1.82639
\(352\) 0 0
\(353\) 4.53541 0.241396 0.120698 0.992689i \(-0.461487\pi\)
0.120698 + 0.992689i \(0.461487\pi\)
\(354\) 0 0
\(355\) 25.5758 1.35742
\(356\) 0 0
\(357\) −3.60037 −0.190552
\(358\) 0 0
\(359\) −1.06421 −0.0561670 −0.0280835 0.999606i \(-0.508940\pi\)
−0.0280835 + 0.999606i \(0.508940\pi\)
\(360\) 0 0
\(361\) 12.2173 0.643017
\(362\) 0 0
\(363\) −17.8309 −0.935880
\(364\) 0 0
\(365\) 36.6213 1.91684
\(366\) 0 0
\(367\) 23.9923 1.25239 0.626193 0.779668i \(-0.284612\pi\)
0.626193 + 0.779668i \(0.284612\pi\)
\(368\) 0 0
\(369\) −52.7904 −2.74816
\(370\) 0 0
\(371\) 10.5625 0.548376
\(372\) 0 0
\(373\) 28.7593 1.48910 0.744549 0.667567i \(-0.232664\pi\)
0.744549 + 0.667567i \(0.232664\pi\)
\(374\) 0 0
\(375\) −57.5427 −2.97149
\(376\) 0 0
\(377\) −17.0817 −0.879754
\(378\) 0 0
\(379\) −24.7869 −1.27322 −0.636609 0.771187i \(-0.719663\pi\)
−0.636609 + 0.771187i \(0.719663\pi\)
\(380\) 0 0
\(381\) −10.8818 −0.557494
\(382\) 0 0
\(383\) −6.84679 −0.349855 −0.174927 0.984581i \(-0.555969\pi\)
−0.174927 + 0.984581i \(0.555969\pi\)
\(384\) 0 0
\(385\) −17.0593 −0.869422
\(386\) 0 0
\(387\) −20.4608 −1.04008
\(388\) 0 0
\(389\) 19.0487 0.965809 0.482904 0.875673i \(-0.339582\pi\)
0.482904 + 0.875673i \(0.339582\pi\)
\(390\) 0 0
\(391\) 8.79238 0.444650
\(392\) 0 0
\(393\) −23.6158 −1.19126
\(394\) 0 0
\(395\) 21.3259 1.07302
\(396\) 0 0
\(397\) 1.73345 0.0869992 0.0434996 0.999053i \(-0.486149\pi\)
0.0434996 + 0.999053i \(0.486149\pi\)
\(398\) 0 0
\(399\) −20.1162 −1.00707
\(400\) 0 0
\(401\) 27.5134 1.37395 0.686976 0.726680i \(-0.258938\pi\)
0.686976 + 0.726680i \(0.258938\pi\)
\(402\) 0 0
\(403\) 10.5812 0.527085
\(404\) 0 0
\(405\) 103.936 5.16461
\(406\) 0 0
\(407\) 5.25798 0.260629
\(408\) 0 0
\(409\) −0.234273 −0.0115840 −0.00579202 0.999983i \(-0.501844\pi\)
−0.00579202 + 0.999983i \(0.501844\pi\)
\(410\) 0 0
\(411\) 52.0759 2.56871
\(412\) 0 0
\(413\) −1.10063 −0.0541586
\(414\) 0 0
\(415\) −30.9606 −1.51980
\(416\) 0 0
\(417\) 34.5163 1.69027
\(418\) 0 0
\(419\) 9.31142 0.454893 0.227446 0.973791i \(-0.426962\pi\)
0.227446 + 0.973791i \(0.426962\pi\)
\(420\) 0 0
\(421\) 28.3807 1.38319 0.691596 0.722285i \(-0.256908\pi\)
0.691596 + 0.722285i \(0.256908\pi\)
\(422\) 0 0
\(423\) −90.2625 −4.38872
\(424\) 0 0
\(425\) −9.60321 −0.465824
\(426\) 0 0
\(427\) 12.3685 0.598552
\(428\) 0 0
\(429\) −29.5245 −1.42546
\(430\) 0 0
\(431\) −14.4066 −0.693940 −0.346970 0.937876i \(-0.612789\pi\)
−0.346970 + 0.937876i \(0.612789\pi\)
\(432\) 0 0
\(433\) −36.5511 −1.75653 −0.878267 0.478170i \(-0.841300\pi\)
−0.878267 + 0.478170i \(0.841300\pi\)
\(434\) 0 0
\(435\) 95.9575 4.60081
\(436\) 0 0
\(437\) 49.1252 2.34998
\(438\) 0 0
\(439\) 36.2178 1.72858 0.864292 0.502991i \(-0.167767\pi\)
0.864292 + 0.502991i \(0.167767\pi\)
\(440\) 0 0
\(441\) −44.5761 −2.12267
\(442\) 0 0
\(443\) 30.6620 1.45679 0.728397 0.685155i \(-0.240266\pi\)
0.728397 + 0.685155i \(0.240266\pi\)
\(444\) 0 0
\(445\) 32.2917 1.53078
\(446\) 0 0
\(447\) 36.3382 1.71874
\(448\) 0 0
\(449\) −22.7514 −1.07370 −0.536852 0.843676i \(-0.680387\pi\)
−0.536852 + 0.843676i \(0.680387\pi\)
\(450\) 0 0
\(451\) −27.8049 −1.30928
\(452\) 0 0
\(453\) −39.8209 −1.87095
\(454\) 0 0
\(455\) −9.35943 −0.438777
\(456\) 0 0
\(457\) −41.9599 −1.96280 −0.981401 0.191967i \(-0.938513\pi\)
−0.981401 + 0.191967i \(0.938513\pi\)
\(458\) 0 0
\(459\) 15.3768 0.717726
\(460\) 0 0
\(461\) 28.6681 1.33521 0.667603 0.744518i \(-0.267320\pi\)
0.667603 + 0.744518i \(0.267320\pi\)
\(462\) 0 0
\(463\) −33.6589 −1.56426 −0.782131 0.623114i \(-0.785867\pi\)
−0.782131 + 0.623114i \(0.785867\pi\)
\(464\) 0 0
\(465\) −59.4401 −2.75647
\(466\) 0 0
\(467\) −37.3425 −1.72801 −0.864003 0.503487i \(-0.832050\pi\)
−0.864003 + 0.503487i \(0.832050\pi\)
\(468\) 0 0
\(469\) −2.53556 −0.117081
\(470\) 0 0
\(471\) 18.0837 0.833253
\(472\) 0 0
\(473\) −10.7768 −0.495517
\(474\) 0 0
\(475\) −53.6555 −2.46188
\(476\) 0 0
\(477\) −73.9012 −3.38371
\(478\) 0 0
\(479\) −33.0170 −1.50859 −0.754293 0.656538i \(-0.772020\pi\)
−0.754293 + 0.656538i \(0.772020\pi\)
\(480\) 0 0
\(481\) 2.88474 0.131533
\(482\) 0 0
\(483\) −31.6559 −1.44039
\(484\) 0 0
\(485\) −12.7172 −0.577456
\(486\) 0 0
\(487\) 27.2360 1.23418 0.617090 0.786893i \(-0.288311\pi\)
0.617090 + 0.786893i \(0.288311\pi\)
\(488\) 0 0
\(489\) 26.4265 1.19505
\(490\) 0 0
\(491\) −25.6768 −1.15878 −0.579388 0.815052i \(-0.696708\pi\)
−0.579388 + 0.815052i \(0.696708\pi\)
\(492\) 0 0
\(493\) 7.67625 0.345721
\(494\) 0 0
\(495\) 119.357 5.36469
\(496\) 0 0
\(497\) −7.36626 −0.330422
\(498\) 0 0
\(499\) 36.6075 1.63878 0.819389 0.573237i \(-0.194313\pi\)
0.819389 + 0.573237i \(0.194313\pi\)
\(500\) 0 0
\(501\) 21.5085 0.960928
\(502\) 0 0
\(503\) −12.0013 −0.535113 −0.267556 0.963542i \(-0.586216\pi\)
−0.267556 + 0.963542i \(0.586216\pi\)
\(504\) 0 0
\(505\) 20.0426 0.891885
\(506\) 0 0
\(507\) 26.3271 1.16923
\(508\) 0 0
\(509\) −19.1208 −0.847513 −0.423757 0.905776i \(-0.639289\pi\)
−0.423757 + 0.905776i \(0.639289\pi\)
\(510\) 0 0
\(511\) −10.5475 −0.466596
\(512\) 0 0
\(513\) 85.9138 3.79318
\(514\) 0 0
\(515\) −72.4769 −3.19371
\(516\) 0 0
\(517\) −47.5416 −2.09088
\(518\) 0 0
\(519\) −32.2276 −1.41464
\(520\) 0 0
\(521\) 17.9633 0.786985 0.393493 0.919328i \(-0.371267\pi\)
0.393493 + 0.919328i \(0.371267\pi\)
\(522\) 0 0
\(523\) 12.6040 0.551134 0.275567 0.961282i \(-0.411134\pi\)
0.275567 + 0.961282i \(0.411134\pi\)
\(524\) 0 0
\(525\) 34.5751 1.50898
\(526\) 0 0
\(527\) −4.75500 −0.207131
\(528\) 0 0
\(529\) 54.3059 2.36113
\(530\) 0 0
\(531\) 7.70067 0.334180
\(532\) 0 0
\(533\) −15.2549 −0.660763
\(534\) 0 0
\(535\) 47.3999 2.04928
\(536\) 0 0
\(537\) −53.7438 −2.31922
\(538\) 0 0
\(539\) −23.4784 −1.01129
\(540\) 0 0
\(541\) 39.1769 1.68435 0.842174 0.539206i \(-0.181276\pi\)
0.842174 + 0.539206i \(0.181276\pi\)
\(542\) 0 0
\(543\) −6.13669 −0.263351
\(544\) 0 0
\(545\) −3.85695 −0.165214
\(546\) 0 0
\(547\) 21.5389 0.920936 0.460468 0.887676i \(-0.347682\pi\)
0.460468 + 0.887676i \(0.347682\pi\)
\(548\) 0 0
\(549\) −86.5371 −3.69331
\(550\) 0 0
\(551\) 42.8891 1.82714
\(552\) 0 0
\(553\) −6.14221 −0.261193
\(554\) 0 0
\(555\) −16.2052 −0.687872
\(556\) 0 0
\(557\) −4.62692 −0.196049 −0.0980244 0.995184i \(-0.531252\pi\)
−0.0980244 + 0.995184i \(0.531252\pi\)
\(558\) 0 0
\(559\) −5.91258 −0.250075
\(560\) 0 0
\(561\) 13.2678 0.560169
\(562\) 0 0
\(563\) −1.01676 −0.0428513 −0.0214257 0.999770i \(-0.506821\pi\)
−0.0214257 + 0.999770i \(0.506821\pi\)
\(564\) 0 0
\(565\) −29.6889 −1.24902
\(566\) 0 0
\(567\) −29.9353 −1.25716
\(568\) 0 0
\(569\) 18.4491 0.773425 0.386713 0.922200i \(-0.373611\pi\)
0.386713 + 0.922200i \(0.373611\pi\)
\(570\) 0 0
\(571\) 29.4338 1.23177 0.615883 0.787837i \(-0.288799\pi\)
0.615883 + 0.787837i \(0.288799\pi\)
\(572\) 0 0
\(573\) 41.0241 1.71381
\(574\) 0 0
\(575\) −84.4350 −3.52118
\(576\) 0 0
\(577\) −32.4556 −1.35115 −0.675573 0.737293i \(-0.736104\pi\)
−0.675573 + 0.737293i \(0.736104\pi\)
\(578\) 0 0
\(579\) 40.2335 1.67205
\(580\) 0 0
\(581\) 8.91717 0.369947
\(582\) 0 0
\(583\) −38.9241 −1.61207
\(584\) 0 0
\(585\) 65.4840 2.70743
\(586\) 0 0
\(587\) 13.7984 0.569520 0.284760 0.958599i \(-0.408086\pi\)
0.284760 + 0.958599i \(0.408086\pi\)
\(588\) 0 0
\(589\) −26.5673 −1.09469
\(590\) 0 0
\(591\) −78.4798 −3.22823
\(592\) 0 0
\(593\) −47.6437 −1.95649 −0.978245 0.207452i \(-0.933483\pi\)
−0.978245 + 0.207452i \(0.933483\pi\)
\(594\) 0 0
\(595\) 4.20597 0.172428
\(596\) 0 0
\(597\) −63.1199 −2.58333
\(598\) 0 0
\(599\) −11.9684 −0.489017 −0.244508 0.969647i \(-0.578627\pi\)
−0.244508 + 0.969647i \(0.578627\pi\)
\(600\) 0 0
\(601\) 38.1249 1.55515 0.777574 0.628792i \(-0.216450\pi\)
0.777574 + 0.628792i \(0.216450\pi\)
\(602\) 0 0
\(603\) 17.7402 0.722438
\(604\) 0 0
\(605\) 20.8301 0.846866
\(606\) 0 0
\(607\) −48.3892 −1.96406 −0.982029 0.188732i \(-0.939562\pi\)
−0.982029 + 0.188732i \(0.939562\pi\)
\(608\) 0 0
\(609\) −27.6374 −1.11992
\(610\) 0 0
\(611\) −26.0833 −1.05522
\(612\) 0 0
\(613\) −41.0223 −1.65688 −0.828438 0.560080i \(-0.810770\pi\)
−0.828438 + 0.560080i \(0.810770\pi\)
\(614\) 0 0
\(615\) 85.6951 3.45556
\(616\) 0 0
\(617\) −1.83156 −0.0737360 −0.0368680 0.999320i \(-0.511738\pi\)
−0.0368680 + 0.999320i \(0.511738\pi\)
\(618\) 0 0
\(619\) 13.0869 0.526005 0.263003 0.964795i \(-0.415287\pi\)
0.263003 + 0.964795i \(0.415287\pi\)
\(620\) 0 0
\(621\) 135.198 5.42532
\(622\) 0 0
\(623\) −9.30057 −0.372620
\(624\) 0 0
\(625\) 19.2056 0.768222
\(626\) 0 0
\(627\) 74.1307 2.96049
\(628\) 0 0
\(629\) −1.29636 −0.0516891
\(630\) 0 0
\(631\) −20.7142 −0.824618 −0.412309 0.911044i \(-0.635278\pi\)
−0.412309 + 0.911044i \(0.635278\pi\)
\(632\) 0 0
\(633\) −19.3162 −0.767749
\(634\) 0 0
\(635\) 12.7122 0.504469
\(636\) 0 0
\(637\) −12.8812 −0.510372
\(638\) 0 0
\(639\) 51.5387 2.03884
\(640\) 0 0
\(641\) 25.0404 0.989035 0.494518 0.869168i \(-0.335345\pi\)
0.494518 + 0.869168i \(0.335345\pi\)
\(642\) 0 0
\(643\) 0.573937 0.0226339 0.0113169 0.999936i \(-0.496398\pi\)
0.0113169 + 0.999936i \(0.496398\pi\)
\(644\) 0 0
\(645\) 33.2142 1.30781
\(646\) 0 0
\(647\) 13.0674 0.513731 0.256865 0.966447i \(-0.417310\pi\)
0.256865 + 0.966447i \(0.417310\pi\)
\(648\) 0 0
\(649\) 4.05597 0.159211
\(650\) 0 0
\(651\) 17.1198 0.670977
\(652\) 0 0
\(653\) −19.5129 −0.763598 −0.381799 0.924245i \(-0.624695\pi\)
−0.381799 + 0.924245i \(0.624695\pi\)
\(654\) 0 0
\(655\) 27.5880 1.07795
\(656\) 0 0
\(657\) 73.7968 2.87909
\(658\) 0 0
\(659\) 25.7407 1.00271 0.501357 0.865240i \(-0.332834\pi\)
0.501357 + 0.865240i \(0.332834\pi\)
\(660\) 0 0
\(661\) 24.6236 0.957746 0.478873 0.877884i \(-0.341045\pi\)
0.478873 + 0.877884i \(0.341045\pi\)
\(662\) 0 0
\(663\) 7.27928 0.282704
\(664\) 0 0
\(665\) 23.4998 0.911283
\(666\) 0 0
\(667\) 67.4925 2.61332
\(668\) 0 0
\(669\) −58.9466 −2.27901
\(670\) 0 0
\(671\) −45.5794 −1.75957
\(672\) 0 0
\(673\) −20.2603 −0.780977 −0.390488 0.920608i \(-0.627694\pi\)
−0.390488 + 0.920608i \(0.627694\pi\)
\(674\) 0 0
\(675\) −147.666 −5.68368
\(676\) 0 0
\(677\) 16.2029 0.622729 0.311364 0.950291i \(-0.399214\pi\)
0.311364 + 0.950291i \(0.399214\pi\)
\(678\) 0 0
\(679\) 3.66276 0.140564
\(680\) 0 0
\(681\) 51.7688 1.98378
\(682\) 0 0
\(683\) 5.17044 0.197841 0.0989206 0.995095i \(-0.468461\pi\)
0.0989206 + 0.995095i \(0.468461\pi\)
\(684\) 0 0
\(685\) −60.8352 −2.32440
\(686\) 0 0
\(687\) 16.4508 0.627636
\(688\) 0 0
\(689\) −21.3553 −0.813573
\(690\) 0 0
\(691\) 38.6586 1.47064 0.735321 0.677719i \(-0.237031\pi\)
0.735321 + 0.677719i \(0.237031\pi\)
\(692\) 0 0
\(693\) −34.3768 −1.30587
\(694\) 0 0
\(695\) −40.3221 −1.52951
\(696\) 0 0
\(697\) 6.85530 0.259663
\(698\) 0 0
\(699\) −23.2331 −0.878756
\(700\) 0 0
\(701\) 14.5356 0.549003 0.274501 0.961587i \(-0.411487\pi\)
0.274501 + 0.961587i \(0.411487\pi\)
\(702\) 0 0
\(703\) −7.24306 −0.273177
\(704\) 0 0
\(705\) 146.524 5.51841
\(706\) 0 0
\(707\) −5.77262 −0.217102
\(708\) 0 0
\(709\) −10.7826 −0.404948 −0.202474 0.979288i \(-0.564898\pi\)
−0.202474 + 0.979288i \(0.564898\pi\)
\(710\) 0 0
\(711\) 42.9745 1.61167
\(712\) 0 0
\(713\) −41.8077 −1.56571
\(714\) 0 0
\(715\) 34.4907 1.28988
\(716\) 0 0
\(717\) −16.5170 −0.616840
\(718\) 0 0
\(719\) −39.8258 −1.48525 −0.742625 0.669707i \(-0.766420\pi\)
−0.742625 + 0.669707i \(0.766420\pi\)
\(720\) 0 0
\(721\) 20.8746 0.777410
\(722\) 0 0
\(723\) 45.3718 1.68739
\(724\) 0 0
\(725\) −73.7166 −2.73777
\(726\) 0 0
\(727\) −2.38628 −0.0885022 −0.0442511 0.999020i \(-0.514090\pi\)
−0.0442511 + 0.999020i \(0.514090\pi\)
\(728\) 0 0
\(729\) 58.5440 2.16830
\(730\) 0 0
\(731\) 2.65701 0.0982732
\(732\) 0 0
\(733\) 32.2166 1.18995 0.594973 0.803746i \(-0.297163\pi\)
0.594973 + 0.803746i \(0.297163\pi\)
\(734\) 0 0
\(735\) 72.3609 2.66907
\(736\) 0 0
\(737\) 9.34385 0.344185
\(738\) 0 0
\(739\) 51.6588 1.90030 0.950150 0.311792i \(-0.100929\pi\)
0.950150 + 0.311792i \(0.100929\pi\)
\(740\) 0 0
\(741\) 40.6711 1.49409
\(742\) 0 0
\(743\) 51.4392 1.88712 0.943561 0.331199i \(-0.107453\pi\)
0.943561 + 0.331199i \(0.107453\pi\)
\(744\) 0 0
\(745\) −42.4504 −1.55526
\(746\) 0 0
\(747\) −62.3898 −2.28272
\(748\) 0 0
\(749\) −13.6520 −0.498832
\(750\) 0 0
\(751\) −12.1121 −0.441976 −0.220988 0.975277i \(-0.570928\pi\)
−0.220988 + 0.975277i \(0.570928\pi\)
\(752\) 0 0
\(753\) 34.6050 1.26108
\(754\) 0 0
\(755\) 46.5189 1.69300
\(756\) 0 0
\(757\) 29.0001 1.05403 0.527014 0.849857i \(-0.323312\pi\)
0.527014 + 0.849857i \(0.323312\pi\)
\(758\) 0 0
\(759\) 116.656 4.23434
\(760\) 0 0
\(761\) −6.67684 −0.242035 −0.121018 0.992650i \(-0.538616\pi\)
−0.121018 + 0.992650i \(0.538616\pi\)
\(762\) 0 0
\(763\) 1.11087 0.0402161
\(764\) 0 0
\(765\) −29.4274 −1.06395
\(766\) 0 0
\(767\) 2.22527 0.0803499
\(768\) 0 0
\(769\) −37.9377 −1.36807 −0.684034 0.729450i \(-0.739776\pi\)
−0.684034 + 0.729450i \(0.739776\pi\)
\(770\) 0 0
\(771\) −62.8835 −2.26469
\(772\) 0 0
\(773\) 9.39476 0.337906 0.168953 0.985624i \(-0.445961\pi\)
0.168953 + 0.985624i \(0.445961\pi\)
\(774\) 0 0
\(775\) 45.6632 1.64027
\(776\) 0 0
\(777\) 4.66737 0.167441
\(778\) 0 0
\(779\) 38.3023 1.37232
\(780\) 0 0
\(781\) 27.1456 0.971346
\(782\) 0 0
\(783\) 118.036 4.21826
\(784\) 0 0
\(785\) −21.1255 −0.754000
\(786\) 0 0
\(787\) 48.5118 1.72926 0.864630 0.502410i \(-0.167553\pi\)
0.864630 + 0.502410i \(0.167553\pi\)
\(788\) 0 0
\(789\) −10.9027 −0.388146
\(790\) 0 0
\(791\) 8.55090 0.304035
\(792\) 0 0
\(793\) −25.0067 −0.888014
\(794\) 0 0
\(795\) 119.965 4.25470
\(796\) 0 0
\(797\) 17.8000 0.630509 0.315254 0.949007i \(-0.397910\pi\)
0.315254 + 0.949007i \(0.397910\pi\)
\(798\) 0 0
\(799\) 11.7214 0.414673
\(800\) 0 0
\(801\) 65.0722 2.29921
\(802\) 0 0
\(803\) 38.8691 1.37166
\(804\) 0 0
\(805\) 36.9805 1.30339
\(806\) 0 0
\(807\) 70.7215 2.48951
\(808\) 0 0
\(809\) −43.7199 −1.53711 −0.768555 0.639784i \(-0.779024\pi\)
−0.768555 + 0.639784i \(0.779024\pi\)
\(810\) 0 0
\(811\) −10.2920 −0.361400 −0.180700 0.983538i \(-0.557836\pi\)
−0.180700 + 0.983538i \(0.557836\pi\)
\(812\) 0 0
\(813\) −57.3671 −2.01195
\(814\) 0 0
\(815\) −30.8715 −1.08138
\(816\) 0 0
\(817\) 14.8454 0.519375
\(818\) 0 0
\(819\) −18.8605 −0.659040
\(820\) 0 0
\(821\) −2.85285 −0.0995651 −0.0497826 0.998760i \(-0.515853\pi\)
−0.0497826 + 0.998760i \(0.515853\pi\)
\(822\) 0 0
\(823\) 39.7632 1.38606 0.693030 0.720909i \(-0.256275\pi\)
0.693030 + 0.720909i \(0.256275\pi\)
\(824\) 0 0
\(825\) −127.414 −4.43598
\(826\) 0 0
\(827\) 44.2553 1.53891 0.769454 0.638702i \(-0.220529\pi\)
0.769454 + 0.638702i \(0.220529\pi\)
\(828\) 0 0
\(829\) −21.8192 −0.757811 −0.378905 0.925435i \(-0.623699\pi\)
−0.378905 + 0.925435i \(0.623699\pi\)
\(830\) 0 0
\(831\) 66.7911 2.31696
\(832\) 0 0
\(833\) 5.78861 0.200563
\(834\) 0 0
\(835\) −25.1263 −0.869531
\(836\) 0 0
\(837\) −73.1165 −2.52727
\(838\) 0 0
\(839\) −9.77123 −0.337340 −0.168670 0.985673i \(-0.553947\pi\)
−0.168670 + 0.985673i \(0.553947\pi\)
\(840\) 0 0
\(841\) 29.9248 1.03189
\(842\) 0 0
\(843\) 31.3167 1.07860
\(844\) 0 0
\(845\) −30.7554 −1.05802
\(846\) 0 0
\(847\) −5.99944 −0.206143
\(848\) 0 0
\(849\) 65.5742 2.25050
\(850\) 0 0
\(851\) −11.3981 −0.390720
\(852\) 0 0
\(853\) 33.6353 1.15165 0.575826 0.817573i \(-0.304681\pi\)
0.575826 + 0.817573i \(0.304681\pi\)
\(854\) 0 0
\(855\) −164.418 −5.62299
\(856\) 0 0
\(857\) 2.09687 0.0716278 0.0358139 0.999358i \(-0.488598\pi\)
0.0358139 + 0.999358i \(0.488598\pi\)
\(858\) 0 0
\(859\) −40.5154 −1.38237 −0.691183 0.722680i \(-0.742910\pi\)
−0.691183 + 0.722680i \(0.742910\pi\)
\(860\) 0 0
\(861\) −24.6817 −0.841149
\(862\) 0 0
\(863\) −34.0458 −1.15893 −0.579466 0.814996i \(-0.696739\pi\)
−0.579466 + 0.814996i \(0.696739\pi\)
\(864\) 0 0
\(865\) 37.6484 1.28009
\(866\) 0 0
\(867\) −3.27119 −0.111095
\(868\) 0 0
\(869\) 22.6348 0.767834
\(870\) 0 0
\(871\) 5.12641 0.173702
\(872\) 0 0
\(873\) −25.6268 −0.867335
\(874\) 0 0
\(875\) −19.3610 −0.654520
\(876\) 0 0
\(877\) 30.9700 1.04578 0.522892 0.852399i \(-0.324853\pi\)
0.522892 + 0.852399i \(0.324853\pi\)
\(878\) 0 0
\(879\) 58.1176 1.96026
\(880\) 0 0
\(881\) 16.3507 0.550868 0.275434 0.961320i \(-0.411178\pi\)
0.275434 + 0.961320i \(0.411178\pi\)
\(882\) 0 0
\(883\) −51.3129 −1.72682 −0.863409 0.504505i \(-0.831675\pi\)
−0.863409 + 0.504505i \(0.831675\pi\)
\(884\) 0 0
\(885\) −12.5006 −0.420202
\(886\) 0 0
\(887\) −5.76280 −0.193496 −0.0967479 0.995309i \(-0.530844\pi\)
−0.0967479 + 0.995309i \(0.530844\pi\)
\(888\) 0 0
\(889\) −3.66133 −0.122797
\(890\) 0 0
\(891\) 110.315 3.69570
\(892\) 0 0
\(893\) 65.4903 2.19155
\(894\) 0 0
\(895\) 62.7837 2.09863
\(896\) 0 0
\(897\) 64.0021 2.13697
\(898\) 0 0
\(899\) −36.5006 −1.21736
\(900\) 0 0
\(901\) 9.59673 0.319714
\(902\) 0 0
\(903\) −9.56625 −0.318345
\(904\) 0 0
\(905\) 7.16891 0.238303
\(906\) 0 0
\(907\) −21.6904 −0.720218 −0.360109 0.932910i \(-0.617261\pi\)
−0.360109 + 0.932910i \(0.617261\pi\)
\(908\) 0 0
\(909\) 40.3886 1.33961
\(910\) 0 0
\(911\) 17.7764 0.588957 0.294479 0.955658i \(-0.404854\pi\)
0.294479 + 0.955658i \(0.404854\pi\)
\(912\) 0 0
\(913\) −32.8609 −1.08754
\(914\) 0 0
\(915\) 140.476 4.64401
\(916\) 0 0
\(917\) −7.94582 −0.262394
\(918\) 0 0
\(919\) −29.0756 −0.959117 −0.479558 0.877510i \(-0.659203\pi\)
−0.479558 + 0.877510i \(0.659203\pi\)
\(920\) 0 0
\(921\) −39.2841 −1.29445
\(922\) 0 0
\(923\) 14.8932 0.490215
\(924\) 0 0
\(925\) 12.4492 0.409327
\(926\) 0 0
\(927\) −146.051 −4.79694
\(928\) 0 0
\(929\) −13.6276 −0.447108 −0.223554 0.974692i \(-0.571766\pi\)
−0.223554 + 0.974692i \(0.571766\pi\)
\(930\) 0 0
\(931\) 32.3424 1.05998
\(932\) 0 0
\(933\) 65.8038 2.15432
\(934\) 0 0
\(935\) −15.4995 −0.506889
\(936\) 0 0
\(937\) −29.3366 −0.958384 −0.479192 0.877710i \(-0.659070\pi\)
−0.479192 + 0.877710i \(0.659070\pi\)
\(938\) 0 0
\(939\) −43.8715 −1.43169
\(940\) 0 0
\(941\) −55.3831 −1.80544 −0.902718 0.430232i \(-0.858432\pi\)
−0.902718 + 0.430232i \(0.858432\pi\)
\(942\) 0 0
\(943\) 60.2744 1.96280
\(944\) 0 0
\(945\) 64.6742 2.10385
\(946\) 0 0
\(947\) 25.8521 0.840080 0.420040 0.907505i \(-0.362016\pi\)
0.420040 + 0.907505i \(0.362016\pi\)
\(948\) 0 0
\(949\) 21.3251 0.692243
\(950\) 0 0
\(951\) −55.8922 −1.81243
\(952\) 0 0
\(953\) −28.0028 −0.907100 −0.453550 0.891231i \(-0.649843\pi\)
−0.453550 + 0.891231i \(0.649843\pi\)
\(954\) 0 0
\(955\) −47.9246 −1.55080
\(956\) 0 0
\(957\) 101.847 3.29225
\(958\) 0 0
\(959\) 17.5216 0.565802
\(960\) 0 0
\(961\) −8.39000 −0.270645
\(962\) 0 0
\(963\) 95.5172 3.07800
\(964\) 0 0
\(965\) −47.0009 −1.51301
\(966\) 0 0
\(967\) −42.3369 −1.36146 −0.680732 0.732533i \(-0.738338\pi\)
−0.680732 + 0.732533i \(0.738338\pi\)
\(968\) 0 0
\(969\) −18.2769 −0.587140
\(970\) 0 0
\(971\) −33.4135 −1.07229 −0.536145 0.844126i \(-0.680120\pi\)
−0.536145 + 0.844126i \(0.680120\pi\)
\(972\) 0 0
\(973\) 11.6135 0.372310
\(974\) 0 0
\(975\) −69.9044 −2.23873
\(976\) 0 0
\(977\) 24.3795 0.779969 0.389984 0.920821i \(-0.372480\pi\)
0.389984 + 0.920821i \(0.372480\pi\)
\(978\) 0 0
\(979\) 34.2738 1.09540
\(980\) 0 0
\(981\) −7.77228 −0.248150
\(982\) 0 0
\(983\) −49.0524 −1.56453 −0.782265 0.622946i \(-0.785936\pi\)
−0.782265 + 0.622946i \(0.785936\pi\)
\(984\) 0 0
\(985\) 91.6804 2.92118
\(986\) 0 0
\(987\) −42.2014 −1.34329
\(988\) 0 0
\(989\) 23.3615 0.742852
\(990\) 0 0
\(991\) −50.6874 −1.61014 −0.805068 0.593182i \(-0.797872\pi\)
−0.805068 + 0.593182i \(0.797872\pi\)
\(992\) 0 0
\(993\) 85.0157 2.69789
\(994\) 0 0
\(995\) 73.7369 2.33762
\(996\) 0 0
\(997\) −33.7304 −1.06825 −0.534126 0.845405i \(-0.679359\pi\)
−0.534126 + 0.845405i \(0.679359\pi\)
\(998\) 0 0
\(999\) −19.9338 −0.630676
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 \(a_p\))