Properties

Label 6040.2.a.l.1.4
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-0.357360\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.13091 q^{3}\) \(+1.00000 q^{5}\) \(+2.44094 q^{7}\) \(-1.72105 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.13091 q^{3}\) \(+1.00000 q^{5}\) \(+2.44094 q^{7}\) \(-1.72105 q^{9}\) \(+3.35337 q^{11}\) \(-0.198969 q^{13}\) \(-1.13091 q^{15}\) \(+1.66140 q^{17}\) \(-2.14406 q^{19}\) \(-2.76048 q^{21}\) \(-7.53018 q^{23}\) \(+1.00000 q^{25}\) \(+5.33907 q^{27}\) \(-5.30691 q^{29}\) \(-3.84940 q^{31}\) \(-3.79236 q^{33}\) \(+2.44094 q^{35}\) \(+4.72724 q^{37}\) \(+0.225016 q^{39}\) \(+0.116463 q^{41}\) \(-10.5866 q^{43}\) \(-1.72105 q^{45}\) \(-1.58286 q^{47}\) \(-1.04181 q^{49}\) \(-1.87889 q^{51}\) \(-8.98581 q^{53}\) \(+3.35337 q^{55}\) \(+2.42473 q^{57}\) \(-4.35181 q^{59}\) \(-5.10391 q^{61}\) \(-4.20097 q^{63}\) \(-0.198969 q^{65}\) \(-2.74968 q^{67}\) \(+8.51594 q^{69}\) \(+5.00885 q^{71}\) \(-3.52920 q^{73}\) \(-1.13091 q^{75}\) \(+8.18539 q^{77}\) \(+17.1699 q^{79}\) \(-0.874857 q^{81}\) \(+5.89400 q^{83}\) \(+1.66140 q^{85}\) \(+6.00163 q^{87}\) \(-10.7276 q^{89}\) \(-0.485673 q^{91}\) \(+4.35332 q^{93}\) \(-2.14406 q^{95}\) \(-8.51560 q^{97}\) \(-5.77131 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut -\mathstrut 9q^{21} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 9q^{25} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 22q^{47} \) \(\mathstrut -\mathstrut 29q^{49} \) \(\mathstrut +\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut 20q^{57} \) \(\mathstrut +\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 22q^{61} \) \(\mathstrut -\mathstrut 12q^{63} \) \(\mathstrut -\mathstrut 9q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 5q^{69} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 5q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 3q^{83} \) \(\mathstrut -\mathstrut 2q^{85} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 21q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut 15q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.13091 −0.652930 −0.326465 0.945209i \(-0.605858\pi\)
−0.326465 + 0.945209i \(0.605858\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 2.44094 0.922589 0.461294 0.887247i \(-0.347385\pi\)
0.461294 + 0.887247i \(0.347385\pi\)
\(8\) 0 0
\(9\) −1.72105 −0.573682
\(10\) 0 0
\(11\) 3.35337 1.01108 0.505540 0.862803i \(-0.331293\pi\)
0.505540 + 0.862803i \(0.331293\pi\)
\(12\) 0 0
\(13\) −0.198969 −0.0551842 −0.0275921 0.999619i \(-0.508784\pi\)
−0.0275921 + 0.999619i \(0.508784\pi\)
\(14\) 0 0
\(15\) −1.13091 −0.291999
\(16\) 0 0
\(17\) 1.66140 0.402949 0.201475 0.979494i \(-0.435427\pi\)
0.201475 + 0.979494i \(0.435427\pi\)
\(18\) 0 0
\(19\) −2.14406 −0.491881 −0.245940 0.969285i \(-0.579097\pi\)
−0.245940 + 0.969285i \(0.579097\pi\)
\(20\) 0 0
\(21\) −2.76048 −0.602386
\(22\) 0 0
\(23\) −7.53018 −1.57015 −0.785076 0.619400i \(-0.787376\pi\)
−0.785076 + 0.619400i \(0.787376\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.33907 1.02750
\(28\) 0 0
\(29\) −5.30691 −0.985468 −0.492734 0.870180i \(-0.664002\pi\)
−0.492734 + 0.870180i \(0.664002\pi\)
\(30\) 0 0
\(31\) −3.84940 −0.691373 −0.345687 0.938350i \(-0.612354\pi\)
−0.345687 + 0.938350i \(0.612354\pi\)
\(32\) 0 0
\(33\) −3.79236 −0.660165
\(34\) 0 0
\(35\) 2.44094 0.412594
\(36\) 0 0
\(37\) 4.72724 0.777153 0.388577 0.921416i \(-0.372967\pi\)
0.388577 + 0.921416i \(0.372967\pi\)
\(38\) 0 0
\(39\) 0.225016 0.0360314
\(40\) 0 0
\(41\) 0.116463 0.0181885 0.00909423 0.999959i \(-0.497105\pi\)
0.00909423 + 0.999959i \(0.497105\pi\)
\(42\) 0 0
\(43\) −10.5866 −1.61443 −0.807217 0.590254i \(-0.799028\pi\)
−0.807217 + 0.590254i \(0.799028\pi\)
\(44\) 0 0
\(45\) −1.72105 −0.256559
\(46\) 0 0
\(47\) −1.58286 −0.230884 −0.115442 0.993314i \(-0.536828\pi\)
−0.115442 + 0.993314i \(0.536828\pi\)
\(48\) 0 0
\(49\) −1.04181 −0.148830
\(50\) 0 0
\(51\) −1.87889 −0.263098
\(52\) 0 0
\(53\) −8.98581 −1.23430 −0.617148 0.786847i \(-0.711712\pi\)
−0.617148 + 0.786847i \(0.711712\pi\)
\(54\) 0 0
\(55\) 3.35337 0.452169
\(56\) 0 0
\(57\) 2.42473 0.321164
\(58\) 0 0
\(59\) −4.35181 −0.566557 −0.283279 0.959038i \(-0.591422\pi\)
−0.283279 + 0.959038i \(0.591422\pi\)
\(60\) 0 0
\(61\) −5.10391 −0.653489 −0.326744 0.945113i \(-0.605952\pi\)
−0.326744 + 0.945113i \(0.605952\pi\)
\(62\) 0 0
\(63\) −4.20097 −0.529273
\(64\) 0 0
\(65\) −0.198969 −0.0246791
\(66\) 0 0
\(67\) −2.74968 −0.335927 −0.167964 0.985793i \(-0.553719\pi\)
−0.167964 + 0.985793i \(0.553719\pi\)
\(68\) 0 0
\(69\) 8.51594 1.02520
\(70\) 0 0
\(71\) 5.00885 0.594441 0.297220 0.954809i \(-0.403940\pi\)
0.297220 + 0.954809i \(0.403940\pi\)
\(72\) 0 0
\(73\) −3.52920 −0.413062 −0.206531 0.978440i \(-0.566217\pi\)
−0.206531 + 0.978440i \(0.566217\pi\)
\(74\) 0 0
\(75\) −1.13091 −0.130586
\(76\) 0 0
\(77\) 8.18539 0.932811
\(78\) 0 0
\(79\) 17.1699 1.93176 0.965881 0.258988i \(-0.0833889\pi\)
0.965881 + 0.258988i \(0.0833889\pi\)
\(80\) 0 0
\(81\) −0.874857 −0.0972064
\(82\) 0 0
\(83\) 5.89400 0.646951 0.323475 0.946237i \(-0.395149\pi\)
0.323475 + 0.946237i \(0.395149\pi\)
\(84\) 0 0
\(85\) 1.66140 0.180204
\(86\) 0 0
\(87\) 6.00163 0.643442
\(88\) 0 0
\(89\) −10.7276 −1.13713 −0.568564 0.822639i \(-0.692501\pi\)
−0.568564 + 0.822639i \(0.692501\pi\)
\(90\) 0 0
\(91\) −0.485673 −0.0509123
\(92\) 0 0
\(93\) 4.35332 0.451419
\(94\) 0 0
\(95\) −2.14406 −0.219976
\(96\) 0 0
\(97\) −8.51560 −0.864628 −0.432314 0.901723i \(-0.642303\pi\)
−0.432314 + 0.901723i \(0.642303\pi\)
\(98\) 0 0
\(99\) −5.77131 −0.580039
\(100\) 0 0
\(101\) 11.1214 1.10662 0.553311 0.832975i \(-0.313364\pi\)
0.553311 + 0.832975i \(0.313364\pi\)
\(102\) 0 0
\(103\) −10.1255 −0.997692 −0.498846 0.866691i \(-0.666243\pi\)
−0.498846 + 0.866691i \(0.666243\pi\)
\(104\) 0 0
\(105\) −2.76048 −0.269395
\(106\) 0 0
\(107\) −13.4945 −1.30456 −0.652281 0.757978i \(-0.726188\pi\)
−0.652281 + 0.757978i \(0.726188\pi\)
\(108\) 0 0
\(109\) −6.96707 −0.667324 −0.333662 0.942693i \(-0.608284\pi\)
−0.333662 + 0.942693i \(0.608284\pi\)
\(110\) 0 0
\(111\) −5.34607 −0.507427
\(112\) 0 0
\(113\) −4.78171 −0.449825 −0.224913 0.974379i \(-0.572210\pi\)
−0.224913 + 0.974379i \(0.572210\pi\)
\(114\) 0 0
\(115\) −7.53018 −0.702193
\(116\) 0 0
\(117\) 0.342436 0.0316582
\(118\) 0 0
\(119\) 4.05538 0.371757
\(120\) 0 0
\(121\) 0.245115 0.0222832
\(122\) 0 0
\(123\) −0.131709 −0.0118758
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 13.1165 1.16390 0.581950 0.813225i \(-0.302290\pi\)
0.581950 + 0.813225i \(0.302290\pi\)
\(128\) 0 0
\(129\) 11.9724 1.05411
\(130\) 0 0
\(131\) −9.93206 −0.867768 −0.433884 0.900969i \(-0.642857\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(132\) 0 0
\(133\) −5.23352 −0.453804
\(134\) 0 0
\(135\) 5.33907 0.459514
\(136\) 0 0
\(137\) 5.99158 0.511895 0.255947 0.966691i \(-0.417613\pi\)
0.255947 + 0.966691i \(0.417613\pi\)
\(138\) 0 0
\(139\) 19.3817 1.64393 0.821966 0.569537i \(-0.192877\pi\)
0.821966 + 0.569537i \(0.192877\pi\)
\(140\) 0 0
\(141\) 1.79007 0.150751
\(142\) 0 0
\(143\) −0.667219 −0.0557957
\(144\) 0 0
\(145\) −5.30691 −0.440715
\(146\) 0 0
\(147\) 1.17819 0.0971753
\(148\) 0 0
\(149\) −9.41614 −0.771400 −0.385700 0.922624i \(-0.626040\pi\)
−0.385700 + 0.922624i \(0.626040\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788
\(152\) 0 0
\(153\) −2.85935 −0.231165
\(154\) 0 0
\(155\) −3.84940 −0.309192
\(156\) 0 0
\(157\) 0.995474 0.0794475 0.0397237 0.999211i \(-0.487352\pi\)
0.0397237 + 0.999211i \(0.487352\pi\)
\(158\) 0 0
\(159\) 10.1621 0.805909
\(160\) 0 0
\(161\) −18.3807 −1.44860
\(162\) 0 0
\(163\) 19.2392 1.50693 0.753464 0.657490i \(-0.228382\pi\)
0.753464 + 0.657490i \(0.228382\pi\)
\(164\) 0 0
\(165\) −3.79236 −0.295235
\(166\) 0 0
\(167\) 20.4959 1.58602 0.793009 0.609210i \(-0.208513\pi\)
0.793009 + 0.609210i \(0.208513\pi\)
\(168\) 0 0
\(169\) −12.9604 −0.996955
\(170\) 0 0
\(171\) 3.69003 0.282183
\(172\) 0 0
\(173\) 8.69187 0.660831 0.330415 0.943836i \(-0.392811\pi\)
0.330415 + 0.943836i \(0.392811\pi\)
\(174\) 0 0
\(175\) 2.44094 0.184518
\(176\) 0 0
\(177\) 4.92149 0.369922
\(178\) 0 0
\(179\) 15.6278 1.16808 0.584038 0.811726i \(-0.301472\pi\)
0.584038 + 0.811726i \(0.301472\pi\)
\(180\) 0 0
\(181\) −12.7628 −0.948650 −0.474325 0.880350i \(-0.657308\pi\)
−0.474325 + 0.880350i \(0.657308\pi\)
\(182\) 0 0
\(183\) 5.77205 0.426682
\(184\) 0 0
\(185\) 4.72724 0.347554
\(186\) 0 0
\(187\) 5.57130 0.407414
\(188\) 0 0
\(189\) 13.0324 0.947964
\(190\) 0 0
\(191\) −11.5290 −0.834206 −0.417103 0.908859i \(-0.636955\pi\)
−0.417103 + 0.908859i \(0.636955\pi\)
\(192\) 0 0
\(193\) 16.0918 1.15832 0.579158 0.815215i \(-0.303381\pi\)
0.579158 + 0.815215i \(0.303381\pi\)
\(194\) 0 0
\(195\) 0.225016 0.0161137
\(196\) 0 0
\(197\) −14.7876 −1.05357 −0.526785 0.849999i \(-0.676603\pi\)
−0.526785 + 0.849999i \(0.676603\pi\)
\(198\) 0 0
\(199\) −9.01076 −0.638756 −0.319378 0.947627i \(-0.603474\pi\)
−0.319378 + 0.947627i \(0.603474\pi\)
\(200\) 0 0
\(201\) 3.10964 0.219337
\(202\) 0 0
\(203\) −12.9538 −0.909182
\(204\) 0 0
\(205\) 0.116463 0.00813412
\(206\) 0 0
\(207\) 12.9598 0.900768
\(208\) 0 0
\(209\) −7.18983 −0.497331
\(210\) 0 0
\(211\) −10.8845 −0.749318 −0.374659 0.927163i \(-0.622240\pi\)
−0.374659 + 0.927163i \(0.622240\pi\)
\(212\) 0 0
\(213\) −5.66455 −0.388128
\(214\) 0 0
\(215\) −10.5866 −0.721997
\(216\) 0 0
\(217\) −9.39617 −0.637854
\(218\) 0 0
\(219\) 3.99120 0.269701
\(220\) 0 0
\(221\) −0.330568 −0.0222364
\(222\) 0 0
\(223\) −15.8152 −1.05906 −0.529532 0.848290i \(-0.677632\pi\)
−0.529532 + 0.848290i \(0.677632\pi\)
\(224\) 0 0
\(225\) −1.72105 −0.114736
\(226\) 0 0
\(227\) −21.6778 −1.43880 −0.719402 0.694594i \(-0.755584\pi\)
−0.719402 + 0.694594i \(0.755584\pi\)
\(228\) 0 0
\(229\) −8.78579 −0.580581 −0.290291 0.956938i \(-0.593752\pi\)
−0.290291 + 0.956938i \(0.593752\pi\)
\(230\) 0 0
\(231\) −9.25692 −0.609061
\(232\) 0 0
\(233\) 13.9574 0.914379 0.457189 0.889369i \(-0.348856\pi\)
0.457189 + 0.889369i \(0.348856\pi\)
\(234\) 0 0
\(235\) −1.58286 −0.103254
\(236\) 0 0
\(237\) −19.4175 −1.26131
\(238\) 0 0
\(239\) −17.5846 −1.13745 −0.568726 0.822527i \(-0.692563\pi\)
−0.568726 + 0.822527i \(0.692563\pi\)
\(240\) 0 0
\(241\) −9.13289 −0.588301 −0.294151 0.955759i \(-0.595037\pi\)
−0.294151 + 0.955759i \(0.595037\pi\)
\(242\) 0 0
\(243\) −15.0278 −0.964036
\(244\) 0 0
\(245\) −1.04181 −0.0665586
\(246\) 0 0
\(247\) 0.426602 0.0271441
\(248\) 0 0
\(249\) −6.66557 −0.422414
\(250\) 0 0
\(251\) 14.2777 0.901199 0.450600 0.892726i \(-0.351210\pi\)
0.450600 + 0.892726i \(0.351210\pi\)
\(252\) 0 0
\(253\) −25.2515 −1.58755
\(254\) 0 0
\(255\) −1.87889 −0.117661
\(256\) 0 0
\(257\) −10.4424 −0.651378 −0.325689 0.945477i \(-0.605596\pi\)
−0.325689 + 0.945477i \(0.605596\pi\)
\(258\) 0 0
\(259\) 11.5389 0.716993
\(260\) 0 0
\(261\) 9.13344 0.565346
\(262\) 0 0
\(263\) 28.6768 1.76829 0.884143 0.467217i \(-0.154743\pi\)
0.884143 + 0.467217i \(0.154743\pi\)
\(264\) 0 0
\(265\) −8.98581 −0.551994
\(266\) 0 0
\(267\) 12.1320 0.742465
\(268\) 0 0
\(269\) −19.8884 −1.21262 −0.606310 0.795229i \(-0.707351\pi\)
−0.606310 + 0.795229i \(0.707351\pi\)
\(270\) 0 0
\(271\) −6.96237 −0.422934 −0.211467 0.977385i \(-0.567824\pi\)
−0.211467 + 0.977385i \(0.567824\pi\)
\(272\) 0 0
\(273\) 0.549251 0.0332422
\(274\) 0 0
\(275\) 3.35337 0.202216
\(276\) 0 0
\(277\) 19.3217 1.16093 0.580465 0.814285i \(-0.302871\pi\)
0.580465 + 0.814285i \(0.302871\pi\)
\(278\) 0 0
\(279\) 6.62500 0.396629
\(280\) 0 0
\(281\) −8.84655 −0.527741 −0.263871 0.964558i \(-0.584999\pi\)
−0.263871 + 0.964558i \(0.584999\pi\)
\(282\) 0 0
\(283\) 26.7966 1.59289 0.796447 0.604709i \(-0.206711\pi\)
0.796447 + 0.604709i \(0.206711\pi\)
\(284\) 0 0
\(285\) 2.42473 0.143629
\(286\) 0 0
\(287\) 0.284279 0.0167805
\(288\) 0 0
\(289\) −14.2397 −0.837632
\(290\) 0 0
\(291\) 9.63036 0.564542
\(292\) 0 0
\(293\) −20.2135 −1.18088 −0.590441 0.807081i \(-0.701046\pi\)
−0.590441 + 0.807081i \(0.701046\pi\)
\(294\) 0 0
\(295\) −4.35181 −0.253372
\(296\) 0 0
\(297\) 17.9039 1.03889
\(298\) 0 0
\(299\) 1.49828 0.0866475
\(300\) 0 0
\(301\) −25.8412 −1.48946
\(302\) 0 0
\(303\) −12.5773 −0.722547
\(304\) 0 0
\(305\) −5.10391 −0.292249
\(306\) 0 0
\(307\) 27.5714 1.57359 0.786793 0.617218i \(-0.211740\pi\)
0.786793 + 0.617218i \(0.211740\pi\)
\(308\) 0 0
\(309\) 11.4510 0.651423
\(310\) 0 0
\(311\) 22.8888 1.29791 0.648953 0.760828i \(-0.275207\pi\)
0.648953 + 0.760828i \(0.275207\pi\)
\(312\) 0 0
\(313\) −18.9361 −1.07033 −0.535165 0.844747i \(-0.679751\pi\)
−0.535165 + 0.844747i \(0.679751\pi\)
\(314\) 0 0
\(315\) −4.20097 −0.236698
\(316\) 0 0
\(317\) −19.2548 −1.08146 −0.540730 0.841196i \(-0.681852\pi\)
−0.540730 + 0.841196i \(0.681852\pi\)
\(318\) 0 0
\(319\) −17.7960 −0.996387
\(320\) 0 0
\(321\) 15.2610 0.851787
\(322\) 0 0
\(323\) −3.56214 −0.198203
\(324\) 0 0
\(325\) −0.198969 −0.0110368
\(326\) 0 0
\(327\) 7.87912 0.435716
\(328\) 0 0
\(329\) −3.86366 −0.213011
\(330\) 0 0
\(331\) −4.04124 −0.222126 −0.111063 0.993813i \(-0.535426\pi\)
−0.111063 + 0.993813i \(0.535426\pi\)
\(332\) 0 0
\(333\) −8.13580 −0.445839
\(334\) 0 0
\(335\) −2.74968 −0.150231
\(336\) 0 0
\(337\) −9.37697 −0.510796 −0.255398 0.966836i \(-0.582207\pi\)
−0.255398 + 0.966836i \(0.582207\pi\)
\(338\) 0 0
\(339\) 5.40767 0.293704
\(340\) 0 0
\(341\) −12.9085 −0.699034
\(342\) 0 0
\(343\) −19.6296 −1.05990
\(344\) 0 0
\(345\) 8.51594 0.458483
\(346\) 0 0
\(347\) 19.3160 1.03694 0.518469 0.855097i \(-0.326502\pi\)
0.518469 + 0.855097i \(0.326502\pi\)
\(348\) 0 0
\(349\) −28.1082 −1.50460 −0.752299 0.658821i \(-0.771055\pi\)
−0.752299 + 0.658821i \(0.771055\pi\)
\(350\) 0 0
\(351\) −1.06231 −0.0567020
\(352\) 0 0
\(353\) 1.92920 0.102681 0.0513406 0.998681i \(-0.483651\pi\)
0.0513406 + 0.998681i \(0.483651\pi\)
\(354\) 0 0
\(355\) 5.00885 0.265842
\(356\) 0 0
\(357\) −4.58627 −0.242731
\(358\) 0 0
\(359\) −20.3442 −1.07373 −0.536864 0.843669i \(-0.680391\pi\)
−0.536864 + 0.843669i \(0.680391\pi\)
\(360\) 0 0
\(361\) −14.4030 −0.758053
\(362\) 0 0
\(363\) −0.277202 −0.0145493
\(364\) 0 0
\(365\) −3.52920 −0.184727
\(366\) 0 0
\(367\) −24.8119 −1.29517 −0.647585 0.761993i \(-0.724221\pi\)
−0.647585 + 0.761993i \(0.724221\pi\)
\(368\) 0 0
\(369\) −0.200438 −0.0104344
\(370\) 0 0
\(371\) −21.9338 −1.13875
\(372\) 0 0
\(373\) 10.5757 0.547589 0.273794 0.961788i \(-0.411721\pi\)
0.273794 + 0.961788i \(0.411721\pi\)
\(374\) 0 0
\(375\) −1.13091 −0.0583998
\(376\) 0 0
\(377\) 1.05591 0.0543823
\(378\) 0 0
\(379\) 32.3181 1.66007 0.830035 0.557711i \(-0.188320\pi\)
0.830035 + 0.557711i \(0.188320\pi\)
\(380\) 0 0
\(381\) −14.8335 −0.759945
\(382\) 0 0
\(383\) 11.8315 0.604563 0.302281 0.953219i \(-0.402252\pi\)
0.302281 + 0.953219i \(0.402252\pi\)
\(384\) 0 0
\(385\) 8.18539 0.417166
\(386\) 0 0
\(387\) 18.2200 0.926173
\(388\) 0 0
\(389\) 1.49412 0.0757550 0.0378775 0.999282i \(-0.487940\pi\)
0.0378775 + 0.999282i \(0.487940\pi\)
\(390\) 0 0
\(391\) −12.5107 −0.632691
\(392\) 0 0
\(393\) 11.2322 0.566592
\(394\) 0 0
\(395\) 17.1699 0.863910
\(396\) 0 0
\(397\) 10.0540 0.504594 0.252297 0.967650i \(-0.418814\pi\)
0.252297 + 0.967650i \(0.418814\pi\)
\(398\) 0 0
\(399\) 5.91863 0.296302
\(400\) 0 0
\(401\) −35.9722 −1.79637 −0.898183 0.439621i \(-0.855113\pi\)
−0.898183 + 0.439621i \(0.855113\pi\)
\(402\) 0 0
\(403\) 0.765914 0.0381529
\(404\) 0 0
\(405\) −0.874857 −0.0434720
\(406\) 0 0
\(407\) 15.8522 0.785764
\(408\) 0 0
\(409\) −3.96029 −0.195824 −0.0979119 0.995195i \(-0.531216\pi\)
−0.0979119 + 0.995195i \(0.531216\pi\)
\(410\) 0 0
\(411\) −6.77592 −0.334232
\(412\) 0 0
\(413\) −10.6225 −0.522699
\(414\) 0 0
\(415\) 5.89400 0.289325
\(416\) 0 0
\(417\) −21.9189 −1.07337
\(418\) 0 0
\(419\) −25.0895 −1.22570 −0.612851 0.790198i \(-0.709978\pi\)
−0.612851 + 0.790198i \(0.709978\pi\)
\(420\) 0 0
\(421\) 26.5350 1.29324 0.646619 0.762813i \(-0.276182\pi\)
0.646619 + 0.762813i \(0.276182\pi\)
\(422\) 0 0
\(423\) 2.72417 0.132454
\(424\) 0 0
\(425\) 1.66140 0.0805898
\(426\) 0 0
\(427\) −12.4583 −0.602901
\(428\) 0 0
\(429\) 0.754563 0.0364307
\(430\) 0 0
\(431\) 0.137974 0.00664596 0.00332298 0.999994i \(-0.498942\pi\)
0.00332298 + 0.999994i \(0.498942\pi\)
\(432\) 0 0
\(433\) −6.08546 −0.292449 −0.146224 0.989251i \(-0.546712\pi\)
−0.146224 + 0.989251i \(0.546712\pi\)
\(434\) 0 0
\(435\) 6.00163 0.287756
\(436\) 0 0
\(437\) 16.1452 0.772327
\(438\) 0 0
\(439\) −4.95618 −0.236546 −0.118273 0.992981i \(-0.537736\pi\)
−0.118273 + 0.992981i \(0.537736\pi\)
\(440\) 0 0
\(441\) 1.79300 0.0853809
\(442\) 0 0
\(443\) 7.14135 0.339296 0.169648 0.985505i \(-0.445737\pi\)
0.169648 + 0.985505i \(0.445737\pi\)
\(444\) 0 0
\(445\) −10.7276 −0.508539
\(446\) 0 0
\(447\) 10.6488 0.503671
\(448\) 0 0
\(449\) 0.502522 0.0237155 0.0118578 0.999930i \(-0.496225\pi\)
0.0118578 + 0.999930i \(0.496225\pi\)
\(450\) 0 0
\(451\) 0.390544 0.0183900
\(452\) 0 0
\(453\) 1.13091 0.0531347
\(454\) 0 0
\(455\) −0.485673 −0.0227687
\(456\) 0 0
\(457\) −1.84207 −0.0861684 −0.0430842 0.999071i \(-0.513718\pi\)
−0.0430842 + 0.999071i \(0.513718\pi\)
\(458\) 0 0
\(459\) 8.87034 0.414032
\(460\) 0 0
\(461\) 17.3926 0.810052 0.405026 0.914305i \(-0.367262\pi\)
0.405026 + 0.914305i \(0.367262\pi\)
\(462\) 0 0
\(463\) −22.6031 −1.05045 −0.525227 0.850962i \(-0.676019\pi\)
−0.525227 + 0.850962i \(0.676019\pi\)
\(464\) 0 0
\(465\) 4.35332 0.201880
\(466\) 0 0
\(467\) 2.90528 0.134440 0.0672202 0.997738i \(-0.478587\pi\)
0.0672202 + 0.997738i \(0.478587\pi\)
\(468\) 0 0
\(469\) −6.71181 −0.309923
\(470\) 0 0
\(471\) −1.12579 −0.0518737
\(472\) 0 0
\(473\) −35.5007 −1.63232
\(474\) 0 0
\(475\) −2.14406 −0.0983762
\(476\) 0 0
\(477\) 15.4650 0.708094
\(478\) 0 0
\(479\) −4.79811 −0.219231 −0.109616 0.993974i \(-0.534962\pi\)
−0.109616 + 0.993974i \(0.534962\pi\)
\(480\) 0 0
\(481\) −0.940576 −0.0428866
\(482\) 0 0
\(483\) 20.7869 0.945837
\(484\) 0 0
\(485\) −8.51560 −0.386674
\(486\) 0 0
\(487\) −26.7769 −1.21338 −0.606689 0.794939i \(-0.707503\pi\)
−0.606689 + 0.794939i \(0.707503\pi\)
\(488\) 0 0
\(489\) −21.7577 −0.983918
\(490\) 0 0
\(491\) −24.7539 −1.11713 −0.558565 0.829461i \(-0.688648\pi\)
−0.558565 + 0.829461i \(0.688648\pi\)
\(492\) 0 0
\(493\) −8.81691 −0.397094
\(494\) 0 0
\(495\) −5.77131 −0.259401
\(496\) 0 0
\(497\) 12.2263 0.548425
\(498\) 0 0
\(499\) 43.5343 1.94886 0.974431 0.224688i \(-0.0721362\pi\)
0.974431 + 0.224688i \(0.0721362\pi\)
\(500\) 0 0
\(501\) −23.1789 −1.03556
\(502\) 0 0
\(503\) −21.2472 −0.947366 −0.473683 0.880695i \(-0.657076\pi\)
−0.473683 + 0.880695i \(0.657076\pi\)
\(504\) 0 0
\(505\) 11.1214 0.494896
\(506\) 0 0
\(507\) 14.6570 0.650942
\(508\) 0 0
\(509\) −10.4378 −0.462648 −0.231324 0.972877i \(-0.574306\pi\)
−0.231324 + 0.972877i \(0.574306\pi\)
\(510\) 0 0
\(511\) −8.61458 −0.381086
\(512\) 0 0
\(513\) −11.4473 −0.505410
\(514\) 0 0
\(515\) −10.1255 −0.446182
\(516\) 0 0
\(517\) −5.30792 −0.233442
\(518\) 0 0
\(519\) −9.82971 −0.431476
\(520\) 0 0
\(521\) 0.906643 0.0397208 0.0198604 0.999803i \(-0.493678\pi\)
0.0198604 + 0.999803i \(0.493678\pi\)
\(522\) 0 0
\(523\) −38.9877 −1.70481 −0.852407 0.522880i \(-0.824858\pi\)
−0.852407 + 0.522880i \(0.824858\pi\)
\(524\) 0 0
\(525\) −2.76048 −0.120477
\(526\) 0 0
\(527\) −6.39541 −0.278588
\(528\) 0 0
\(529\) 33.7036 1.46537
\(530\) 0 0
\(531\) 7.48966 0.325024
\(532\) 0 0
\(533\) −0.0231726 −0.00100372
\(534\) 0 0
\(535\) −13.4945 −0.583417
\(536\) 0 0
\(537\) −17.6736 −0.762672
\(538\) 0 0
\(539\) −3.49357 −0.150479
\(540\) 0 0
\(541\) 17.3447 0.745707 0.372853 0.927890i \(-0.378379\pi\)
0.372853 + 0.927890i \(0.378379\pi\)
\(542\) 0 0
\(543\) 14.4335 0.619402
\(544\) 0 0
\(545\) −6.96707 −0.298437
\(546\) 0 0
\(547\) 4.61497 0.197322 0.0986609 0.995121i \(-0.468544\pi\)
0.0986609 + 0.995121i \(0.468544\pi\)
\(548\) 0 0
\(549\) 8.78407 0.374895
\(550\) 0 0
\(551\) 11.3783 0.484733
\(552\) 0 0
\(553\) 41.9106 1.78222
\(554\) 0 0
\(555\) −5.34607 −0.226928
\(556\) 0 0
\(557\) −2.44894 −0.103765 −0.0518825 0.998653i \(-0.516522\pi\)
−0.0518825 + 0.998653i \(0.516522\pi\)
\(558\) 0 0
\(559\) 2.10640 0.0890913
\(560\) 0 0
\(561\) −6.30063 −0.266013
\(562\) 0 0
\(563\) 42.3632 1.78540 0.892698 0.450656i \(-0.148810\pi\)
0.892698 + 0.450656i \(0.148810\pi\)
\(564\) 0 0
\(565\) −4.78171 −0.201168
\(566\) 0 0
\(567\) −2.13548 −0.0896815
\(568\) 0 0
\(569\) −25.8605 −1.08413 −0.542063 0.840338i \(-0.682357\pi\)
−0.542063 + 0.840338i \(0.682357\pi\)
\(570\) 0 0
\(571\) 0.376183 0.0157428 0.00787138 0.999969i \(-0.497494\pi\)
0.00787138 + 0.999969i \(0.497494\pi\)
\(572\) 0 0
\(573\) 13.0382 0.544678
\(574\) 0 0
\(575\) −7.53018 −0.314030
\(576\) 0 0
\(577\) −36.3461 −1.51311 −0.756554 0.653932i \(-0.773118\pi\)
−0.756554 + 0.653932i \(0.773118\pi\)
\(578\) 0 0
\(579\) −18.1984 −0.756300
\(580\) 0 0
\(581\) 14.3869 0.596870
\(582\) 0 0
\(583\) −30.1328 −1.24797
\(584\) 0 0
\(585\) 0.342436 0.0141580
\(586\) 0 0
\(587\) −23.4691 −0.968672 −0.484336 0.874882i \(-0.660939\pi\)
−0.484336 + 0.874882i \(0.660939\pi\)
\(588\) 0 0
\(589\) 8.25335 0.340073
\(590\) 0 0
\(591\) 16.7234 0.687908
\(592\) 0 0
\(593\) −33.6788 −1.38302 −0.691512 0.722365i \(-0.743055\pi\)
−0.691512 + 0.722365i \(0.743055\pi\)
\(594\) 0 0
\(595\) 4.05538 0.166255
\(596\) 0 0
\(597\) 10.1903 0.417063
\(598\) 0 0
\(599\) −11.3536 −0.463895 −0.231947 0.972728i \(-0.574510\pi\)
−0.231947 + 0.972728i \(0.574510\pi\)
\(600\) 0 0
\(601\) 27.1506 1.10750 0.553748 0.832685i \(-0.313197\pi\)
0.553748 + 0.832685i \(0.313197\pi\)
\(602\) 0 0
\(603\) 4.73233 0.192716
\(604\) 0 0
\(605\) 0.245115 0.00996533
\(606\) 0 0
\(607\) −6.91947 −0.280853 −0.140426 0.990091i \(-0.544847\pi\)
−0.140426 + 0.990091i \(0.544847\pi\)
\(608\) 0 0
\(609\) 14.6496 0.593632
\(610\) 0 0
\(611\) 0.314941 0.0127411
\(612\) 0 0
\(613\) −19.3458 −0.781369 −0.390684 0.920525i \(-0.627762\pi\)
−0.390684 + 0.920525i \(0.627762\pi\)
\(614\) 0 0
\(615\) −0.131709 −0.00531101
\(616\) 0 0
\(617\) 33.2507 1.33862 0.669312 0.742981i \(-0.266589\pi\)
0.669312 + 0.742981i \(0.266589\pi\)
\(618\) 0 0
\(619\) −47.1497 −1.89511 −0.947553 0.319598i \(-0.896452\pi\)
−0.947553 + 0.319598i \(0.896452\pi\)
\(620\) 0 0
\(621\) −40.2042 −1.61334
\(622\) 0 0
\(623\) −26.1855 −1.04910
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 8.13104 0.324722
\(628\) 0 0
\(629\) 7.85385 0.313153
\(630\) 0 0
\(631\) 2.61682 0.104174 0.0520871 0.998643i \(-0.483413\pi\)
0.0520871 + 0.998643i \(0.483413\pi\)
\(632\) 0 0
\(633\) 12.3093 0.489253
\(634\) 0 0
\(635\) 13.1165 0.520512
\(636\) 0 0
\(637\) 0.207288 0.00821304
\(638\) 0 0
\(639\) −8.62046 −0.341020
\(640\) 0 0
\(641\) −39.1341 −1.54571 −0.772853 0.634586i \(-0.781171\pi\)
−0.772853 + 0.634586i \(0.781171\pi\)
\(642\) 0 0
\(643\) 40.9147 1.61352 0.806759 0.590881i \(-0.201220\pi\)
0.806759 + 0.590881i \(0.201220\pi\)
\(644\) 0 0
\(645\) 11.9724 0.471414
\(646\) 0 0
\(647\) −11.6779 −0.459104 −0.229552 0.973296i \(-0.573726\pi\)
−0.229552 + 0.973296i \(0.573726\pi\)
\(648\) 0 0
\(649\) −14.5932 −0.572835
\(650\) 0 0
\(651\) 10.6262 0.416474
\(652\) 0 0
\(653\) 19.2020 0.751434 0.375717 0.926735i \(-0.377397\pi\)
0.375717 + 0.926735i \(0.377397\pi\)
\(654\) 0 0
\(655\) −9.93206 −0.388078
\(656\) 0 0
\(657\) 6.07392 0.236966
\(658\) 0 0
\(659\) −34.7455 −1.35349 −0.676747 0.736216i \(-0.736611\pi\)
−0.676747 + 0.736216i \(0.736611\pi\)
\(660\) 0 0
\(661\) 44.0490 1.71331 0.856654 0.515892i \(-0.172539\pi\)
0.856654 + 0.515892i \(0.172539\pi\)
\(662\) 0 0
\(663\) 0.373842 0.0145188
\(664\) 0 0
\(665\) −5.23352 −0.202947
\(666\) 0 0
\(667\) 39.9620 1.54733
\(668\) 0 0
\(669\) 17.8855 0.691494
\(670\) 0 0
\(671\) −17.1153 −0.660729
\(672\) 0 0
\(673\) 11.1127 0.428364 0.214182 0.976794i \(-0.431291\pi\)
0.214182 + 0.976794i \(0.431291\pi\)
\(674\) 0 0
\(675\) 5.33907 0.205501
\(676\) 0 0
\(677\) 29.1378 1.11986 0.559928 0.828541i \(-0.310829\pi\)
0.559928 + 0.828541i \(0.310829\pi\)
\(678\) 0 0
\(679\) −20.7861 −0.797697
\(680\) 0 0
\(681\) 24.5156 0.939438
\(682\) 0 0
\(683\) −31.6326 −1.21039 −0.605194 0.796078i \(-0.706905\pi\)
−0.605194 + 0.796078i \(0.706905\pi\)
\(684\) 0 0
\(685\) 5.99158 0.228926
\(686\) 0 0
\(687\) 9.93592 0.379079
\(688\) 0 0
\(689\) 1.78790 0.0681136
\(690\) 0 0
\(691\) −19.4846 −0.741230 −0.370615 0.928787i \(-0.620853\pi\)
−0.370615 + 0.928787i \(0.620853\pi\)
\(692\) 0 0
\(693\) −14.0874 −0.535137
\(694\) 0 0
\(695\) 19.3817 0.735189
\(696\) 0 0
\(697\) 0.193492 0.00732902
\(698\) 0 0
\(699\) −15.7845 −0.597026
\(700\) 0 0
\(701\) −20.1850 −0.762376 −0.381188 0.924497i \(-0.624485\pi\)
−0.381188 + 0.924497i \(0.624485\pi\)
\(702\) 0 0
\(703\) −10.1355 −0.382267
\(704\) 0 0
\(705\) 1.79007 0.0674178
\(706\) 0 0
\(707\) 27.1467 1.02096
\(708\) 0 0
\(709\) 16.7330 0.628420 0.314210 0.949353i \(-0.398260\pi\)
0.314210 + 0.949353i \(0.398260\pi\)
\(710\) 0 0
\(711\) −29.5502 −1.10822
\(712\) 0 0
\(713\) 28.9867 1.08556
\(714\) 0 0
\(715\) −0.667219 −0.0249526
\(716\) 0 0
\(717\) 19.8865 0.742676
\(718\) 0 0
\(719\) 14.4716 0.539699 0.269850 0.962902i \(-0.413026\pi\)
0.269850 + 0.962902i \(0.413026\pi\)
\(720\) 0 0
\(721\) −24.7157 −0.920460
\(722\) 0 0
\(723\) 10.3285 0.384120
\(724\) 0 0
\(725\) −5.30691 −0.197094
\(726\) 0 0
\(727\) 27.9699 1.03735 0.518673 0.854973i \(-0.326426\pi\)
0.518673 + 0.854973i \(0.326426\pi\)
\(728\) 0 0
\(729\) 19.6197 0.726654
\(730\) 0 0
\(731\) −17.5885 −0.650535
\(732\) 0 0
\(733\) 19.0631 0.704110 0.352055 0.935979i \(-0.385483\pi\)
0.352055 + 0.935979i \(0.385483\pi\)
\(734\) 0 0
\(735\) 1.17819 0.0434581
\(736\) 0 0
\(737\) −9.22071 −0.339649
\(738\) 0 0
\(739\) −43.3709 −1.59542 −0.797712 0.603039i \(-0.793956\pi\)
−0.797712 + 0.603039i \(0.793956\pi\)
\(740\) 0 0
\(741\) −0.482448 −0.0177232
\(742\) 0 0
\(743\) 26.5437 0.973795 0.486897 0.873459i \(-0.338129\pi\)
0.486897 + 0.873459i \(0.338129\pi\)
\(744\) 0 0
\(745\) −9.41614 −0.344981
\(746\) 0 0
\(747\) −10.1439 −0.371144
\(748\) 0 0
\(749\) −32.9392 −1.20357
\(750\) 0 0
\(751\) 21.3480 0.778998 0.389499 0.921027i \(-0.372648\pi\)
0.389499 + 0.921027i \(0.372648\pi\)
\(752\) 0 0
\(753\) −16.1467 −0.588420
\(754\) 0 0
\(755\) −1.00000 −0.0363937
\(756\) 0 0
\(757\) −10.5792 −0.384508 −0.192254 0.981345i \(-0.561580\pi\)
−0.192254 + 0.981345i \(0.561580\pi\)
\(758\) 0 0
\(759\) 28.5571 1.03656
\(760\) 0 0
\(761\) 17.2481 0.625242 0.312621 0.949878i \(-0.398793\pi\)
0.312621 + 0.949878i \(0.398793\pi\)
\(762\) 0 0
\(763\) −17.0062 −0.615666
\(764\) 0 0
\(765\) −2.85935 −0.103380
\(766\) 0 0
\(767\) 0.865877 0.0312650
\(768\) 0 0
\(769\) 47.3872 1.70883 0.854413 0.519595i \(-0.173917\pi\)
0.854413 + 0.519595i \(0.173917\pi\)
\(770\) 0 0
\(771\) 11.8094 0.425304
\(772\) 0 0
\(773\) 54.0333 1.94344 0.971722 0.236129i \(-0.0758787\pi\)
0.971722 + 0.236129i \(0.0758787\pi\)
\(774\) 0 0
\(775\) −3.84940 −0.138275
\(776\) 0 0
\(777\) −13.0495 −0.468146
\(778\) 0 0
\(779\) −0.249703 −0.00894655
\(780\) 0 0
\(781\) 16.7965 0.601027
\(782\) 0 0
\(783\) −28.3340 −1.01257
\(784\) 0 0
\(785\) 0.995474 0.0355300
\(786\) 0 0
\(787\) −0.834839 −0.0297588 −0.0148794 0.999889i \(-0.504736\pi\)
−0.0148794 + 0.999889i \(0.504736\pi\)
\(788\) 0 0
\(789\) −32.4308 −1.15457
\(790\) 0 0
\(791\) −11.6719 −0.415004
\(792\) 0 0
\(793\) 1.01552 0.0360623
\(794\) 0 0
\(795\) 10.1621 0.360413
\(796\) 0 0
\(797\) −54.8458 −1.94274 −0.971368 0.237578i \(-0.923646\pi\)
−0.971368 + 0.237578i \(0.923646\pi\)
\(798\) 0 0
\(799\) −2.62976 −0.0930344
\(800\) 0 0
\(801\) 18.4628 0.652350
\(802\) 0 0
\(803\) −11.8347 −0.417639
\(804\) 0 0
\(805\) −18.3807 −0.647835
\(806\) 0 0
\(807\) 22.4920 0.791756
\(808\) 0 0
\(809\) 3.74437 0.131645 0.0658225 0.997831i \(-0.479033\pi\)
0.0658225 + 0.997831i \(0.479033\pi\)
\(810\) 0 0
\(811\) 5.12257 0.179878 0.0899388 0.995947i \(-0.471333\pi\)
0.0899388 + 0.995947i \(0.471333\pi\)
\(812\) 0 0
\(813\) 7.87380 0.276146
\(814\) 0 0
\(815\) 19.2392 0.673918
\(816\) 0 0
\(817\) 22.6982 0.794110
\(818\) 0 0
\(819\) 0.835866 0.0292075
\(820\) 0 0
\(821\) 7.83602 0.273479 0.136739 0.990607i \(-0.456338\pi\)
0.136739 + 0.990607i \(0.456338\pi\)
\(822\) 0 0
\(823\) −11.5164 −0.401435 −0.200718 0.979649i \(-0.564327\pi\)
−0.200718 + 0.979649i \(0.564327\pi\)
\(824\) 0 0
\(825\) −3.79236 −0.132033
\(826\) 0 0
\(827\) 24.9604 0.867956 0.433978 0.900923i \(-0.357109\pi\)
0.433978 + 0.900923i \(0.357109\pi\)
\(828\) 0 0
\(829\) −31.4255 −1.09145 −0.545727 0.837963i \(-0.683746\pi\)
−0.545727 + 0.837963i \(0.683746\pi\)
\(830\) 0 0
\(831\) −21.8511 −0.758006
\(832\) 0 0
\(833\) −1.73086 −0.0599707
\(834\) 0 0
\(835\) 20.4959 0.709289
\(836\) 0 0
\(837\) −20.5522 −0.710389
\(838\) 0 0
\(839\) 29.9262 1.03317 0.516583 0.856237i \(-0.327204\pi\)
0.516583 + 0.856237i \(0.327204\pi\)
\(840\) 0 0
\(841\) −0.836731 −0.0288528
\(842\) 0 0
\(843\) 10.0046 0.344578
\(844\) 0 0
\(845\) −12.9604 −0.445852
\(846\) 0 0
\(847\) 0.598311 0.0205582
\(848\) 0 0
\(849\) −30.3045 −1.04005
\(850\) 0 0
\(851\) −35.5970 −1.22025
\(852\) 0 0
\(853\) 20.4132 0.698936 0.349468 0.936948i \(-0.386362\pi\)
0.349468 + 0.936948i \(0.386362\pi\)
\(854\) 0 0
\(855\) 3.69003 0.126196
\(856\) 0 0
\(857\) 5.03424 0.171966 0.0859832 0.996297i \(-0.472597\pi\)
0.0859832 + 0.996297i \(0.472597\pi\)
\(858\) 0 0
\(859\) 40.7649 1.39088 0.695441 0.718583i \(-0.255209\pi\)
0.695441 + 0.718583i \(0.255209\pi\)
\(860\) 0 0
\(861\) −0.321494 −0.0109565
\(862\) 0 0
\(863\) −8.83449 −0.300730 −0.150365 0.988631i \(-0.548045\pi\)
−0.150365 + 0.988631i \(0.548045\pi\)
\(864\) 0 0
\(865\) 8.69187 0.295533
\(866\) 0 0
\(867\) 16.1038 0.546915
\(868\) 0 0
\(869\) 57.5770 1.95317
\(870\) 0 0
\(871\) 0.547103 0.0185379
\(872\) 0 0
\(873\) 14.6558 0.496022
\(874\) 0 0
\(875\) 2.44094 0.0825189
\(876\) 0 0
\(877\) −48.0641 −1.62301 −0.811504 0.584347i \(-0.801351\pi\)
−0.811504 + 0.584347i \(0.801351\pi\)
\(878\) 0 0
\(879\) 22.8596 0.771034
\(880\) 0 0
\(881\) −40.7722 −1.37365 −0.686826 0.726822i \(-0.740996\pi\)
−0.686826 + 0.726822i \(0.740996\pi\)
\(882\) 0 0
\(883\) 24.6362 0.829075 0.414538 0.910032i \(-0.363943\pi\)
0.414538 + 0.910032i \(0.363943\pi\)
\(884\) 0 0
\(885\) 4.92149 0.165434
\(886\) 0 0
\(887\) 47.1737 1.58394 0.791968 0.610562i \(-0.209056\pi\)
0.791968 + 0.610562i \(0.209056\pi\)
\(888\) 0 0
\(889\) 32.0166 1.07380
\(890\) 0 0
\(891\) −2.93372 −0.0982834
\(892\) 0 0
\(893\) 3.39374 0.113567
\(894\) 0 0
\(895\) 15.6278 0.522380
\(896\) 0 0
\(897\) −1.69441 −0.0565748
\(898\) 0 0
\(899\) 20.4284 0.681326
\(900\) 0 0
\(901\) −14.9290 −0.497358
\(902\) 0 0
\(903\) 29.2240 0.972513
\(904\) 0 0
\(905\) −12.7628 −0.424249
\(906\) 0 0
\(907\) 48.3376 1.60502 0.802512 0.596636i \(-0.203496\pi\)
0.802512 + 0.596636i \(0.203496\pi\)
\(908\) 0 0
\(909\) −19.1405 −0.634849
\(910\) 0 0
\(911\) −29.5260 −0.978240 −0.489120 0.872217i \(-0.662682\pi\)
−0.489120 + 0.872217i \(0.662682\pi\)
\(912\) 0 0
\(913\) 19.7648 0.654119
\(914\) 0 0
\(915\) 5.77205 0.190818
\(916\) 0 0
\(917\) −24.2436 −0.800593
\(918\) 0 0
\(919\) 28.1114 0.927310 0.463655 0.886016i \(-0.346538\pi\)
0.463655 + 0.886016i \(0.346538\pi\)
\(920\) 0 0
\(921\) −31.1808 −1.02744
\(922\) 0 0
\(923\) −0.996608 −0.0328038
\(924\) 0 0
\(925\) 4.72724 0.155431
\(926\) 0 0
\(927\) 17.4264 0.572358
\(928\) 0 0
\(929\) −17.0190 −0.558377 −0.279188 0.960236i \(-0.590065\pi\)
−0.279188 + 0.960236i \(0.590065\pi\)
\(930\) 0 0
\(931\) 2.23370 0.0732064
\(932\) 0 0
\(933\) −25.8852 −0.847442
\(934\) 0 0
\(935\) 5.57130 0.182201
\(936\) 0 0
\(937\) 29.9572 0.978658 0.489329 0.872099i \(-0.337242\pi\)
0.489329 + 0.872099i \(0.337242\pi\)
\(938\) 0 0
\(939\) 21.4150 0.698851
\(940\) 0 0
\(941\) 18.0806 0.589411 0.294705 0.955588i \(-0.404778\pi\)
0.294705 + 0.955588i \(0.404778\pi\)
\(942\) 0 0
\(943\) −0.876987 −0.0285586
\(944\) 0 0
\(945\) 13.0324 0.423943
\(946\) 0 0
\(947\) 11.1862 0.363502 0.181751 0.983345i \(-0.441823\pi\)
0.181751 + 0.983345i \(0.441823\pi\)
\(948\) 0 0
\(949\) 0.702204 0.0227945
\(950\) 0 0
\(951\) 21.7755 0.706118
\(952\) 0 0
\(953\) 30.4732 0.987124 0.493562 0.869711i \(-0.335695\pi\)
0.493562 + 0.869711i \(0.335695\pi\)
\(954\) 0 0
\(955\) −11.5290 −0.373068
\(956\) 0 0
\(957\) 20.1257 0.650571
\(958\) 0 0
\(959\) 14.6251 0.472269
\(960\) 0 0
\(961\) −16.1821 −0.522003
\(962\) 0 0
\(963\) 23.2246 0.748404
\(964\) 0 0
\(965\) 16.0918 0.518015
\(966\) 0 0
\(967\) 22.0386 0.708714 0.354357 0.935110i \(-0.384700\pi\)
0.354357 + 0.935110i \(0.384700\pi\)
\(968\) 0 0
\(969\) 4.02846 0.129413
\(970\) 0 0
\(971\) −35.9016 −1.15214 −0.576068 0.817402i \(-0.695414\pi\)
−0.576068 + 0.817402i \(0.695414\pi\)
\(972\) 0 0
\(973\) 47.3095 1.51667
\(974\) 0 0
\(975\) 0.225016 0.00720629
\(976\) 0 0
\(977\) −11.8177 −0.378081 −0.189040 0.981969i \(-0.560538\pi\)
−0.189040 + 0.981969i \(0.560538\pi\)
\(978\) 0 0
\(979\) −35.9738 −1.14973
\(980\) 0 0
\(981\) 11.9907 0.382832
\(982\) 0 0
\(983\) −7.73874 −0.246827 −0.123414 0.992355i \(-0.539384\pi\)
−0.123414 + 0.992355i \(0.539384\pi\)
\(984\) 0 0
\(985\) −14.7876 −0.471171
\(986\) 0 0
\(987\) 4.36945 0.139081
\(988\) 0 0
\(989\) 79.7187 2.53491
\(990\) 0 0
\(991\) 11.7375 0.372854 0.186427 0.982469i \(-0.440309\pi\)
0.186427 + 0.982469i \(0.440309\pi\)
\(992\) 0 0
\(993\) 4.57027 0.145033
\(994\) 0 0
\(995\) −9.01076 −0.285660
\(996\) 0 0
\(997\) 47.3078 1.49825 0.749127 0.662426i \(-0.230473\pi\)
0.749127 + 0.662426i \(0.230473\pi\)
\(998\) 0 0
\(999\) 25.2391 0.798529
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 \(a_p\))