Properties

Label 6036.2.a.i.1.19
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 26
CM No

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(0\)
Dimension: \(26\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+2.09204 q^{5}\) \(-1.11995 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+2.09204 q^{5}\) \(-1.11995 q^{7}\) \(+1.00000 q^{9}\) \(-3.05871 q^{11}\) \(-6.80855 q^{13}\) \(-2.09204 q^{15}\) \(+6.88548 q^{17}\) \(-6.06064 q^{19}\) \(+1.11995 q^{21}\) \(-0.508351 q^{23}\) \(-0.623348 q^{25}\) \(-1.00000 q^{27}\) \(-4.52700 q^{29}\) \(+1.62475 q^{31}\) \(+3.05871 q^{33}\) \(-2.34300 q^{35}\) \(+4.52706 q^{37}\) \(+6.80855 q^{39}\) \(+3.40458 q^{41}\) \(-7.55017 q^{43}\) \(+2.09204 q^{45}\) \(+12.9657 q^{47}\) \(-5.74570 q^{49}\) \(-6.88548 q^{51}\) \(+5.82613 q^{53}\) \(-6.39895 q^{55}\) \(+6.06064 q^{57}\) \(+7.98329 q^{59}\) \(-11.2818 q^{61}\) \(-1.11995 q^{63}\) \(-14.2438 q^{65}\) \(+7.90749 q^{67}\) \(+0.508351 q^{69}\) \(+3.42324 q^{71}\) \(+14.4660 q^{73}\) \(+0.623348 q^{75}\) \(+3.42561 q^{77}\) \(-4.06975 q^{79}\) \(+1.00000 q^{81}\) \(-4.08357 q^{83}\) \(+14.4047 q^{85}\) \(+4.52700 q^{87}\) \(+17.2613 q^{89}\) \(+7.62527 q^{91}\) \(-1.62475 q^{93}\) \(-12.6791 q^{95}\) \(+14.8285 q^{97}\) \(-3.05871 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 2.09204 0.935591 0.467795 0.883837i \(-0.345048\pi\)
0.467795 + 0.883837i \(0.345048\pi\)
\(6\) 0 0
\(7\) −1.11995 −0.423303 −0.211652 0.977345i \(-0.567884\pi\)
−0.211652 + 0.977345i \(0.567884\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.05871 −0.922234 −0.461117 0.887339i \(-0.652551\pi\)
−0.461117 + 0.887339i \(0.652551\pi\)
\(12\) 0 0
\(13\) −6.80855 −1.88835 −0.944177 0.329440i \(-0.893140\pi\)
−0.944177 + 0.329440i \(0.893140\pi\)
\(14\) 0 0
\(15\) −2.09204 −0.540164
\(16\) 0 0
\(17\) 6.88548 1.66997 0.834987 0.550270i \(-0.185475\pi\)
0.834987 + 0.550270i \(0.185475\pi\)
\(18\) 0 0
\(19\) −6.06064 −1.39041 −0.695203 0.718813i \(-0.744686\pi\)
−0.695203 + 0.718813i \(0.744686\pi\)
\(20\) 0 0
\(21\) 1.11995 0.244394
\(22\) 0 0
\(23\) −0.508351 −0.105998 −0.0529992 0.998595i \(-0.516878\pi\)
−0.0529992 + 0.998595i \(0.516878\pi\)
\(24\) 0 0
\(25\) −0.623348 −0.124670
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −4.52700 −0.840643 −0.420322 0.907375i \(-0.638083\pi\)
−0.420322 + 0.907375i \(0.638083\pi\)
\(30\) 0 0
\(31\) 1.62475 0.291814 0.145907 0.989298i \(-0.453390\pi\)
0.145907 + 0.989298i \(0.453390\pi\)
\(32\) 0 0
\(33\) 3.05871 0.532452
\(34\) 0 0
\(35\) −2.34300 −0.396039
\(36\) 0 0
\(37\) 4.52706 0.744244 0.372122 0.928184i \(-0.378630\pi\)
0.372122 + 0.928184i \(0.378630\pi\)
\(38\) 0 0
\(39\) 6.80855 1.09024
\(40\) 0 0
\(41\) 3.40458 0.531707 0.265853 0.964014i \(-0.414346\pi\)
0.265853 + 0.964014i \(0.414346\pi\)
\(42\) 0 0
\(43\) −7.55017 −1.15139 −0.575695 0.817664i \(-0.695269\pi\)
−0.575695 + 0.817664i \(0.695269\pi\)
\(44\) 0 0
\(45\) 2.09204 0.311864
\(46\) 0 0
\(47\) 12.9657 1.89125 0.945624 0.325262i \(-0.105452\pi\)
0.945624 + 0.325262i \(0.105452\pi\)
\(48\) 0 0
\(49\) −5.74570 −0.820815
\(50\) 0 0
\(51\) −6.88548 −0.964159
\(52\) 0 0
\(53\) 5.82613 0.800281 0.400140 0.916454i \(-0.368961\pi\)
0.400140 + 0.916454i \(0.368961\pi\)
\(54\) 0 0
\(55\) −6.39895 −0.862834
\(56\) 0 0
\(57\) 6.06064 0.802752
\(58\) 0 0
\(59\) 7.98329 1.03934 0.519668 0.854368i \(-0.326056\pi\)
0.519668 + 0.854368i \(0.326056\pi\)
\(60\) 0 0
\(61\) −11.2818 −1.44449 −0.722244 0.691638i \(-0.756889\pi\)
−0.722244 + 0.691638i \(0.756889\pi\)
\(62\) 0 0
\(63\) −1.11995 −0.141101
\(64\) 0 0
\(65\) −14.2438 −1.76673
\(66\) 0 0
\(67\) 7.90749 0.966054 0.483027 0.875605i \(-0.339537\pi\)
0.483027 + 0.875605i \(0.339537\pi\)
\(68\) 0 0
\(69\) 0.508351 0.0611982
\(70\) 0 0
\(71\) 3.42324 0.406263 0.203132 0.979151i \(-0.434888\pi\)
0.203132 + 0.979151i \(0.434888\pi\)
\(72\) 0 0
\(73\) 14.4660 1.69311 0.846556 0.532299i \(-0.178672\pi\)
0.846556 + 0.532299i \(0.178672\pi\)
\(74\) 0 0
\(75\) 0.623348 0.0719780
\(76\) 0 0
\(77\) 3.42561 0.390385
\(78\) 0 0
\(79\) −4.06975 −0.457883 −0.228941 0.973440i \(-0.573526\pi\)
−0.228941 + 0.973440i \(0.573526\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −4.08357 −0.448230 −0.224115 0.974563i \(-0.571949\pi\)
−0.224115 + 0.974563i \(0.571949\pi\)
\(84\) 0 0
\(85\) 14.4047 1.56241
\(86\) 0 0
\(87\) 4.52700 0.485346
\(88\) 0 0
\(89\) 17.2613 1.82969 0.914845 0.403806i \(-0.132313\pi\)
0.914845 + 0.403806i \(0.132313\pi\)
\(90\) 0 0
\(91\) 7.62527 0.799346
\(92\) 0 0
\(93\) −1.62475 −0.168479
\(94\) 0 0
\(95\) −12.6791 −1.30085
\(96\) 0 0
\(97\) 14.8285 1.50561 0.752804 0.658244i \(-0.228701\pi\)
0.752804 + 0.658244i \(0.228701\pi\)
\(98\) 0 0
\(99\) −3.05871 −0.307411
\(100\) 0 0
\(101\) 15.0157 1.49412 0.747060 0.664757i \(-0.231465\pi\)
0.747060 + 0.664757i \(0.231465\pi\)
\(102\) 0 0
\(103\) −3.48792 −0.343675 −0.171838 0.985125i \(-0.554970\pi\)
−0.171838 + 0.985125i \(0.554970\pi\)
\(104\) 0 0
\(105\) 2.34300 0.228653
\(106\) 0 0
\(107\) −2.50472 −0.242140 −0.121070 0.992644i \(-0.538633\pi\)
−0.121070 + 0.992644i \(0.538633\pi\)
\(108\) 0 0
\(109\) 15.5936 1.49359 0.746796 0.665054i \(-0.231591\pi\)
0.746796 + 0.665054i \(0.231591\pi\)
\(110\) 0 0
\(111\) −4.52706 −0.429689
\(112\) 0 0
\(113\) 16.8534 1.58543 0.792716 0.609591i \(-0.208666\pi\)
0.792716 + 0.609591i \(0.208666\pi\)
\(114\) 0 0
\(115\) −1.06349 −0.0991712
\(116\) 0 0
\(117\) −6.80855 −0.629451
\(118\) 0 0
\(119\) −7.71142 −0.706905
\(120\) 0 0
\(121\) −1.64432 −0.149484
\(122\) 0 0
\(123\) −3.40458 −0.306981
\(124\) 0 0
\(125\) −11.7643 −1.05223
\(126\) 0 0
\(127\) 13.5676 1.20393 0.601964 0.798523i \(-0.294385\pi\)
0.601964 + 0.798523i \(0.294385\pi\)
\(128\) 0 0
\(129\) 7.55017 0.664756
\(130\) 0 0
\(131\) −15.4825 −1.35272 −0.676358 0.736573i \(-0.736443\pi\)
−0.676358 + 0.736573i \(0.736443\pi\)
\(132\) 0 0
\(133\) 6.78764 0.588563
\(134\) 0 0
\(135\) −2.09204 −0.180055
\(136\) 0 0
\(137\) −1.68605 −0.144049 −0.0720245 0.997403i \(-0.522946\pi\)
−0.0720245 + 0.997403i \(0.522946\pi\)
\(138\) 0 0
\(139\) −21.0299 −1.78374 −0.891868 0.452297i \(-0.850605\pi\)
−0.891868 + 0.452297i \(0.850605\pi\)
\(140\) 0 0
\(141\) −12.9657 −1.09191
\(142\) 0 0
\(143\) 20.8254 1.74150
\(144\) 0 0
\(145\) −9.47069 −0.786498
\(146\) 0 0
\(147\) 5.74570 0.473897
\(148\) 0 0
\(149\) 15.5986 1.27788 0.638942 0.769255i \(-0.279372\pi\)
0.638942 + 0.769255i \(0.279372\pi\)
\(150\) 0 0
\(151\) −12.9393 −1.05299 −0.526494 0.850179i \(-0.676494\pi\)
−0.526494 + 0.850179i \(0.676494\pi\)
\(152\) 0 0
\(153\) 6.88548 0.556658
\(154\) 0 0
\(155\) 3.39905 0.273018
\(156\) 0 0
\(157\) −21.1717 −1.68969 −0.844844 0.535012i \(-0.820307\pi\)
−0.844844 + 0.535012i \(0.820307\pi\)
\(158\) 0 0
\(159\) −5.82613 −0.462042
\(160\) 0 0
\(161\) 0.569330 0.0448695
\(162\) 0 0
\(163\) 3.09855 0.242697 0.121349 0.992610i \(-0.461278\pi\)
0.121349 + 0.992610i \(0.461278\pi\)
\(164\) 0 0
\(165\) 6.39895 0.498158
\(166\) 0 0
\(167\) −0.274953 −0.0212765 −0.0106383 0.999943i \(-0.503386\pi\)
−0.0106383 + 0.999943i \(0.503386\pi\)
\(168\) 0 0
\(169\) 33.3564 2.56588
\(170\) 0 0
\(171\) −6.06064 −0.463469
\(172\) 0 0
\(173\) −16.5216 −1.25612 −0.628058 0.778166i \(-0.716150\pi\)
−0.628058 + 0.778166i \(0.716150\pi\)
\(174\) 0 0
\(175\) 0.698122 0.0527730
\(176\) 0 0
\(177\) −7.98329 −0.600061
\(178\) 0 0
\(179\) 13.5841 1.01532 0.507662 0.861556i \(-0.330510\pi\)
0.507662 + 0.861556i \(0.330510\pi\)
\(180\) 0 0
\(181\) −3.00685 −0.223498 −0.111749 0.993736i \(-0.535645\pi\)
−0.111749 + 0.993736i \(0.535645\pi\)
\(182\) 0 0
\(183\) 11.2818 0.833976
\(184\) 0 0
\(185\) 9.47081 0.696308
\(186\) 0 0
\(187\) −21.0606 −1.54011
\(188\) 0 0
\(189\) 1.11995 0.0814647
\(190\) 0 0
\(191\) 6.40033 0.463111 0.231556 0.972822i \(-0.425618\pi\)
0.231556 + 0.972822i \(0.425618\pi\)
\(192\) 0 0
\(193\) −10.8903 −0.783899 −0.391949 0.919987i \(-0.628199\pi\)
−0.391949 + 0.919987i \(0.628199\pi\)
\(194\) 0 0
\(195\) 14.2438 1.02002
\(196\) 0 0
\(197\) 12.6911 0.904207 0.452103 0.891966i \(-0.350674\pi\)
0.452103 + 0.891966i \(0.350674\pi\)
\(198\) 0 0
\(199\) 18.7361 1.32817 0.664085 0.747657i \(-0.268821\pi\)
0.664085 + 0.747657i \(0.268821\pi\)
\(200\) 0 0
\(201\) −7.90749 −0.557752
\(202\) 0 0
\(203\) 5.07004 0.355847
\(204\) 0 0
\(205\) 7.12254 0.497460
\(206\) 0 0
\(207\) −0.508351 −0.0353328
\(208\) 0 0
\(209\) 18.5377 1.28228
\(210\) 0 0
\(211\) −9.31292 −0.641128 −0.320564 0.947227i \(-0.603872\pi\)
−0.320564 + 0.947227i \(0.603872\pi\)
\(212\) 0 0
\(213\) −3.42324 −0.234556
\(214\) 0 0
\(215\) −15.7953 −1.07723
\(216\) 0 0
\(217\) −1.81965 −0.123526
\(218\) 0 0
\(219\) −14.4660 −0.977519
\(220\) 0 0
\(221\) −46.8801 −3.15350
\(222\) 0 0
\(223\) 3.37856 0.226245 0.113123 0.993581i \(-0.463915\pi\)
0.113123 + 0.993581i \(0.463915\pi\)
\(224\) 0 0
\(225\) −0.623348 −0.0415565
\(226\) 0 0
\(227\) 14.9597 0.992912 0.496456 0.868062i \(-0.334634\pi\)
0.496456 + 0.868062i \(0.334634\pi\)
\(228\) 0 0
\(229\) 18.6901 1.23508 0.617538 0.786541i \(-0.288130\pi\)
0.617538 + 0.786541i \(0.288130\pi\)
\(230\) 0 0
\(231\) −3.42561 −0.225389
\(232\) 0 0
\(233\) 2.10866 0.138143 0.0690713 0.997612i \(-0.477996\pi\)
0.0690713 + 0.997612i \(0.477996\pi\)
\(234\) 0 0
\(235\) 27.1249 1.76943
\(236\) 0 0
\(237\) 4.06975 0.264359
\(238\) 0 0
\(239\) −7.09270 −0.458789 −0.229394 0.973334i \(-0.573675\pi\)
−0.229394 + 0.973334i \(0.573675\pi\)
\(240\) 0 0
\(241\) 6.11396 0.393835 0.196917 0.980420i \(-0.436907\pi\)
0.196917 + 0.980420i \(0.436907\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −12.0203 −0.767947
\(246\) 0 0
\(247\) 41.2642 2.62558
\(248\) 0 0
\(249\) 4.08357 0.258786
\(250\) 0 0
\(251\) 2.80434 0.177008 0.0885040 0.996076i \(-0.471791\pi\)
0.0885040 + 0.996076i \(0.471791\pi\)
\(252\) 0 0
\(253\) 1.55489 0.0977554
\(254\) 0 0
\(255\) −14.4047 −0.902059
\(256\) 0 0
\(257\) −25.2183 −1.57308 −0.786538 0.617542i \(-0.788129\pi\)
−0.786538 + 0.617542i \(0.788129\pi\)
\(258\) 0 0
\(259\) −5.07010 −0.315041
\(260\) 0 0
\(261\) −4.52700 −0.280214
\(262\) 0 0
\(263\) 13.6148 0.839526 0.419763 0.907634i \(-0.362113\pi\)
0.419763 + 0.907634i \(0.362113\pi\)
\(264\) 0 0
\(265\) 12.1885 0.748735
\(266\) 0 0
\(267\) −17.2613 −1.05637
\(268\) 0 0
\(269\) −7.70251 −0.469631 −0.234815 0.972040i \(-0.575449\pi\)
−0.234815 + 0.972040i \(0.575449\pi\)
\(270\) 0 0
\(271\) −25.8369 −1.56948 −0.784741 0.619824i \(-0.787204\pi\)
−0.784741 + 0.619824i \(0.787204\pi\)
\(272\) 0 0
\(273\) −7.62527 −0.461502
\(274\) 0 0
\(275\) 1.90664 0.114975
\(276\) 0 0
\(277\) 5.94164 0.356999 0.178499 0.983940i \(-0.442876\pi\)
0.178499 + 0.983940i \(0.442876\pi\)
\(278\) 0 0
\(279\) 1.62475 0.0972712
\(280\) 0 0
\(281\) −5.87340 −0.350378 −0.175189 0.984535i \(-0.556054\pi\)
−0.175189 + 0.984535i \(0.556054\pi\)
\(282\) 0 0
\(283\) −22.8593 −1.35884 −0.679422 0.733747i \(-0.737770\pi\)
−0.679422 + 0.733747i \(0.737770\pi\)
\(284\) 0 0
\(285\) 12.6791 0.751047
\(286\) 0 0
\(287\) −3.81298 −0.225073
\(288\) 0 0
\(289\) 30.4098 1.78881
\(290\) 0 0
\(291\) −14.8285 −0.869264
\(292\) 0 0
\(293\) 10.1271 0.591630 0.295815 0.955245i \(-0.404409\pi\)
0.295815 + 0.955245i \(0.404409\pi\)
\(294\) 0 0
\(295\) 16.7014 0.972394
\(296\) 0 0
\(297\) 3.05871 0.177484
\(298\) 0 0
\(299\) 3.46113 0.200162
\(300\) 0 0
\(301\) 8.45585 0.487387
\(302\) 0 0
\(303\) −15.0157 −0.862630
\(304\) 0 0
\(305\) −23.6021 −1.35145
\(306\) 0 0
\(307\) −9.08360 −0.518429 −0.259214 0.965820i \(-0.583464\pi\)
−0.259214 + 0.965820i \(0.583464\pi\)
\(308\) 0 0
\(309\) 3.48792 0.198421
\(310\) 0 0
\(311\) 28.1435 1.59587 0.797937 0.602741i \(-0.205925\pi\)
0.797937 + 0.602741i \(0.205925\pi\)
\(312\) 0 0
\(313\) 2.15160 0.121616 0.0608078 0.998149i \(-0.480632\pi\)
0.0608078 + 0.998149i \(0.480632\pi\)
\(314\) 0 0
\(315\) −2.34300 −0.132013
\(316\) 0 0
\(317\) −17.9505 −1.00820 −0.504100 0.863645i \(-0.668176\pi\)
−0.504100 + 0.863645i \(0.668176\pi\)
\(318\) 0 0
\(319\) 13.8468 0.775270
\(320\) 0 0
\(321\) 2.50472 0.139800
\(322\) 0 0
\(323\) −41.7304 −2.32194
\(324\) 0 0
\(325\) 4.24410 0.235420
\(326\) 0 0
\(327\) −15.5936 −0.862325
\(328\) 0 0
\(329\) −14.5210 −0.800571
\(330\) 0 0
\(331\) −0.828334 −0.0455293 −0.0227647 0.999741i \(-0.507247\pi\)
−0.0227647 + 0.999741i \(0.507247\pi\)
\(332\) 0 0
\(333\) 4.52706 0.248081
\(334\) 0 0
\(335\) 16.5428 0.903831
\(336\) 0 0
\(337\) 15.9706 0.869974 0.434987 0.900437i \(-0.356753\pi\)
0.434987 + 0.900437i \(0.356753\pi\)
\(338\) 0 0
\(339\) −16.8534 −0.915350
\(340\) 0 0
\(341\) −4.96963 −0.269121
\(342\) 0 0
\(343\) 14.2746 0.770756
\(344\) 0 0
\(345\) 1.06349 0.0572565
\(346\) 0 0
\(347\) −2.09974 −0.112720 −0.0563599 0.998411i \(-0.517949\pi\)
−0.0563599 + 0.998411i \(0.517949\pi\)
\(348\) 0 0
\(349\) 12.0394 0.644452 0.322226 0.946663i \(-0.395569\pi\)
0.322226 + 0.946663i \(0.395569\pi\)
\(350\) 0 0
\(351\) 6.80855 0.363414
\(352\) 0 0
\(353\) −4.61169 −0.245456 −0.122728 0.992440i \(-0.539164\pi\)
−0.122728 + 0.992440i \(0.539164\pi\)
\(354\) 0 0
\(355\) 7.16157 0.380096
\(356\) 0 0
\(357\) 7.71142 0.408132
\(358\) 0 0
\(359\) −5.45226 −0.287759 −0.143880 0.989595i \(-0.545958\pi\)
−0.143880 + 0.989595i \(0.545958\pi\)
\(360\) 0 0
\(361\) 17.7314 0.933231
\(362\) 0 0
\(363\) 1.64432 0.0863044
\(364\) 0 0
\(365\) 30.2634 1.58406
\(366\) 0 0
\(367\) 16.4642 0.859422 0.429711 0.902967i \(-0.358615\pi\)
0.429711 + 0.902967i \(0.358615\pi\)
\(368\) 0 0
\(369\) 3.40458 0.177236
\(370\) 0 0
\(371\) −6.52500 −0.338761
\(372\) 0 0
\(373\) −14.1213 −0.731171 −0.365586 0.930778i \(-0.619131\pi\)
−0.365586 + 0.930778i \(0.619131\pi\)
\(374\) 0 0
\(375\) 11.7643 0.607506
\(376\) 0 0
\(377\) 30.8223 1.58743
\(378\) 0 0
\(379\) −1.80636 −0.0927863 −0.0463932 0.998923i \(-0.514773\pi\)
−0.0463932 + 0.998923i \(0.514773\pi\)
\(380\) 0 0
\(381\) −13.5676 −0.695088
\(382\) 0 0
\(383\) −36.3146 −1.85559 −0.927794 0.373092i \(-0.878298\pi\)
−0.927794 + 0.373092i \(0.878298\pi\)
\(384\) 0 0
\(385\) 7.16653 0.365240
\(386\) 0 0
\(387\) −7.55017 −0.383797
\(388\) 0 0
\(389\) −16.2430 −0.823553 −0.411776 0.911285i \(-0.635091\pi\)
−0.411776 + 0.911285i \(0.635091\pi\)
\(390\) 0 0
\(391\) −3.50024 −0.177015
\(392\) 0 0
\(393\) 15.4825 0.780991
\(394\) 0 0
\(395\) −8.51410 −0.428391
\(396\) 0 0
\(397\) 33.4869 1.68066 0.840329 0.542077i \(-0.182362\pi\)
0.840329 + 0.542077i \(0.182362\pi\)
\(398\) 0 0
\(399\) −6.78764 −0.339807
\(400\) 0 0
\(401\) 17.4558 0.871703 0.435852 0.900019i \(-0.356447\pi\)
0.435852 + 0.900019i \(0.356447\pi\)
\(402\) 0 0
\(403\) −11.0622 −0.551047
\(404\) 0 0
\(405\) 2.09204 0.103955
\(406\) 0 0
\(407\) −13.8469 −0.686367
\(408\) 0 0
\(409\) 1.44472 0.0714369 0.0357185 0.999362i \(-0.488628\pi\)
0.0357185 + 0.999362i \(0.488628\pi\)
\(410\) 0 0
\(411\) 1.68605 0.0831667
\(412\) 0 0
\(413\) −8.94093 −0.439954
\(414\) 0 0
\(415\) −8.54302 −0.419360
\(416\) 0 0
\(417\) 21.0299 1.02984
\(418\) 0 0
\(419\) 25.1475 1.22854 0.614268 0.789097i \(-0.289451\pi\)
0.614268 + 0.789097i \(0.289451\pi\)
\(420\) 0 0
\(421\) 38.5780 1.88017 0.940087 0.340934i \(-0.110743\pi\)
0.940087 + 0.340934i \(0.110743\pi\)
\(422\) 0 0
\(423\) 12.9657 0.630416
\(424\) 0 0
\(425\) −4.29205 −0.208195
\(426\) 0 0
\(427\) 12.6351 0.611456
\(428\) 0 0
\(429\) −20.8254 −1.00546
\(430\) 0 0
\(431\) 34.3908 1.65655 0.828273 0.560324i \(-0.189324\pi\)
0.828273 + 0.560324i \(0.189324\pi\)
\(432\) 0 0
\(433\) 1.64164 0.0788923 0.0394461 0.999222i \(-0.487441\pi\)
0.0394461 + 0.999222i \(0.487441\pi\)
\(434\) 0 0
\(435\) 9.47069 0.454085
\(436\) 0 0
\(437\) 3.08093 0.147381
\(438\) 0 0
\(439\) −9.97093 −0.475887 −0.237943 0.971279i \(-0.576473\pi\)
−0.237943 + 0.971279i \(0.576473\pi\)
\(440\) 0 0
\(441\) −5.74570 −0.273605
\(442\) 0 0
\(443\) 16.2845 0.773700 0.386850 0.922143i \(-0.373563\pi\)
0.386850 + 0.922143i \(0.373563\pi\)
\(444\) 0 0
\(445\) 36.1113 1.71184
\(446\) 0 0
\(447\) −15.5986 −0.737787
\(448\) 0 0
\(449\) 0.982830 0.0463826 0.0231913 0.999731i \(-0.492617\pi\)
0.0231913 + 0.999731i \(0.492617\pi\)
\(450\) 0 0
\(451\) −10.4136 −0.490358
\(452\) 0 0
\(453\) 12.9393 0.607943
\(454\) 0 0
\(455\) 15.9524 0.747861
\(456\) 0 0
\(457\) −4.74202 −0.221823 −0.110911 0.993830i \(-0.535377\pi\)
−0.110911 + 0.993830i \(0.535377\pi\)
\(458\) 0 0
\(459\) −6.88548 −0.321386
\(460\) 0 0
\(461\) 11.4949 0.535369 0.267685 0.963507i \(-0.413742\pi\)
0.267685 + 0.963507i \(0.413742\pi\)
\(462\) 0 0
\(463\) 20.8843 0.970575 0.485287 0.874355i \(-0.338715\pi\)
0.485287 + 0.874355i \(0.338715\pi\)
\(464\) 0 0
\(465\) −3.39905 −0.157627
\(466\) 0 0
\(467\) 0.744771 0.0344639 0.0172320 0.999852i \(-0.494515\pi\)
0.0172320 + 0.999852i \(0.494515\pi\)
\(468\) 0 0
\(469\) −8.85603 −0.408934
\(470\) 0 0
\(471\) 21.1717 0.975542
\(472\) 0 0
\(473\) 23.0938 1.06185
\(474\) 0 0
\(475\) 3.77789 0.173341
\(476\) 0 0
\(477\) 5.82613 0.266760
\(478\) 0 0
\(479\) 8.84492 0.404135 0.202067 0.979372i \(-0.435234\pi\)
0.202067 + 0.979372i \(0.435234\pi\)
\(480\) 0 0
\(481\) −30.8227 −1.40540
\(482\) 0 0
\(483\) −0.569330 −0.0259054
\(484\) 0 0
\(485\) 31.0219 1.40863
\(486\) 0 0
\(487\) −25.2217 −1.14290 −0.571452 0.820635i \(-0.693620\pi\)
−0.571452 + 0.820635i \(0.693620\pi\)
\(488\) 0 0
\(489\) −3.09855 −0.140121
\(490\) 0 0
\(491\) 19.7997 0.893546 0.446773 0.894647i \(-0.352573\pi\)
0.446773 + 0.894647i \(0.352573\pi\)
\(492\) 0 0
\(493\) −31.1706 −1.40385
\(494\) 0 0
\(495\) −6.39895 −0.287611
\(496\) 0 0
\(497\) −3.83387 −0.171973
\(498\) 0 0
\(499\) 19.6848 0.881212 0.440606 0.897701i \(-0.354764\pi\)
0.440606 + 0.897701i \(0.354764\pi\)
\(500\) 0 0
\(501\) 0.274953 0.0122840
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 31.4136 1.39788
\(506\) 0 0
\(507\) −33.3564 −1.48141
\(508\) 0 0
\(509\) 16.0171 0.709947 0.354974 0.934876i \(-0.384490\pi\)
0.354974 + 0.934876i \(0.384490\pi\)
\(510\) 0 0
\(511\) −16.2012 −0.716700
\(512\) 0 0
\(513\) 6.06064 0.267584
\(514\) 0 0
\(515\) −7.29689 −0.321540
\(516\) 0 0
\(517\) −39.6584 −1.74417
\(518\) 0 0
\(519\) 16.5216 0.725219
\(520\) 0 0
\(521\) −22.9713 −1.00639 −0.503195 0.864173i \(-0.667842\pi\)
−0.503195 + 0.864173i \(0.667842\pi\)
\(522\) 0 0
\(523\) 40.4831 1.77020 0.885101 0.465399i \(-0.154089\pi\)
0.885101 + 0.465399i \(0.154089\pi\)
\(524\) 0 0
\(525\) −0.698122 −0.0304685
\(526\) 0 0
\(527\) 11.1872 0.487321
\(528\) 0 0
\(529\) −22.7416 −0.988764
\(530\) 0 0
\(531\) 7.98329 0.346445
\(532\) 0 0
\(533\) −23.1803 −1.00405
\(534\) 0 0
\(535\) −5.23998 −0.226544
\(536\) 0 0
\(537\) −13.5841 −0.586198
\(538\) 0 0
\(539\) 17.5744 0.756983
\(540\) 0 0
\(541\) 32.0601 1.37837 0.689186 0.724584i \(-0.257968\pi\)
0.689186 + 0.724584i \(0.257968\pi\)
\(542\) 0 0
\(543\) 3.00685 0.129036
\(544\) 0 0
\(545\) 32.6224 1.39739
\(546\) 0 0
\(547\) −6.90685 −0.295316 −0.147658 0.989039i \(-0.547173\pi\)
−0.147658 + 0.989039i \(0.547173\pi\)
\(548\) 0 0
\(549\) −11.2818 −0.481496
\(550\) 0 0
\(551\) 27.4365 1.16884
\(552\) 0 0
\(553\) 4.55794 0.193823
\(554\) 0 0
\(555\) −9.47081 −0.402013
\(556\) 0 0
\(557\) 34.8776 1.47781 0.738906 0.673808i \(-0.235343\pi\)
0.738906 + 0.673808i \(0.235343\pi\)
\(558\) 0 0
\(559\) 51.4058 2.17423
\(560\) 0 0
\(561\) 21.0606 0.889181
\(562\) 0 0
\(563\) 41.8681 1.76453 0.882264 0.470755i \(-0.156018\pi\)
0.882264 + 0.470755i \(0.156018\pi\)
\(564\) 0 0
\(565\) 35.2580 1.48332
\(566\) 0 0
\(567\) −1.11995 −0.0470337
\(568\) 0 0
\(569\) 5.52575 0.231651 0.115826 0.993270i \(-0.463049\pi\)
0.115826 + 0.993270i \(0.463049\pi\)
\(570\) 0 0
\(571\) −22.8981 −0.958256 −0.479128 0.877745i \(-0.659047\pi\)
−0.479128 + 0.877745i \(0.659047\pi\)
\(572\) 0 0
\(573\) −6.40033 −0.267378
\(574\) 0 0
\(575\) 0.316879 0.0132148
\(576\) 0 0
\(577\) −10.1018 −0.420543 −0.210272 0.977643i \(-0.567435\pi\)
−0.210272 + 0.977643i \(0.567435\pi\)
\(578\) 0 0
\(579\) 10.8903 0.452584
\(580\) 0 0
\(581\) 4.57342 0.189737
\(582\) 0 0
\(583\) −17.8204 −0.738046
\(584\) 0 0
\(585\) −14.2438 −0.588909
\(586\) 0 0
\(587\) −4.81788 −0.198855 −0.0994275 0.995045i \(-0.531701\pi\)
−0.0994275 + 0.995045i \(0.531701\pi\)
\(588\) 0 0
\(589\) −9.84702 −0.405740
\(590\) 0 0
\(591\) −12.6911 −0.522044
\(592\) 0 0
\(593\) −23.7096 −0.973636 −0.486818 0.873504i \(-0.661842\pi\)
−0.486818 + 0.873504i \(0.661842\pi\)
\(594\) 0 0
\(595\) −16.1326 −0.661374
\(596\) 0 0
\(597\) −18.7361 −0.766819
\(598\) 0 0
\(599\) 10.3607 0.423325 0.211662 0.977343i \(-0.432112\pi\)
0.211662 + 0.977343i \(0.432112\pi\)
\(600\) 0 0
\(601\) −34.9778 −1.42677 −0.713387 0.700770i \(-0.752840\pi\)
−0.713387 + 0.700770i \(0.752840\pi\)
\(602\) 0 0
\(603\) 7.90749 0.322018
\(604\) 0 0
\(605\) −3.43999 −0.139856
\(606\) 0 0
\(607\) −12.7927 −0.519241 −0.259620 0.965711i \(-0.583597\pi\)
−0.259620 + 0.965711i \(0.583597\pi\)
\(608\) 0 0
\(609\) −5.07004 −0.205448
\(610\) 0 0
\(611\) −88.2780 −3.57134
\(612\) 0 0
\(613\) 18.4144 0.743749 0.371874 0.928283i \(-0.378715\pi\)
0.371874 + 0.928283i \(0.378715\pi\)
\(614\) 0 0
\(615\) −7.12254 −0.287209
\(616\) 0 0
\(617\) −2.35116 −0.0946540 −0.0473270 0.998879i \(-0.515070\pi\)
−0.0473270 + 0.998879i \(0.515070\pi\)
\(618\) 0 0
\(619\) 28.4460 1.14334 0.571671 0.820483i \(-0.306296\pi\)
0.571671 + 0.820483i \(0.306296\pi\)
\(620\) 0 0
\(621\) 0.508351 0.0203994
\(622\) 0 0
\(623\) −19.3318 −0.774513
\(624\) 0 0
\(625\) −21.4947 −0.859788
\(626\) 0 0
\(627\) −18.5377 −0.740325
\(628\) 0 0
\(629\) 31.1709 1.24287
\(630\) 0 0
\(631\) 12.6592 0.503955 0.251977 0.967733i \(-0.418919\pi\)
0.251977 + 0.967733i \(0.418919\pi\)
\(632\) 0 0
\(633\) 9.31292 0.370155
\(634\) 0 0
\(635\) 28.3840 1.12638
\(636\) 0 0
\(637\) 39.1199 1.54999
\(638\) 0 0
\(639\) 3.42324 0.135421
\(640\) 0 0
\(641\) 14.8200 0.585353 0.292677 0.956211i \(-0.405454\pi\)
0.292677 + 0.956211i \(0.405454\pi\)
\(642\) 0 0
\(643\) −43.9859 −1.73463 −0.867316 0.497757i \(-0.834157\pi\)
−0.867316 + 0.497757i \(0.834157\pi\)
\(644\) 0 0
\(645\) 15.7953 0.621939
\(646\) 0 0
\(647\) −39.1606 −1.53956 −0.769781 0.638308i \(-0.779635\pi\)
−0.769781 + 0.638308i \(0.779635\pi\)
\(648\) 0 0
\(649\) −24.4185 −0.958512
\(650\) 0 0
\(651\) 1.81965 0.0713175
\(652\) 0 0
\(653\) 2.24871 0.0879989 0.0439994 0.999032i \(-0.485990\pi\)
0.0439994 + 0.999032i \(0.485990\pi\)
\(654\) 0 0
\(655\) −32.3902 −1.26559
\(656\) 0 0
\(657\) 14.4660 0.564371
\(658\) 0 0
\(659\) −3.93412 −0.153251 −0.0766257 0.997060i \(-0.524415\pi\)
−0.0766257 + 0.997060i \(0.524415\pi\)
\(660\) 0 0
\(661\) 20.4901 0.796971 0.398486 0.917175i \(-0.369536\pi\)
0.398486 + 0.917175i \(0.369536\pi\)
\(662\) 0 0
\(663\) 46.8801 1.82067
\(664\) 0 0
\(665\) 14.2001 0.550655
\(666\) 0 0
\(667\) 2.30130 0.0891069
\(668\) 0 0
\(669\) −3.37856 −0.130623
\(670\) 0 0
\(671\) 34.5078 1.33216
\(672\) 0 0
\(673\) −31.4063 −1.21062 −0.605312 0.795988i \(-0.706952\pi\)
−0.605312 + 0.795988i \(0.706952\pi\)
\(674\) 0 0
\(675\) 0.623348 0.0239927
\(676\) 0 0
\(677\) 30.0000 1.15299 0.576496 0.817100i \(-0.304420\pi\)
0.576496 + 0.817100i \(0.304420\pi\)
\(678\) 0 0
\(679\) −16.6073 −0.637329
\(680\) 0 0
\(681\) −14.9597 −0.573258
\(682\) 0 0
\(683\) −15.7273 −0.601790 −0.300895 0.953657i \(-0.597285\pi\)
−0.300895 + 0.953657i \(0.597285\pi\)
\(684\) 0 0
\(685\) −3.52729 −0.134771
\(686\) 0 0
\(687\) −18.6901 −0.713071
\(688\) 0 0
\(689\) −39.6675 −1.51121
\(690\) 0 0
\(691\) 28.4104 1.08078 0.540392 0.841414i \(-0.318276\pi\)
0.540392 + 0.841414i \(0.318276\pi\)
\(692\) 0 0
\(693\) 3.42561 0.130128
\(694\) 0 0
\(695\) −43.9956 −1.66885
\(696\) 0 0
\(697\) 23.4422 0.887936
\(698\) 0 0
\(699\) −2.10866 −0.0797567
\(700\) 0 0
\(701\) 8.57137 0.323736 0.161868 0.986812i \(-0.448248\pi\)
0.161868 + 0.986812i \(0.448248\pi\)
\(702\) 0 0
\(703\) −27.4369 −1.03480
\(704\) 0 0
\(705\) −27.1249 −1.02158
\(706\) 0 0
\(707\) −16.8169 −0.632466
\(708\) 0 0
\(709\) 25.5151 0.958240 0.479120 0.877749i \(-0.340956\pi\)
0.479120 + 0.877749i \(0.340956\pi\)
\(710\) 0 0
\(711\) −4.06975 −0.152628
\(712\) 0 0
\(713\) −0.825942 −0.0309318
\(714\) 0 0
\(715\) 43.5676 1.62934
\(716\) 0 0
\(717\) 7.09270 0.264882
\(718\) 0 0
\(719\) −41.0285 −1.53011 −0.765053 0.643968i \(-0.777287\pi\)
−0.765053 + 0.643968i \(0.777287\pi\)
\(720\) 0 0
\(721\) 3.90632 0.145479
\(722\) 0 0
\(723\) −6.11396 −0.227380
\(724\) 0 0
\(725\) 2.82190 0.104803
\(726\) 0 0
\(727\) −3.91694 −0.145271 −0.0726356 0.997359i \(-0.523141\pi\)
−0.0726356 + 0.997359i \(0.523141\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −51.9865 −1.92279
\(732\) 0 0
\(733\) −14.5673 −0.538057 −0.269028 0.963132i \(-0.586703\pi\)
−0.269028 + 0.963132i \(0.586703\pi\)
\(734\) 0 0
\(735\) 12.0203 0.443374
\(736\) 0 0
\(737\) −24.1867 −0.890928
\(738\) 0 0
\(739\) 43.9158 1.61547 0.807734 0.589547i \(-0.200694\pi\)
0.807734 + 0.589547i \(0.200694\pi\)
\(740\) 0 0
\(741\) −41.2642 −1.51588
\(742\) 0 0
\(743\) −9.07407 −0.332895 −0.166448 0.986050i \(-0.553230\pi\)
−0.166448 + 0.986050i \(0.553230\pi\)
\(744\) 0 0
\(745\) 32.6329 1.19558
\(746\) 0 0
\(747\) −4.08357 −0.149410
\(748\) 0 0
\(749\) 2.80517 0.102499
\(750\) 0 0
\(751\) 6.65730 0.242929 0.121464 0.992596i \(-0.461241\pi\)
0.121464 + 0.992596i \(0.461241\pi\)
\(752\) 0 0
\(753\) −2.80434 −0.102196
\(754\) 0 0
\(755\) −27.0697 −0.985166
\(756\) 0 0
\(757\) −19.6664 −0.714788 −0.357394 0.933954i \(-0.616335\pi\)
−0.357394 + 0.933954i \(0.616335\pi\)
\(758\) 0 0
\(759\) −1.55489 −0.0564391
\(760\) 0 0
\(761\) 5.81481 0.210787 0.105393 0.994431i \(-0.466390\pi\)
0.105393 + 0.994431i \(0.466390\pi\)
\(762\) 0 0
\(763\) −17.4641 −0.632242
\(764\) 0 0
\(765\) 14.4047 0.520804
\(766\) 0 0
\(767\) −54.3547 −1.96263
\(768\) 0 0
\(769\) −6.58954 −0.237625 −0.118813 0.992917i \(-0.537909\pi\)
−0.118813 + 0.992917i \(0.537909\pi\)
\(770\) 0 0
\(771\) 25.2183 0.908216
\(772\) 0 0
\(773\) 19.8195 0.712857 0.356429 0.934323i \(-0.383994\pi\)
0.356429 + 0.934323i \(0.383994\pi\)
\(774\) 0 0
\(775\) −1.01278 −0.0363803
\(776\) 0 0
\(777\) 5.07010 0.181889
\(778\) 0 0
\(779\) −20.6340 −0.739288
\(780\) 0 0
\(781\) −10.4707 −0.374670
\(782\) 0 0
\(783\) 4.52700 0.161782
\(784\) 0 0
\(785\) −44.2922 −1.58086
\(786\) 0 0
\(787\) 17.6843 0.630376 0.315188 0.949029i \(-0.397932\pi\)
0.315188 + 0.949029i \(0.397932\pi\)
\(788\) 0 0
\(789\) −13.6148 −0.484701
\(790\) 0 0
\(791\) −18.8750 −0.671118
\(792\) 0 0
\(793\) 76.8129 2.72770
\(794\) 0 0
\(795\) −12.1885 −0.432283
\(796\) 0 0
\(797\) −40.7996 −1.44520 −0.722598 0.691269i \(-0.757052\pi\)
−0.722598 + 0.691269i \(0.757052\pi\)
\(798\) 0 0
\(799\) 89.2753 3.15833
\(800\) 0 0
\(801\) 17.2613 0.609897
\(802\) 0 0
\(803\) −44.2471 −1.56145
\(804\) 0 0
\(805\) 1.19106 0.0419795
\(806\) 0 0
\(807\) 7.70251 0.271141
\(808\) 0 0
\(809\) −2.95407 −0.103859 −0.0519297 0.998651i \(-0.516537\pi\)
−0.0519297 + 0.998651i \(0.516537\pi\)
\(810\) 0 0
\(811\) 6.87439 0.241392 0.120696 0.992689i \(-0.461487\pi\)
0.120696 + 0.992689i \(0.461487\pi\)
\(812\) 0 0
\(813\) 25.8369 0.906141
\(814\) 0 0
\(815\) 6.48231 0.227065
\(816\) 0 0
\(817\) 45.7589 1.60090
\(818\) 0 0
\(819\) 7.62527 0.266449
\(820\) 0 0
\(821\) −27.1421 −0.947267 −0.473634 0.880722i \(-0.657058\pi\)
−0.473634 + 0.880722i \(0.657058\pi\)
\(822\) 0 0
\(823\) −9.66658 −0.336956 −0.168478 0.985705i \(-0.553885\pi\)
−0.168478 + 0.985705i \(0.553885\pi\)
\(824\) 0 0
\(825\) −1.90664 −0.0663806
\(826\) 0 0
\(827\) −30.2680 −1.05252 −0.526260 0.850324i \(-0.676406\pi\)
−0.526260 + 0.850324i \(0.676406\pi\)
\(828\) 0 0
\(829\) −18.0675 −0.627512 −0.313756 0.949504i \(-0.601587\pi\)
−0.313756 + 0.949504i \(0.601587\pi\)
\(830\) 0 0
\(831\) −5.94164 −0.206113
\(832\) 0 0
\(833\) −39.5619 −1.37074
\(834\) 0 0
\(835\) −0.575215 −0.0199061
\(836\) 0 0
\(837\) −1.62475 −0.0561595
\(838\) 0 0
\(839\) 13.9450 0.481434 0.240717 0.970595i \(-0.422617\pi\)
0.240717 + 0.970595i \(0.422617\pi\)
\(840\) 0 0
\(841\) −8.50626 −0.293319
\(842\) 0 0
\(843\) 5.87340 0.202291
\(844\) 0 0
\(845\) 69.7831 2.40061
\(846\) 0 0
\(847\) 1.84156 0.0632769
\(848\) 0 0
\(849\) 22.8593 0.784529
\(850\) 0 0
\(851\) −2.30133 −0.0788887
\(852\) 0 0
\(853\) 23.9459 0.819891 0.409946 0.912110i \(-0.365548\pi\)
0.409946 + 0.912110i \(0.365548\pi\)
\(854\) 0 0
\(855\) −12.6791 −0.433617
\(856\) 0 0
\(857\) 12.0017 0.409971 0.204985 0.978765i \(-0.434285\pi\)
0.204985 + 0.978765i \(0.434285\pi\)
\(858\) 0 0
\(859\) 8.27441 0.282319 0.141160 0.989987i \(-0.454917\pi\)
0.141160 + 0.989987i \(0.454917\pi\)
\(860\) 0 0
\(861\) 3.81298 0.129946
\(862\) 0 0
\(863\) −20.6687 −0.703569 −0.351785 0.936081i \(-0.614425\pi\)
−0.351785 + 0.936081i \(0.614425\pi\)
\(864\) 0 0
\(865\) −34.5640 −1.17521
\(866\) 0 0
\(867\) −30.4098 −1.03277
\(868\) 0 0
\(869\) 12.4482 0.422275
\(870\) 0 0
\(871\) −53.8386 −1.82425
\(872\) 0 0
\(873\) 14.8285 0.501870
\(874\) 0 0
\(875\) 13.1755 0.445412
\(876\) 0 0
\(877\) −52.8954 −1.78615 −0.893075 0.449908i \(-0.851457\pi\)
−0.893075 + 0.449908i \(0.851457\pi\)
\(878\) 0 0
\(879\) −10.1271 −0.341578
\(880\) 0 0
\(881\) 48.1444 1.62203 0.811013 0.585029i \(-0.198917\pi\)
0.811013 + 0.585029i \(0.198917\pi\)
\(882\) 0 0
\(883\) −24.7916 −0.834304 −0.417152 0.908837i \(-0.636972\pi\)
−0.417152 + 0.908837i \(0.636972\pi\)
\(884\) 0 0
\(885\) −16.7014 −0.561412
\(886\) 0 0
\(887\) −32.0672 −1.07671 −0.538355 0.842718i \(-0.680954\pi\)
−0.538355 + 0.842718i \(0.680954\pi\)
\(888\) 0 0
\(889\) −15.1951 −0.509626
\(890\) 0 0
\(891\) −3.05871 −0.102470
\(892\) 0 0
\(893\) −78.5807 −2.62960
\(894\) 0 0
\(895\) 28.4186 0.949928
\(896\) 0 0
\(897\) −3.46113 −0.115564
\(898\) 0 0
\(899\) −7.35524 −0.245311
\(900\) 0 0
\(901\) 40.1157 1.33645
\(902\) 0 0
\(903\) −8.45585 −0.281393
\(904\) 0 0
\(905\) −6.29047 −0.209102
\(906\) 0 0
\(907\) 10.3373 0.343245 0.171623 0.985163i \(-0.445099\pi\)
0.171623 + 0.985163i \(0.445099\pi\)
\(908\) 0 0
\(909\) 15.0157 0.498040
\(910\) 0 0
\(911\) 28.4505 0.942608 0.471304 0.881971i \(-0.343783\pi\)
0.471304 + 0.881971i \(0.343783\pi\)
\(912\) 0 0
\(913\) 12.4904 0.413374
\(914\) 0 0
\(915\) 23.6021 0.780260
\(916\) 0 0
\(917\) 17.3397 0.572609
\(918\) 0 0
\(919\) −36.6977 −1.21055 −0.605273 0.796018i \(-0.706936\pi\)
−0.605273 + 0.796018i \(0.706936\pi\)
\(920\) 0 0
\(921\) 9.08360 0.299315
\(922\) 0 0
\(923\) −23.3073 −0.767169
\(924\) 0 0
\(925\) −2.82193 −0.0927846
\(926\) 0 0
\(927\) −3.48792 −0.114558
\(928\) 0 0
\(929\) 24.0358 0.788589 0.394295 0.918984i \(-0.370989\pi\)
0.394295 + 0.918984i \(0.370989\pi\)
\(930\) 0 0
\(931\) 34.8226 1.14127
\(932\) 0 0
\(933\) −28.1435 −0.921378
\(934\) 0 0
\(935\) −44.0598 −1.44091
\(936\) 0 0
\(937\) 40.6241 1.32713 0.663566 0.748118i \(-0.269042\pi\)
0.663566 + 0.748118i \(0.269042\pi\)
\(938\) 0 0
\(939\) −2.15160 −0.0702148
\(940\) 0 0
\(941\) −17.9401 −0.584832 −0.292416 0.956291i \(-0.594459\pi\)
−0.292416 + 0.956291i \(0.594459\pi\)
\(942\) 0 0
\(943\) −1.73072 −0.0563601
\(944\) 0 0
\(945\) 2.34300 0.0762176
\(946\) 0 0
\(947\) 35.4771 1.15285 0.576426 0.817149i \(-0.304447\pi\)
0.576426 + 0.817149i \(0.304447\pi\)
\(948\) 0 0
\(949\) −98.4923 −3.19719
\(950\) 0 0
\(951\) 17.9505 0.582084
\(952\) 0 0
\(953\) −56.9687 −1.84540 −0.922699 0.385521i \(-0.874022\pi\)
−0.922699 + 0.385521i \(0.874022\pi\)
\(954\) 0 0
\(955\) 13.3898 0.433283
\(956\) 0 0
\(957\) −13.8468 −0.447602
\(958\) 0 0
\(959\) 1.88830 0.0609764
\(960\) 0 0
\(961\) −28.3602 −0.914845
\(962\) 0 0
\(963\) −2.50472 −0.0807134
\(964\) 0 0
\(965\) −22.7829 −0.733408
\(966\) 0 0
\(967\) 31.2070 1.00355 0.501775 0.864998i \(-0.332681\pi\)
0.501775 + 0.864998i \(0.332681\pi\)
\(968\) 0 0
\(969\) 41.7304 1.34057
\(970\) 0 0
\(971\) 54.2592 1.74126 0.870630 0.491938i \(-0.163711\pi\)
0.870630 + 0.491938i \(0.163711\pi\)
\(972\) 0 0
\(973\) 23.5526 0.755061
\(974\) 0 0
\(975\) −4.24410 −0.135920
\(976\) 0 0
\(977\) −3.73365 −0.119450 −0.0597251 0.998215i \(-0.519022\pi\)
−0.0597251 + 0.998215i \(0.519022\pi\)
\(978\) 0 0
\(979\) −52.7971 −1.68740
\(980\) 0 0
\(981\) 15.5936 0.497864
\(982\) 0 0
\(983\) 48.4077 1.54397 0.771983 0.635643i \(-0.219265\pi\)
0.771983 + 0.635643i \(0.219265\pi\)
\(984\) 0 0
\(985\) 26.5505 0.845968
\(986\) 0 0
\(987\) 14.5210 0.462210
\(988\) 0 0
\(989\) 3.83814 0.122046
\(990\) 0 0
\(991\) −32.3082 −1.02631 −0.513153 0.858297i \(-0.671523\pi\)
−0.513153 + 0.858297i \(0.671523\pi\)
\(992\) 0 0
\(993\) 0.828334 0.0262864
\(994\) 0 0
\(995\) 39.1968 1.24262
\(996\) 0 0
\(997\) 34.4280 1.09035 0.545173 0.838323i \(-0.316464\pi\)
0.545173 + 0.838323i \(0.316464\pi\)
\(998\) 0 0
\(999\) −4.52706 −0.143230
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 \(a_p\))