Properties

Label 6036.2.a.g.1.13
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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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: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(3.48442\)
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+2.48442 q^{5}\) \(+1.05465 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+2.48442 q^{5}\) \(+1.05465 q^{7}\) \(+1.00000 q^{9}\) \(-4.01743 q^{11}\) \(-4.37086 q^{13}\) \(+2.48442 q^{15}\) \(-5.30462 q^{17}\) \(+4.18305 q^{19}\) \(+1.05465 q^{21}\) \(-5.97856 q^{23}\) \(+1.17232 q^{25}\) \(+1.00000 q^{27}\) \(-2.50134 q^{29}\) \(-0.980193 q^{31}\) \(-4.01743 q^{33}\) \(+2.62020 q^{35}\) \(+0.119159 q^{37}\) \(-4.37086 q^{39}\) \(-2.22539 q^{41}\) \(-0.812728 q^{43}\) \(+2.48442 q^{45}\) \(-4.81548 q^{47}\) \(-5.88770 q^{49}\) \(-5.30462 q^{51}\) \(+0.831360 q^{53}\) \(-9.98098 q^{55}\) \(+4.18305 q^{57}\) \(+4.34939 q^{59}\) \(+3.11748 q^{61}\) \(+1.05465 q^{63}\) \(-10.8590 q^{65}\) \(-2.10873 q^{67}\) \(-5.97856 q^{69}\) \(-11.8866 q^{71}\) \(+13.6096 q^{73}\) \(+1.17232 q^{75}\) \(-4.23700 q^{77}\) \(-4.21360 q^{79}\) \(+1.00000 q^{81}\) \(-9.78346 q^{83}\) \(-13.1789 q^{85}\) \(-2.50134 q^{87}\) \(+15.2828 q^{89}\) \(-4.60974 q^{91}\) \(-0.980193 q^{93}\) \(+10.3924 q^{95}\) \(-11.5419 q^{97}\) \(-4.01743 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 11q^{45} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 15q^{81} \) \(\mathstrut -\mathstrut 17q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 23q^{87} \) \(\mathstrut -\mathstrut 23q^{89} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 13q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 2.48442 1.11106 0.555532 0.831495i \(-0.312515\pi\)
0.555532 + 0.831495i \(0.312515\pi\)
\(6\) 0 0
\(7\) 1.05465 0.398622 0.199311 0.979936i \(-0.436130\pi\)
0.199311 + 0.979936i \(0.436130\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.01743 −1.21130 −0.605651 0.795730i \(-0.707087\pi\)
−0.605651 + 0.795730i \(0.707087\pi\)
\(12\) 0 0
\(13\) −4.37086 −1.21226 −0.606129 0.795367i \(-0.707278\pi\)
−0.606129 + 0.795367i \(0.707278\pi\)
\(14\) 0 0
\(15\) 2.48442 0.641473
\(16\) 0 0
\(17\) −5.30462 −1.28656 −0.643280 0.765631i \(-0.722427\pi\)
−0.643280 + 0.765631i \(0.722427\pi\)
\(18\) 0 0
\(19\) 4.18305 0.959656 0.479828 0.877362i \(-0.340699\pi\)
0.479828 + 0.877362i \(0.340699\pi\)
\(20\) 0 0
\(21\) 1.05465 0.230144
\(22\) 0 0
\(23\) −5.97856 −1.24662 −0.623308 0.781977i \(-0.714212\pi\)
−0.623308 + 0.781977i \(0.714212\pi\)
\(24\) 0 0
\(25\) 1.17232 0.234464
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −2.50134 −0.464488 −0.232244 0.972658i \(-0.574607\pi\)
−0.232244 + 0.972658i \(0.574607\pi\)
\(30\) 0 0
\(31\) −0.980193 −0.176048 −0.0880239 0.996118i \(-0.528055\pi\)
−0.0880239 + 0.996118i \(0.528055\pi\)
\(32\) 0 0
\(33\) −4.01743 −0.699346
\(34\) 0 0
\(35\) 2.62020 0.442895
\(36\) 0 0
\(37\) 0.119159 0.0195896 0.00979482 0.999952i \(-0.496882\pi\)
0.00979482 + 0.999952i \(0.496882\pi\)
\(38\) 0 0
\(39\) −4.37086 −0.699897
\(40\) 0 0
\(41\) −2.22539 −0.347548 −0.173774 0.984786i \(-0.555596\pi\)
−0.173774 + 0.984786i \(0.555596\pi\)
\(42\) 0 0
\(43\) −0.812728 −0.123940 −0.0619699 0.998078i \(-0.519738\pi\)
−0.0619699 + 0.998078i \(0.519738\pi\)
\(44\) 0 0
\(45\) 2.48442 0.370355
\(46\) 0 0
\(47\) −4.81548 −0.702409 −0.351205 0.936299i \(-0.614228\pi\)
−0.351205 + 0.936299i \(0.614228\pi\)
\(48\) 0 0
\(49\) −5.88770 −0.841101
\(50\) 0 0
\(51\) −5.30462 −0.742795
\(52\) 0 0
\(53\) 0.831360 0.114196 0.0570980 0.998369i \(-0.481815\pi\)
0.0570980 + 0.998369i \(0.481815\pi\)
\(54\) 0 0
\(55\) −9.98098 −1.34583
\(56\) 0 0
\(57\) 4.18305 0.554058
\(58\) 0 0
\(59\) 4.34939 0.566243 0.283121 0.959084i \(-0.408630\pi\)
0.283121 + 0.959084i \(0.408630\pi\)
\(60\) 0 0
\(61\) 3.11748 0.399153 0.199576 0.979882i \(-0.436043\pi\)
0.199576 + 0.979882i \(0.436043\pi\)
\(62\) 0 0
\(63\) 1.05465 0.132874
\(64\) 0 0
\(65\) −10.8590 −1.34690
\(66\) 0 0
\(67\) −2.10873 −0.257622 −0.128811 0.991669i \(-0.541116\pi\)
−0.128811 + 0.991669i \(0.541116\pi\)
\(68\) 0 0
\(69\) −5.97856 −0.719734
\(70\) 0 0
\(71\) −11.8866 −1.41068 −0.705342 0.708867i \(-0.749207\pi\)
−0.705342 + 0.708867i \(0.749207\pi\)
\(72\) 0 0
\(73\) 13.6096 1.59288 0.796440 0.604718i \(-0.206714\pi\)
0.796440 + 0.604718i \(0.206714\pi\)
\(74\) 0 0
\(75\) 1.17232 0.135368
\(76\) 0 0
\(77\) −4.23700 −0.482851
\(78\) 0 0
\(79\) −4.21360 −0.474067 −0.237033 0.971502i \(-0.576175\pi\)
−0.237033 + 0.971502i \(0.576175\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −9.78346 −1.07387 −0.536937 0.843622i \(-0.680419\pi\)
−0.536937 + 0.843622i \(0.680419\pi\)
\(84\) 0 0
\(85\) −13.1789 −1.42945
\(86\) 0 0
\(87\) −2.50134 −0.268172
\(88\) 0 0
\(89\) 15.2828 1.61998 0.809989 0.586445i \(-0.199473\pi\)
0.809989 + 0.586445i \(0.199473\pi\)
\(90\) 0 0
\(91\) −4.60974 −0.483232
\(92\) 0 0
\(93\) −0.980193 −0.101641
\(94\) 0 0
\(95\) 10.3924 1.06624
\(96\) 0 0
\(97\) −11.5419 −1.17190 −0.585949 0.810348i \(-0.699278\pi\)
−0.585949 + 0.810348i \(0.699278\pi\)
\(98\) 0 0
\(99\) −4.01743 −0.403767
\(100\) 0 0
\(101\) −19.7358 −1.96379 −0.981893 0.189439i \(-0.939333\pi\)
−0.981893 + 0.189439i \(0.939333\pi\)
\(102\) 0 0
\(103\) 8.48413 0.835966 0.417983 0.908455i \(-0.362737\pi\)
0.417983 + 0.908455i \(0.362737\pi\)
\(104\) 0 0
\(105\) 2.62020 0.255705
\(106\) 0 0
\(107\) −12.5953 −1.21764 −0.608818 0.793310i \(-0.708356\pi\)
−0.608818 + 0.793310i \(0.708356\pi\)
\(108\) 0 0
\(109\) 12.8417 1.23001 0.615004 0.788524i \(-0.289154\pi\)
0.615004 + 0.788524i \(0.289154\pi\)
\(110\) 0 0
\(111\) 0.119159 0.0113101
\(112\) 0 0
\(113\) −10.8335 −1.01913 −0.509564 0.860433i \(-0.670193\pi\)
−0.509564 + 0.860433i \(0.670193\pi\)
\(114\) 0 0
\(115\) −14.8532 −1.38507
\(116\) 0 0
\(117\) −4.37086 −0.404086
\(118\) 0 0
\(119\) −5.59454 −0.512851
\(120\) 0 0
\(121\) 5.13978 0.467252
\(122\) 0 0
\(123\) −2.22539 −0.200657
\(124\) 0 0
\(125\) −9.50955 −0.850560
\(126\) 0 0
\(127\) −1.98049 −0.175740 −0.0878701 0.996132i \(-0.528006\pi\)
−0.0878701 + 0.996132i \(0.528006\pi\)
\(128\) 0 0
\(129\) −0.812728 −0.0715567
\(130\) 0 0
\(131\) 19.0312 1.66277 0.831383 0.555700i \(-0.187550\pi\)
0.831383 + 0.555700i \(0.187550\pi\)
\(132\) 0 0
\(133\) 4.41167 0.382540
\(134\) 0 0
\(135\) 2.48442 0.213824
\(136\) 0 0
\(137\) 15.9477 1.36250 0.681251 0.732050i \(-0.261436\pi\)
0.681251 + 0.732050i \(0.261436\pi\)
\(138\) 0 0
\(139\) −12.5090 −1.06100 −0.530498 0.847686i \(-0.677995\pi\)
−0.530498 + 0.847686i \(0.677995\pi\)
\(140\) 0 0
\(141\) −4.81548 −0.405536
\(142\) 0 0
\(143\) 17.5596 1.46841
\(144\) 0 0
\(145\) −6.21438 −0.516076
\(146\) 0 0
\(147\) −5.88770 −0.485610
\(148\) 0 0
\(149\) −21.4384 −1.75630 −0.878151 0.478383i \(-0.841223\pi\)
−0.878151 + 0.478383i \(0.841223\pi\)
\(150\) 0 0
\(151\) −9.67697 −0.787500 −0.393750 0.919217i \(-0.628822\pi\)
−0.393750 + 0.919217i \(0.628822\pi\)
\(152\) 0 0
\(153\) −5.30462 −0.428853
\(154\) 0 0
\(155\) −2.43521 −0.195600
\(156\) 0 0
\(157\) −12.0099 −0.958497 −0.479249 0.877679i \(-0.659091\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(158\) 0 0
\(159\) 0.831360 0.0659311
\(160\) 0 0
\(161\) −6.30531 −0.496928
\(162\) 0 0
\(163\) −2.49487 −0.195413 −0.0977065 0.995215i \(-0.531151\pi\)
−0.0977065 + 0.995215i \(0.531151\pi\)
\(164\) 0 0
\(165\) −9.98098 −0.777018
\(166\) 0 0
\(167\) 12.9914 1.00531 0.502654 0.864488i \(-0.332357\pi\)
0.502654 + 0.864488i \(0.332357\pi\)
\(168\) 0 0
\(169\) 6.10439 0.469568
\(170\) 0 0
\(171\) 4.18305 0.319885
\(172\) 0 0
\(173\) 11.1085 0.844566 0.422283 0.906464i \(-0.361229\pi\)
0.422283 + 0.906464i \(0.361229\pi\)
\(174\) 0 0
\(175\) 1.23639 0.0934625
\(176\) 0 0
\(177\) 4.34939 0.326920
\(178\) 0 0
\(179\) 0.128562 0.00960917 0.00480459 0.999988i \(-0.498471\pi\)
0.00480459 + 0.999988i \(0.498471\pi\)
\(180\) 0 0
\(181\) −1.48913 −0.110686 −0.0553432 0.998467i \(-0.517625\pi\)
−0.0553432 + 0.998467i \(0.517625\pi\)
\(182\) 0 0
\(183\) 3.11748 0.230451
\(184\) 0 0
\(185\) 0.296041 0.0217654
\(186\) 0 0
\(187\) 21.3110 1.55841
\(188\) 0 0
\(189\) 1.05465 0.0767148
\(190\) 0 0
\(191\) 24.1225 1.74544 0.872720 0.488220i \(-0.162354\pi\)
0.872720 + 0.488220i \(0.162354\pi\)
\(192\) 0 0
\(193\) −3.41216 −0.245613 −0.122806 0.992431i \(-0.539189\pi\)
−0.122806 + 0.992431i \(0.539189\pi\)
\(194\) 0 0
\(195\) −10.8590 −0.777631
\(196\) 0 0
\(197\) 4.66110 0.332090 0.166045 0.986118i \(-0.446900\pi\)
0.166045 + 0.986118i \(0.446900\pi\)
\(198\) 0 0
\(199\) 10.4261 0.739088 0.369544 0.929213i \(-0.379514\pi\)
0.369544 + 0.929213i \(0.379514\pi\)
\(200\) 0 0
\(201\) −2.10873 −0.148738
\(202\) 0 0
\(203\) −2.63805 −0.185155
\(204\) 0 0
\(205\) −5.52880 −0.386148
\(206\) 0 0
\(207\) −5.97856 −0.415539
\(208\) 0 0
\(209\) −16.8051 −1.16243
\(210\) 0 0
\(211\) −15.9315 −1.09677 −0.548384 0.836226i \(-0.684757\pi\)
−0.548384 + 0.836226i \(0.684757\pi\)
\(212\) 0 0
\(213\) −11.8866 −0.814459
\(214\) 0 0
\(215\) −2.01915 −0.137705
\(216\) 0 0
\(217\) −1.03376 −0.0701765
\(218\) 0 0
\(219\) 13.6096 0.919649
\(220\) 0 0
\(221\) 23.1857 1.55964
\(222\) 0 0
\(223\) 13.5783 0.909270 0.454635 0.890678i \(-0.349770\pi\)
0.454635 + 0.890678i \(0.349770\pi\)
\(224\) 0 0
\(225\) 1.17232 0.0781547
\(226\) 0 0
\(227\) 1.76364 0.117057 0.0585283 0.998286i \(-0.481359\pi\)
0.0585283 + 0.998286i \(0.481359\pi\)
\(228\) 0 0
\(229\) −3.21524 −0.212469 −0.106234 0.994341i \(-0.533879\pi\)
−0.106234 + 0.994341i \(0.533879\pi\)
\(230\) 0 0
\(231\) −4.23700 −0.278774
\(232\) 0 0
\(233\) 25.8981 1.69664 0.848321 0.529482i \(-0.177614\pi\)
0.848321 + 0.529482i \(0.177614\pi\)
\(234\) 0 0
\(235\) −11.9636 −0.780422
\(236\) 0 0
\(237\) −4.21360 −0.273703
\(238\) 0 0
\(239\) −2.26966 −0.146812 −0.0734062 0.997302i \(-0.523387\pi\)
−0.0734062 + 0.997302i \(0.523387\pi\)
\(240\) 0 0
\(241\) 5.61835 0.361910 0.180955 0.983491i \(-0.442081\pi\)
0.180955 + 0.983491i \(0.442081\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −14.6275 −0.934517
\(246\) 0 0
\(247\) −18.2835 −1.16335
\(248\) 0 0
\(249\) −9.78346 −0.620002
\(250\) 0 0
\(251\) 14.3387 0.905048 0.452524 0.891752i \(-0.350524\pi\)
0.452524 + 0.891752i \(0.350524\pi\)
\(252\) 0 0
\(253\) 24.0185 1.51003
\(254\) 0 0
\(255\) −13.1789 −0.825293
\(256\) 0 0
\(257\) 1.56506 0.0976257 0.0488128 0.998808i \(-0.484456\pi\)
0.0488128 + 0.998808i \(0.484456\pi\)
\(258\) 0 0
\(259\) 0.125672 0.00780886
\(260\) 0 0
\(261\) −2.50134 −0.154829
\(262\) 0 0
\(263\) 26.0080 1.60372 0.801862 0.597510i \(-0.203843\pi\)
0.801862 + 0.597510i \(0.203843\pi\)
\(264\) 0 0
\(265\) 2.06544 0.126879
\(266\) 0 0
\(267\) 15.2828 0.935295
\(268\) 0 0
\(269\) −25.3580 −1.54610 −0.773052 0.634343i \(-0.781271\pi\)
−0.773052 + 0.634343i \(0.781271\pi\)
\(270\) 0 0
\(271\) 5.93004 0.360224 0.180112 0.983646i \(-0.442354\pi\)
0.180112 + 0.983646i \(0.442354\pi\)
\(272\) 0 0
\(273\) −4.60974 −0.278994
\(274\) 0 0
\(275\) −4.70972 −0.284007
\(276\) 0 0
\(277\) −3.14081 −0.188713 −0.0943566 0.995538i \(-0.530079\pi\)
−0.0943566 + 0.995538i \(0.530079\pi\)
\(278\) 0 0
\(279\) −0.980193 −0.0586826
\(280\) 0 0
\(281\) −22.5471 −1.34505 −0.672524 0.740076i \(-0.734790\pi\)
−0.672524 + 0.740076i \(0.734790\pi\)
\(282\) 0 0
\(283\) 31.0880 1.84799 0.923995 0.382404i \(-0.124904\pi\)
0.923995 + 0.382404i \(0.124904\pi\)
\(284\) 0 0
\(285\) 10.3924 0.615594
\(286\) 0 0
\(287\) −2.34702 −0.138540
\(288\) 0 0
\(289\) 11.1390 0.655234
\(290\) 0 0
\(291\) −11.5419 −0.676596
\(292\) 0 0
\(293\) 12.6151 0.736983 0.368492 0.929631i \(-0.379874\pi\)
0.368492 + 0.929631i \(0.379874\pi\)
\(294\) 0 0
\(295\) 10.8057 0.629132
\(296\) 0 0
\(297\) −4.01743 −0.233115
\(298\) 0 0
\(299\) 26.1314 1.51122
\(300\) 0 0
\(301\) −0.857147 −0.0494051
\(302\) 0 0
\(303\) −19.7358 −1.13379
\(304\) 0 0
\(305\) 7.74512 0.443484
\(306\) 0 0
\(307\) 12.4460 0.710332 0.355166 0.934803i \(-0.384424\pi\)
0.355166 + 0.934803i \(0.384424\pi\)
\(308\) 0 0
\(309\) 8.48413 0.482645
\(310\) 0 0
\(311\) 17.8323 1.01118 0.505588 0.862775i \(-0.331276\pi\)
0.505588 + 0.862775i \(0.331276\pi\)
\(312\) 0 0
\(313\) −26.8191 −1.51591 −0.757953 0.652309i \(-0.773800\pi\)
−0.757953 + 0.652309i \(0.773800\pi\)
\(314\) 0 0
\(315\) 2.62020 0.147632
\(316\) 0 0
\(317\) −18.9847 −1.06629 −0.533144 0.846024i \(-0.678990\pi\)
−0.533144 + 0.846024i \(0.678990\pi\)
\(318\) 0 0
\(319\) 10.0490 0.562635
\(320\) 0 0
\(321\) −12.5953 −0.703003
\(322\) 0 0
\(323\) −22.1895 −1.23465
\(324\) 0 0
\(325\) −5.12404 −0.284231
\(326\) 0 0
\(327\) 12.8417 0.710145
\(328\) 0 0
\(329\) −5.07866 −0.279996
\(330\) 0 0
\(331\) 14.3796 0.790372 0.395186 0.918601i \(-0.370680\pi\)
0.395186 + 0.918601i \(0.370680\pi\)
\(332\) 0 0
\(333\) 0.119159 0.00652988
\(334\) 0 0
\(335\) −5.23896 −0.286235
\(336\) 0 0
\(337\) 0.924650 0.0503689 0.0251845 0.999683i \(-0.491983\pi\)
0.0251845 + 0.999683i \(0.491983\pi\)
\(338\) 0 0
\(339\) −10.8335 −0.588393
\(340\) 0 0
\(341\) 3.93786 0.213247
\(342\) 0 0
\(343\) −13.5921 −0.733903
\(344\) 0 0
\(345\) −14.8532 −0.799671
\(346\) 0 0
\(347\) 1.79552 0.0963884 0.0481942 0.998838i \(-0.484653\pi\)
0.0481942 + 0.998838i \(0.484653\pi\)
\(348\) 0 0
\(349\) 9.74494 0.521635 0.260817 0.965388i \(-0.416008\pi\)
0.260817 + 0.965388i \(0.416008\pi\)
\(350\) 0 0
\(351\) −4.37086 −0.233299
\(352\) 0 0
\(353\) −27.0143 −1.43783 −0.718913 0.695100i \(-0.755360\pi\)
−0.718913 + 0.695100i \(0.755360\pi\)
\(354\) 0 0
\(355\) −29.5313 −1.56736
\(356\) 0 0
\(357\) −5.59454 −0.296094
\(358\) 0 0
\(359\) −21.8620 −1.15383 −0.576916 0.816803i \(-0.695744\pi\)
−0.576916 + 0.816803i \(0.695744\pi\)
\(360\) 0 0
\(361\) −1.50213 −0.0790595
\(362\) 0 0
\(363\) 5.13978 0.269768
\(364\) 0 0
\(365\) 33.8118 1.76979
\(366\) 0 0
\(367\) 12.7030 0.663090 0.331545 0.943439i \(-0.392430\pi\)
0.331545 + 0.943439i \(0.392430\pi\)
\(368\) 0 0
\(369\) −2.22539 −0.115849
\(370\) 0 0
\(371\) 0.876797 0.0455211
\(372\) 0 0
\(373\) 20.4999 1.06144 0.530722 0.847546i \(-0.321921\pi\)
0.530722 + 0.847546i \(0.321921\pi\)
\(374\) 0 0
\(375\) −9.50955 −0.491071
\(376\) 0 0
\(377\) 10.9330 0.563079
\(378\) 0 0
\(379\) −9.86234 −0.506594 −0.253297 0.967389i \(-0.581515\pi\)
−0.253297 + 0.967389i \(0.581515\pi\)
\(380\) 0 0
\(381\) −1.98049 −0.101464
\(382\) 0 0
\(383\) 18.0799 0.923840 0.461920 0.886922i \(-0.347161\pi\)
0.461920 + 0.886922i \(0.347161\pi\)
\(384\) 0 0
\(385\) −10.5265 −0.536479
\(386\) 0 0
\(387\) −0.812728 −0.0413133
\(388\) 0 0
\(389\) −34.5027 −1.74936 −0.874679 0.484703i \(-0.838928\pi\)
−0.874679 + 0.484703i \(0.838928\pi\)
\(390\) 0 0
\(391\) 31.7140 1.60384
\(392\) 0 0
\(393\) 19.0312 0.959998
\(394\) 0 0
\(395\) −10.4683 −0.526719
\(396\) 0 0
\(397\) 30.3398 1.52271 0.761356 0.648335i \(-0.224534\pi\)
0.761356 + 0.648335i \(0.224534\pi\)
\(398\) 0 0
\(399\) 4.41167 0.220860
\(400\) 0 0
\(401\) −11.7104 −0.584790 −0.292395 0.956298i \(-0.594452\pi\)
−0.292395 + 0.956298i \(0.594452\pi\)
\(402\) 0 0
\(403\) 4.28428 0.213415
\(404\) 0 0
\(405\) 2.48442 0.123452
\(406\) 0 0
\(407\) −0.478714 −0.0237290
\(408\) 0 0
\(409\) 15.5699 0.769880 0.384940 0.922942i \(-0.374222\pi\)
0.384940 + 0.922942i \(0.374222\pi\)
\(410\) 0 0
\(411\) 15.9477 0.786641
\(412\) 0 0
\(413\) 4.58711 0.225717
\(414\) 0 0
\(415\) −24.3062 −1.19314
\(416\) 0 0
\(417\) −12.5090 −0.612566
\(418\) 0 0
\(419\) 14.7342 0.719815 0.359907 0.932988i \(-0.382808\pi\)
0.359907 + 0.932988i \(0.382808\pi\)
\(420\) 0 0
\(421\) 2.76643 0.134828 0.0674139 0.997725i \(-0.478525\pi\)
0.0674139 + 0.997725i \(0.478525\pi\)
\(422\) 0 0
\(423\) −4.81548 −0.234136
\(424\) 0 0
\(425\) −6.21871 −0.301652
\(426\) 0 0
\(427\) 3.28787 0.159111
\(428\) 0 0
\(429\) 17.5596 0.847787
\(430\) 0 0
\(431\) −2.30117 −0.110843 −0.0554216 0.998463i \(-0.517650\pi\)
−0.0554216 + 0.998463i \(0.517650\pi\)
\(432\) 0 0
\(433\) −25.8309 −1.24135 −0.620676 0.784067i \(-0.713142\pi\)
−0.620676 + 0.784067i \(0.713142\pi\)
\(434\) 0 0
\(435\) −6.21438 −0.297957
\(436\) 0 0
\(437\) −25.0086 −1.19632
\(438\) 0 0
\(439\) −13.8806 −0.662485 −0.331242 0.943546i \(-0.607468\pi\)
−0.331242 + 0.943546i \(0.607468\pi\)
\(440\) 0 0
\(441\) −5.88770 −0.280367
\(442\) 0 0
\(443\) −10.2269 −0.485897 −0.242948 0.970039i \(-0.578115\pi\)
−0.242948 + 0.970039i \(0.578115\pi\)
\(444\) 0 0
\(445\) 37.9689 1.79990
\(446\) 0 0
\(447\) −21.4384 −1.01400
\(448\) 0 0
\(449\) −35.2839 −1.66515 −0.832576 0.553911i \(-0.813135\pi\)
−0.832576 + 0.553911i \(0.813135\pi\)
\(450\) 0 0
\(451\) 8.94036 0.420985
\(452\) 0 0
\(453\) −9.67697 −0.454664
\(454\) 0 0
\(455\) −11.4525 −0.536902
\(456\) 0 0
\(457\) −8.66677 −0.405414 −0.202707 0.979239i \(-0.564974\pi\)
−0.202707 + 0.979239i \(0.564974\pi\)
\(458\) 0 0
\(459\) −5.30462 −0.247598
\(460\) 0 0
\(461\) −17.1021 −0.796525 −0.398263 0.917271i \(-0.630387\pi\)
−0.398263 + 0.917271i \(0.630387\pi\)
\(462\) 0 0
\(463\) −18.8628 −0.876629 −0.438315 0.898822i \(-0.644424\pi\)
−0.438315 + 0.898822i \(0.644424\pi\)
\(464\) 0 0
\(465\) −2.43521 −0.112930
\(466\) 0 0
\(467\) −23.1846 −1.07286 −0.536428 0.843946i \(-0.680227\pi\)
−0.536428 + 0.843946i \(0.680227\pi\)
\(468\) 0 0
\(469\) −2.22398 −0.102694
\(470\) 0 0
\(471\) −12.0099 −0.553389
\(472\) 0 0
\(473\) 3.26508 0.150129
\(474\) 0 0
\(475\) 4.90387 0.225005
\(476\) 0 0
\(477\) 0.831360 0.0380654
\(478\) 0 0
\(479\) −29.2657 −1.33718 −0.668592 0.743629i \(-0.733103\pi\)
−0.668592 + 0.743629i \(0.733103\pi\)
\(480\) 0 0
\(481\) −0.520828 −0.0237477
\(482\) 0 0
\(483\) −6.30531 −0.286902
\(484\) 0 0
\(485\) −28.6748 −1.30205
\(486\) 0 0
\(487\) 23.1260 1.04794 0.523969 0.851737i \(-0.324451\pi\)
0.523969 + 0.851737i \(0.324451\pi\)
\(488\) 0 0
\(489\) −2.49487 −0.112822
\(490\) 0 0
\(491\) −5.75991 −0.259941 −0.129970 0.991518i \(-0.541488\pi\)
−0.129970 + 0.991518i \(0.541488\pi\)
\(492\) 0 0
\(493\) 13.2687 0.597591
\(494\) 0 0
\(495\) −9.98098 −0.448611
\(496\) 0 0
\(497\) −12.5363 −0.562330
\(498\) 0 0
\(499\) 11.5592 0.517461 0.258731 0.965950i \(-0.416696\pi\)
0.258731 + 0.965950i \(0.416696\pi\)
\(500\) 0 0
\(501\) 12.9914 0.580414
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −49.0319 −2.18189
\(506\) 0 0
\(507\) 6.10439 0.271105
\(508\) 0 0
\(509\) −35.3469 −1.56672 −0.783361 0.621567i \(-0.786496\pi\)
−0.783361 + 0.621567i \(0.786496\pi\)
\(510\) 0 0
\(511\) 14.3534 0.634957
\(512\) 0 0
\(513\) 4.18305 0.184686
\(514\) 0 0
\(515\) 21.0781 0.928812
\(516\) 0 0
\(517\) 19.3459 0.850830
\(518\) 0 0
\(519\) 11.1085 0.487610
\(520\) 0 0
\(521\) −9.01232 −0.394837 −0.197418 0.980319i \(-0.563256\pi\)
−0.197418 + 0.980319i \(0.563256\pi\)
\(522\) 0 0
\(523\) 10.5324 0.460550 0.230275 0.973126i \(-0.426037\pi\)
0.230275 + 0.973126i \(0.426037\pi\)
\(524\) 0 0
\(525\) 1.23639 0.0539606
\(526\) 0 0
\(527\) 5.19955 0.226496
\(528\) 0 0
\(529\) 12.7432 0.554051
\(530\) 0 0
\(531\) 4.34939 0.188748
\(532\) 0 0
\(533\) 9.72686 0.421317
\(534\) 0 0
\(535\) −31.2920 −1.35287
\(536\) 0 0
\(537\) 0.128562 0.00554786
\(538\) 0 0
\(539\) 23.6535 1.01883
\(540\) 0 0
\(541\) −20.2771 −0.871779 −0.435889 0.900000i \(-0.643566\pi\)
−0.435889 + 0.900000i \(0.643566\pi\)
\(542\) 0 0
\(543\) −1.48913 −0.0639049
\(544\) 0 0
\(545\) 31.9040 1.36662
\(546\) 0 0
\(547\) 37.3092 1.59523 0.797613 0.603170i \(-0.206096\pi\)
0.797613 + 0.603170i \(0.206096\pi\)
\(548\) 0 0
\(549\) 3.11748 0.133051
\(550\) 0 0
\(551\) −10.4632 −0.445749
\(552\) 0 0
\(553\) −4.44389 −0.188973
\(554\) 0 0
\(555\) 0.296041 0.0125662
\(556\) 0 0
\(557\) −29.4072 −1.24602 −0.623011 0.782213i \(-0.714091\pi\)
−0.623011 + 0.782213i \(0.714091\pi\)
\(558\) 0 0
\(559\) 3.55232 0.150247
\(560\) 0 0
\(561\) 21.3110 0.899749
\(562\) 0 0
\(563\) 25.0200 1.05447 0.527233 0.849721i \(-0.323229\pi\)
0.527233 + 0.849721i \(0.323229\pi\)
\(564\) 0 0
\(565\) −26.9148 −1.13232
\(566\) 0 0
\(567\) 1.05465 0.0442913
\(568\) 0 0
\(569\) −8.67473 −0.363664 −0.181832 0.983330i \(-0.558203\pi\)
−0.181832 + 0.983330i \(0.558203\pi\)
\(570\) 0 0
\(571\) −31.2510 −1.30781 −0.653907 0.756575i \(-0.726871\pi\)
−0.653907 + 0.756575i \(0.726871\pi\)
\(572\) 0 0
\(573\) 24.1225 1.00773
\(574\) 0 0
\(575\) −7.00879 −0.292287
\(576\) 0 0
\(577\) −1.79266 −0.0746295 −0.0373148 0.999304i \(-0.511880\pi\)
−0.0373148 + 0.999304i \(0.511880\pi\)
\(578\) 0 0
\(579\) −3.41216 −0.141804
\(580\) 0 0
\(581\) −10.3182 −0.428070
\(582\) 0 0
\(583\) −3.33993 −0.138326
\(584\) 0 0
\(585\) −10.8590 −0.448965
\(586\) 0 0
\(587\) −2.03057 −0.0838105 −0.0419052 0.999122i \(-0.513343\pi\)
−0.0419052 + 0.999122i \(0.513343\pi\)
\(588\) 0 0
\(589\) −4.10019 −0.168945
\(590\) 0 0
\(591\) 4.66110 0.191732
\(592\) 0 0
\(593\) 32.6066 1.33899 0.669497 0.742815i \(-0.266510\pi\)
0.669497 + 0.742815i \(0.266510\pi\)
\(594\) 0 0
\(595\) −13.8992 −0.569810
\(596\) 0 0
\(597\) 10.4261 0.426713
\(598\) 0 0
\(599\) −34.2306 −1.39862 −0.699311 0.714817i \(-0.746510\pi\)
−0.699311 + 0.714817i \(0.746510\pi\)
\(600\) 0 0
\(601\) 3.20890 0.130894 0.0654468 0.997856i \(-0.479153\pi\)
0.0654468 + 0.997856i \(0.479153\pi\)
\(602\) 0 0
\(603\) −2.10873 −0.0858741
\(604\) 0 0
\(605\) 12.7693 0.519148
\(606\) 0 0
\(607\) −11.2556 −0.456851 −0.228425 0.973561i \(-0.573358\pi\)
−0.228425 + 0.973561i \(0.573358\pi\)
\(608\) 0 0
\(609\) −2.63805 −0.106899
\(610\) 0 0
\(611\) 21.0478 0.851501
\(612\) 0 0
\(613\) 26.4653 1.06892 0.534461 0.845193i \(-0.320515\pi\)
0.534461 + 0.845193i \(0.320515\pi\)
\(614\) 0 0
\(615\) −5.52880 −0.222943
\(616\) 0 0
\(617\) −11.3482 −0.456863 −0.228431 0.973560i \(-0.573360\pi\)
−0.228431 + 0.973560i \(0.573360\pi\)
\(618\) 0 0
\(619\) −39.5468 −1.58952 −0.794760 0.606924i \(-0.792403\pi\)
−0.794760 + 0.606924i \(0.792403\pi\)
\(620\) 0 0
\(621\) −5.97856 −0.239911
\(622\) 0 0
\(623\) 16.1181 0.645759
\(624\) 0 0
\(625\) −29.4873 −1.17949
\(626\) 0 0
\(627\) −16.8051 −0.671131
\(628\) 0 0
\(629\) −0.632094 −0.0252032
\(630\) 0 0
\(631\) 11.9826 0.477022 0.238511 0.971140i \(-0.423341\pi\)
0.238511 + 0.971140i \(0.423341\pi\)
\(632\) 0 0
\(633\) −15.9315 −0.633220
\(634\) 0 0
\(635\) −4.92037 −0.195259
\(636\) 0 0
\(637\) 25.7343 1.01963
\(638\) 0 0
\(639\) −11.8866 −0.470228
\(640\) 0 0
\(641\) 16.5716 0.654540 0.327270 0.944931i \(-0.393871\pi\)
0.327270 + 0.944931i \(0.393871\pi\)
\(642\) 0 0
\(643\) −2.28524 −0.0901211 −0.0450606 0.998984i \(-0.514348\pi\)
−0.0450606 + 0.998984i \(0.514348\pi\)
\(644\) 0 0
\(645\) −2.01915 −0.0795041
\(646\) 0 0
\(647\) 23.3807 0.919191 0.459596 0.888128i \(-0.347994\pi\)
0.459596 + 0.888128i \(0.347994\pi\)
\(648\) 0 0
\(649\) −17.4734 −0.685891
\(650\) 0 0
\(651\) −1.03376 −0.0405164
\(652\) 0 0
\(653\) −8.17792 −0.320027 −0.160013 0.987115i \(-0.551154\pi\)
−0.160013 + 0.987115i \(0.551154\pi\)
\(654\) 0 0
\(655\) 47.2815 1.84744
\(656\) 0 0
\(657\) 13.6096 0.530960
\(658\) 0 0
\(659\) 8.67048 0.337754 0.168877 0.985637i \(-0.445986\pi\)
0.168877 + 0.985637i \(0.445986\pi\)
\(660\) 0 0
\(661\) −8.16325 −0.317514 −0.158757 0.987318i \(-0.550749\pi\)
−0.158757 + 0.987318i \(0.550749\pi\)
\(662\) 0 0
\(663\) 23.1857 0.900459
\(664\) 0 0
\(665\) 10.9604 0.425027
\(666\) 0 0
\(667\) 14.9544 0.579038
\(668\) 0 0
\(669\) 13.5783 0.524968
\(670\) 0 0
\(671\) −12.5243 −0.483495
\(672\) 0 0
\(673\) 32.8917 1.26788 0.633942 0.773381i \(-0.281436\pi\)
0.633942 + 0.773381i \(0.281436\pi\)
\(674\) 0 0
\(675\) 1.17232 0.0451226
\(676\) 0 0
\(677\) −22.4717 −0.863658 −0.431829 0.901956i \(-0.642132\pi\)
−0.431829 + 0.901956i \(0.642132\pi\)
\(678\) 0 0
\(679\) −12.1727 −0.467144
\(680\) 0 0
\(681\) 1.76364 0.0675827
\(682\) 0 0
\(683\) −7.64770 −0.292631 −0.146316 0.989238i \(-0.546741\pi\)
−0.146316 + 0.989238i \(0.546741\pi\)
\(684\) 0 0
\(685\) 39.6206 1.51383
\(686\) 0 0
\(687\) −3.21524 −0.122669
\(688\) 0 0
\(689\) −3.63376 −0.138435
\(690\) 0 0
\(691\) −30.6141 −1.16462 −0.582308 0.812968i \(-0.697850\pi\)
−0.582308 + 0.812968i \(0.697850\pi\)
\(692\) 0 0
\(693\) −4.23700 −0.160950
\(694\) 0 0
\(695\) −31.0774 −1.17883
\(696\) 0 0
\(697\) 11.8049 0.447141
\(698\) 0 0
\(699\) 25.8981 0.979557
\(700\) 0 0
\(701\) 8.36913 0.316098 0.158049 0.987431i \(-0.449480\pi\)
0.158049 + 0.987431i \(0.449480\pi\)
\(702\) 0 0
\(703\) 0.498448 0.0187993
\(704\) 0 0
\(705\) −11.9636 −0.450577
\(706\) 0 0
\(707\) −20.8144 −0.782808
\(708\) 0 0
\(709\) 27.3941 1.02881 0.514403 0.857549i \(-0.328014\pi\)
0.514403 + 0.857549i \(0.328014\pi\)
\(710\) 0 0
\(711\) −4.21360 −0.158022
\(712\) 0 0
\(713\) 5.86014 0.219464
\(714\) 0 0
\(715\) 43.6254 1.63150
\(716\) 0 0
\(717\) −2.26966 −0.0847621
\(718\) 0 0
\(719\) 22.5167 0.839732 0.419866 0.907586i \(-0.362077\pi\)
0.419866 + 0.907586i \(0.362077\pi\)
\(720\) 0 0
\(721\) 8.94782 0.333234
\(722\) 0 0
\(723\) 5.61835 0.208949
\(724\) 0 0
\(725\) −2.93238 −0.108906
\(726\) 0 0
\(727\) 17.0213 0.631285 0.315643 0.948878i \(-0.397780\pi\)
0.315643 + 0.948878i \(0.397780\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 4.31121 0.159456
\(732\) 0 0
\(733\) −10.6392 −0.392968 −0.196484 0.980507i \(-0.562952\pi\)
−0.196484 + 0.980507i \(0.562952\pi\)
\(734\) 0 0
\(735\) −14.6275 −0.539544
\(736\) 0 0
\(737\) 8.47168 0.312058
\(738\) 0 0
\(739\) 50.9689 1.87492 0.937460 0.348092i \(-0.113170\pi\)
0.937460 + 0.348092i \(0.113170\pi\)
\(740\) 0 0
\(741\) −18.2835 −0.671661
\(742\) 0 0
\(743\) −15.7645 −0.578344 −0.289172 0.957277i \(-0.593380\pi\)
−0.289172 + 0.957277i \(0.593380\pi\)
\(744\) 0 0
\(745\) −53.2619 −1.95137
\(746\) 0 0
\(747\) −9.78346 −0.357958
\(748\) 0 0
\(749\) −13.2837 −0.485377
\(750\) 0 0
\(751\) −13.1094 −0.478368 −0.239184 0.970974i \(-0.576880\pi\)
−0.239184 + 0.970974i \(0.576880\pi\)
\(752\) 0 0
\(753\) 14.3387 0.522530
\(754\) 0 0
\(755\) −24.0416 −0.874964
\(756\) 0 0
\(757\) −11.6733 −0.424274 −0.212137 0.977240i \(-0.568042\pi\)
−0.212137 + 0.977240i \(0.568042\pi\)
\(758\) 0 0
\(759\) 24.0185 0.871815
\(760\) 0 0
\(761\) −13.4298 −0.486831 −0.243415 0.969922i \(-0.578268\pi\)
−0.243415 + 0.969922i \(0.578268\pi\)
\(762\) 0 0
\(763\) 13.5435 0.490308
\(764\) 0 0
\(765\) −13.1789 −0.476483
\(766\) 0 0
\(767\) −19.0106 −0.686432
\(768\) 0 0
\(769\) 2.33048 0.0840393 0.0420197 0.999117i \(-0.486621\pi\)
0.0420197 + 0.999117i \(0.486621\pi\)
\(770\) 0 0
\(771\) 1.56506 0.0563642
\(772\) 0 0
\(773\) 25.0390 0.900591 0.450296 0.892879i \(-0.351319\pi\)
0.450296 + 0.892879i \(0.351319\pi\)
\(774\) 0 0
\(775\) −1.14910 −0.0412769
\(776\) 0 0
\(777\) 0.125672 0.00450845
\(778\) 0 0
\(779\) −9.30891 −0.333526
\(780\) 0 0
\(781\) 47.7538 1.70876
\(782\) 0 0
\(783\) −2.50134 −0.0893907
\(784\) 0 0
\(785\) −29.8377 −1.06495
\(786\) 0 0
\(787\) 29.5202 1.05228 0.526141 0.850398i \(-0.323639\pi\)
0.526141 + 0.850398i \(0.323639\pi\)
\(788\) 0 0
\(789\) 26.0080 0.925910
\(790\) 0 0
\(791\) −11.4256 −0.406246
\(792\) 0 0
\(793\) −13.6261 −0.483876
\(794\) 0 0
\(795\) 2.06544 0.0732537
\(796\) 0 0
\(797\) 44.1160 1.56267 0.781334 0.624113i \(-0.214540\pi\)
0.781334 + 0.624113i \(0.214540\pi\)
\(798\) 0 0
\(799\) 25.5443 0.903691
\(800\) 0 0
\(801\) 15.2828 0.539993
\(802\) 0 0
\(803\) −54.6755 −1.92946
\(804\) 0 0
\(805\) −15.6650 −0.552119
\(806\) 0 0
\(807\) −25.3580 −0.892643
\(808\) 0 0
\(809\) 18.2833 0.642806 0.321403 0.946942i \(-0.395846\pi\)
0.321403 + 0.946942i \(0.395846\pi\)
\(810\) 0 0
\(811\) −1.91833 −0.0673616 −0.0336808 0.999433i \(-0.510723\pi\)
−0.0336808 + 0.999433i \(0.510723\pi\)
\(812\) 0 0
\(813\) 5.93004 0.207976
\(814\) 0 0
\(815\) −6.19829 −0.217116
\(816\) 0 0
\(817\) −3.39968 −0.118940
\(818\) 0 0
\(819\) −4.60974 −0.161077
\(820\) 0 0
\(821\) −34.8161 −1.21509 −0.607545 0.794286i \(-0.707845\pi\)
−0.607545 + 0.794286i \(0.707845\pi\)
\(822\) 0 0
\(823\) 30.0431 1.04724 0.523618 0.851953i \(-0.324582\pi\)
0.523618 + 0.851953i \(0.324582\pi\)
\(824\) 0 0
\(825\) −4.70972 −0.163971
\(826\) 0 0
\(827\) −20.4809 −0.712192 −0.356096 0.934449i \(-0.615892\pi\)
−0.356096 + 0.934449i \(0.615892\pi\)
\(828\) 0 0
\(829\) 8.60006 0.298692 0.149346 0.988785i \(-0.452283\pi\)
0.149346 + 0.988785i \(0.452283\pi\)
\(830\) 0 0
\(831\) −3.14081 −0.108954
\(832\) 0 0
\(833\) 31.2320 1.08213
\(834\) 0 0
\(835\) 32.2761 1.11696
\(836\) 0 0
\(837\) −0.980193 −0.0338804
\(838\) 0 0
\(839\) 11.0056 0.379957 0.189978 0.981788i \(-0.439158\pi\)
0.189978 + 0.981788i \(0.439158\pi\)
\(840\) 0 0
\(841\) −22.7433 −0.784251
\(842\) 0 0
\(843\) −22.5471 −0.776563
\(844\) 0 0
\(845\) 15.1658 0.521720
\(846\) 0 0
\(847\) 5.42069 0.186257
\(848\) 0 0
\(849\) 31.0880 1.06694
\(850\) 0 0
\(851\) −0.712400 −0.0244208
\(852\) 0 0
\(853\) 24.6178 0.842899 0.421449 0.906852i \(-0.361522\pi\)
0.421449 + 0.906852i \(0.361522\pi\)
\(854\) 0 0
\(855\) 10.3924 0.355413
\(856\) 0 0
\(857\) −6.92536 −0.236566 −0.118283 0.992980i \(-0.537739\pi\)
−0.118283 + 0.992980i \(0.537739\pi\)
\(858\) 0 0
\(859\) −1.13144 −0.0386041 −0.0193021 0.999814i \(-0.506144\pi\)
−0.0193021 + 0.999814i \(0.506144\pi\)
\(860\) 0 0
\(861\) −2.34702 −0.0799862
\(862\) 0 0
\(863\) −2.55593 −0.0870048 −0.0435024 0.999053i \(-0.513852\pi\)
−0.0435024 + 0.999053i \(0.513852\pi\)
\(864\) 0 0
\(865\) 27.5982 0.938367
\(866\) 0 0
\(867\) 11.1390 0.378300
\(868\) 0 0
\(869\) 16.9278 0.574238
\(870\) 0 0
\(871\) 9.21695 0.312304
\(872\) 0 0
\(873\) −11.5419 −0.390633
\(874\) 0 0
\(875\) −10.0293 −0.339052
\(876\) 0 0
\(877\) −32.6626 −1.10294 −0.551468 0.834196i \(-0.685932\pi\)
−0.551468 + 0.834196i \(0.685932\pi\)
\(878\) 0 0
\(879\) 12.6151 0.425498
\(880\) 0 0
\(881\) 1.75551 0.0591446 0.0295723 0.999563i \(-0.490585\pi\)
0.0295723 + 0.999563i \(0.490585\pi\)
\(882\) 0 0
\(883\) −27.9416 −0.940308 −0.470154 0.882584i \(-0.655802\pi\)
−0.470154 + 0.882584i \(0.655802\pi\)
\(884\) 0 0
\(885\) 10.8057 0.363230
\(886\) 0 0
\(887\) −28.0057 −0.940338 −0.470169 0.882576i \(-0.655807\pi\)
−0.470169 + 0.882576i \(0.655807\pi\)
\(888\) 0 0
\(889\) −2.08874 −0.0700539
\(890\) 0 0
\(891\) −4.01743 −0.134589
\(892\) 0 0
\(893\) −20.1434 −0.674072
\(894\) 0 0
\(895\) 0.319401 0.0106764
\(896\) 0 0
\(897\) 26.1314 0.872503
\(898\) 0 0
\(899\) 2.45180 0.0817721
\(900\) 0 0
\(901\) −4.41005 −0.146920
\(902\) 0 0
\(903\) −0.857147 −0.0285241
\(904\) 0 0
\(905\) −3.69963 −0.122980
\(906\) 0 0
\(907\) 19.9592 0.662734 0.331367 0.943502i \(-0.392490\pi\)
0.331367 + 0.943502i \(0.392490\pi\)
\(908\) 0 0
\(909\) −19.7358 −0.654595
\(910\) 0 0
\(911\) −20.8739 −0.691582 −0.345791 0.938312i \(-0.612389\pi\)
−0.345791 + 0.938312i \(0.612389\pi\)
\(912\) 0 0
\(913\) 39.3044 1.30079
\(914\) 0 0
\(915\) 7.74512 0.256046
\(916\) 0 0
\(917\) 20.0714 0.662815
\(918\) 0 0
\(919\) 53.5443 1.76626 0.883132 0.469124i \(-0.155430\pi\)
0.883132 + 0.469124i \(0.155430\pi\)
\(920\) 0 0
\(921\) 12.4460 0.410110
\(922\) 0 0
\(923\) 51.9548 1.71011
\(924\) 0 0
\(925\) 0.139693 0.00459307
\(926\) 0 0
\(927\) 8.48413 0.278655
\(928\) 0 0
\(929\) 54.6576 1.79326 0.896629 0.442783i \(-0.146009\pi\)
0.896629 + 0.442783i \(0.146009\pi\)
\(930\) 0 0
\(931\) −24.6285 −0.807168
\(932\) 0 0
\(933\) 17.8323 0.583803
\(934\) 0 0
\(935\) 52.9453 1.73150
\(936\) 0 0
\(937\) −44.2994 −1.44720 −0.723599 0.690221i \(-0.757513\pi\)
−0.723599 + 0.690221i \(0.757513\pi\)
\(938\) 0 0
\(939\) −26.8191 −0.875209
\(940\) 0 0
\(941\) −53.7847 −1.75333 −0.876666 0.481100i \(-0.840237\pi\)
−0.876666 + 0.481100i \(0.840237\pi\)
\(942\) 0 0
\(943\) 13.3046 0.433258
\(944\) 0 0
\(945\) 2.62020 0.0852351
\(946\) 0 0
\(947\) 39.2958 1.27694 0.638471 0.769646i \(-0.279567\pi\)
0.638471 + 0.769646i \(0.279567\pi\)
\(948\) 0 0
\(949\) −59.4855 −1.93098
\(950\) 0 0
\(951\) −18.9847 −0.615622
\(952\) 0 0
\(953\) 27.4444 0.889013 0.444506 0.895776i \(-0.353379\pi\)
0.444506 + 0.895776i \(0.353379\pi\)
\(954\) 0 0
\(955\) 59.9302 1.93930
\(956\) 0 0
\(957\) 10.0490 0.324838
\(958\) 0 0
\(959\) 16.8193 0.543123
\(960\) 0 0
\(961\) −30.0392 −0.969007
\(962\) 0 0
\(963\) −12.5953 −0.405879
\(964\) 0 0
\(965\) −8.47722 −0.272891
\(966\) 0 0
\(967\) −42.0590 −1.35253 −0.676264 0.736660i \(-0.736402\pi\)
−0.676264 + 0.736660i \(0.736402\pi\)
\(968\) 0 0
\(969\) −22.1895 −0.712828
\(970\) 0 0
\(971\) −22.7144 −0.728940 −0.364470 0.931215i \(-0.618750\pi\)
−0.364470 + 0.931215i \(0.618750\pi\)
\(972\) 0 0
\(973\) −13.1926 −0.422936
\(974\) 0 0
\(975\) −5.12404 −0.164101
\(976\) 0 0
\(977\) −22.1820 −0.709664 −0.354832 0.934930i \(-0.615462\pi\)
−0.354832 + 0.934930i \(0.615462\pi\)
\(978\) 0 0
\(979\) −61.3978 −1.96228
\(980\) 0 0
\(981\) 12.8417 0.410003
\(982\) 0 0
\(983\) −0.722876 −0.0230562 −0.0115281 0.999934i \(-0.503670\pi\)
−0.0115281 + 0.999934i \(0.503670\pi\)
\(984\) 0 0
\(985\) 11.5801 0.368973
\(986\) 0 0
\(987\) −5.07866 −0.161656
\(988\) 0 0
\(989\) 4.85894 0.154505
\(990\) 0 0
\(991\) 43.1987 1.37225 0.686126 0.727482i \(-0.259310\pi\)
0.686126 + 0.727482i \(0.259310\pi\)
\(992\) 0 0
\(993\) 14.3796 0.456321
\(994\) 0 0
\(995\) 25.9028 0.821175
\(996\) 0 0
\(997\) 49.6840 1.57351 0.786755 0.617266i \(-0.211760\pi\)
0.786755 + 0.617266i \(0.211760\pi\)
\(998\) 0 0
\(999\) 0.119159 0.00377003
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 \(a_p\))