Properties

Label 8048.2.a.v.1.20
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.32661 q^{3}\) \(-1.90684 q^{5}\) \(+4.79236 q^{7}\) \(-1.24010 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.32661 q^{3}\) \(-1.90684 q^{5}\) \(+4.79236 q^{7}\) \(-1.24010 q^{9}\) \(-2.55688 q^{11}\) \(+0.665181 q^{13}\) \(-2.52964 q^{15}\) \(+5.36372 q^{17}\) \(-1.67815 q^{19}\) \(+6.35761 q^{21}\) \(-3.24383 q^{23}\) \(-1.36396 q^{25}\) \(-5.62497 q^{27}\) \(-8.72489 q^{29}\) \(-1.57296 q^{31}\) \(-3.39199 q^{33}\) \(-9.13826 q^{35}\) \(-7.50788 q^{37}\) \(+0.882438 q^{39}\) \(+10.1056 q^{41}\) \(-10.0082 q^{43}\) \(+2.36466 q^{45}\) \(+11.2502 q^{47}\) \(+15.9667 q^{49}\) \(+7.11558 q^{51}\) \(+11.5424 q^{53}\) \(+4.87555 q^{55}\) \(-2.22626 q^{57}\) \(-9.37075 q^{59}\) \(-13.7957 q^{61}\) \(-5.94299 q^{63}\) \(-1.26839 q^{65}\) \(-9.41724 q^{67}\) \(-4.30330 q^{69}\) \(-7.91607 q^{71}\) \(-0.999682 q^{73}\) \(-1.80945 q^{75}\) \(-12.2535 q^{77}\) \(+3.57821 q^{79}\) \(-3.74187 q^{81}\) \(-4.87221 q^{83}\) \(-10.2277 q^{85}\) \(-11.5746 q^{87}\) \(-7.53775 q^{89}\) \(+3.18779 q^{91}\) \(-2.08671 q^{93}\) \(+3.19997 q^{95}\) \(-15.0389 q^{97}\) \(+3.17077 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.32661 0.765921 0.382960 0.923765i \(-0.374905\pi\)
0.382960 + 0.923765i \(0.374905\pi\)
\(4\) 0 0
\(5\) −1.90684 −0.852764 −0.426382 0.904543i \(-0.640212\pi\)
−0.426382 + 0.904543i \(0.640212\pi\)
\(6\) 0 0
\(7\) 4.79236 1.81134 0.905671 0.423981i \(-0.139368\pi\)
0.905671 + 0.423981i \(0.139368\pi\)
\(8\) 0 0
\(9\) −1.24010 −0.413365
\(10\) 0 0
\(11\) −2.55688 −0.770927 −0.385464 0.922723i \(-0.625959\pi\)
−0.385464 + 0.922723i \(0.625959\pi\)
\(12\) 0 0
\(13\) 0.665181 0.184488 0.0922440 0.995736i \(-0.470596\pi\)
0.0922440 + 0.995736i \(0.470596\pi\)
\(14\) 0 0
\(15\) −2.52964 −0.653150
\(16\) 0 0
\(17\) 5.36372 1.30089 0.650446 0.759552i \(-0.274582\pi\)
0.650446 + 0.759552i \(0.274582\pi\)
\(18\) 0 0
\(19\) −1.67815 −0.384995 −0.192497 0.981297i \(-0.561659\pi\)
−0.192497 + 0.981297i \(0.561659\pi\)
\(20\) 0 0
\(21\) 6.35761 1.38734
\(22\) 0 0
\(23\) −3.24383 −0.676384 −0.338192 0.941077i \(-0.609815\pi\)
−0.338192 + 0.941077i \(0.609815\pi\)
\(24\) 0 0
\(25\) −1.36396 −0.272793
\(26\) 0 0
\(27\) −5.62497 −1.08253
\(28\) 0 0
\(29\) −8.72489 −1.62017 −0.810086 0.586311i \(-0.800580\pi\)
−0.810086 + 0.586311i \(0.800580\pi\)
\(30\) 0 0
\(31\) −1.57296 −0.282512 −0.141256 0.989973i \(-0.545114\pi\)
−0.141256 + 0.989973i \(0.545114\pi\)
\(32\) 0 0
\(33\) −3.39199 −0.590469
\(34\) 0 0
\(35\) −9.13826 −1.54465
\(36\) 0 0
\(37\) −7.50788 −1.23429 −0.617144 0.786850i \(-0.711710\pi\)
−0.617144 + 0.786850i \(0.711710\pi\)
\(38\) 0 0
\(39\) 0.882438 0.141303
\(40\) 0 0
\(41\) 10.1056 1.57823 0.789113 0.614248i \(-0.210541\pi\)
0.789113 + 0.614248i \(0.210541\pi\)
\(42\) 0 0
\(43\) −10.0082 −1.52623 −0.763115 0.646263i \(-0.776331\pi\)
−0.763115 + 0.646263i \(0.776331\pi\)
\(44\) 0 0
\(45\) 2.36466 0.352503
\(46\) 0 0
\(47\) 11.2502 1.64100 0.820502 0.571643i \(-0.193694\pi\)
0.820502 + 0.571643i \(0.193694\pi\)
\(48\) 0 0
\(49\) 15.9667 2.28096
\(50\) 0 0
\(51\) 7.11558 0.996380
\(52\) 0 0
\(53\) 11.5424 1.58547 0.792737 0.609564i \(-0.208655\pi\)
0.792737 + 0.609564i \(0.208655\pi\)
\(54\) 0 0
\(55\) 4.87555 0.657420
\(56\) 0 0
\(57\) −2.22626 −0.294876
\(58\) 0 0
\(59\) −9.37075 −1.21997 −0.609984 0.792414i \(-0.708824\pi\)
−0.609984 + 0.792414i \(0.708824\pi\)
\(60\) 0 0
\(61\) −13.7957 −1.76636 −0.883182 0.469030i \(-0.844603\pi\)
−0.883182 + 0.469030i \(0.844603\pi\)
\(62\) 0 0
\(63\) −5.94299 −0.748746
\(64\) 0 0
\(65\) −1.26839 −0.157325
\(66\) 0 0
\(67\) −9.41724 −1.15050 −0.575249 0.817978i \(-0.695095\pi\)
−0.575249 + 0.817978i \(0.695095\pi\)
\(68\) 0 0
\(69\) −4.30330 −0.518057
\(70\) 0 0
\(71\) −7.91607 −0.939465 −0.469732 0.882809i \(-0.655650\pi\)
−0.469732 + 0.882809i \(0.655650\pi\)
\(72\) 0 0
\(73\) −0.999682 −0.117004 −0.0585019 0.998287i \(-0.518632\pi\)
−0.0585019 + 0.998287i \(0.518632\pi\)
\(74\) 0 0
\(75\) −1.80945 −0.208938
\(76\) 0 0
\(77\) −12.2535 −1.39641
\(78\) 0 0
\(79\) 3.57821 0.402580 0.201290 0.979532i \(-0.435487\pi\)
0.201290 + 0.979532i \(0.435487\pi\)
\(80\) 0 0
\(81\) −3.74187 −0.415764
\(82\) 0 0
\(83\) −4.87221 −0.534794 −0.267397 0.963586i \(-0.586164\pi\)
−0.267397 + 0.963586i \(0.586164\pi\)
\(84\) 0 0
\(85\) −10.2277 −1.10935
\(86\) 0 0
\(87\) −11.5746 −1.24092
\(88\) 0 0
\(89\) −7.53775 −0.799000 −0.399500 0.916733i \(-0.630816\pi\)
−0.399500 + 0.916733i \(0.630816\pi\)
\(90\) 0 0
\(91\) 3.18779 0.334171
\(92\) 0 0
\(93\) −2.08671 −0.216382
\(94\) 0 0
\(95\) 3.19997 0.328310
\(96\) 0 0
\(97\) −15.0389 −1.52697 −0.763486 0.645825i \(-0.776514\pi\)
−0.763486 + 0.645825i \(0.776514\pi\)
\(98\) 0 0
\(99\) 3.17077 0.318675
\(100\) 0 0
\(101\) −2.54967 −0.253701 −0.126851 0.991922i \(-0.540487\pi\)
−0.126851 + 0.991922i \(0.540487\pi\)
\(102\) 0 0
\(103\) 6.72428 0.662563 0.331282 0.943532i \(-0.392519\pi\)
0.331282 + 0.943532i \(0.392519\pi\)
\(104\) 0 0
\(105\) −12.1229 −1.18308
\(106\) 0 0
\(107\) 4.26681 0.412488 0.206244 0.978501i \(-0.433876\pi\)
0.206244 + 0.978501i \(0.433876\pi\)
\(108\) 0 0
\(109\) 1.78630 0.171097 0.0855485 0.996334i \(-0.472736\pi\)
0.0855485 + 0.996334i \(0.472736\pi\)
\(110\) 0 0
\(111\) −9.96006 −0.945367
\(112\) 0 0
\(113\) −12.5409 −1.17975 −0.589874 0.807495i \(-0.700823\pi\)
−0.589874 + 0.807495i \(0.700823\pi\)
\(114\) 0 0
\(115\) 6.18545 0.576797
\(116\) 0 0
\(117\) −0.824888 −0.0762610
\(118\) 0 0
\(119\) 25.7049 2.35636
\(120\) 0 0
\(121\) −4.46238 −0.405671
\(122\) 0 0
\(123\) 13.4062 1.20880
\(124\) 0 0
\(125\) 12.1351 1.08539
\(126\) 0 0
\(127\) −7.11926 −0.631732 −0.315866 0.948804i \(-0.602295\pi\)
−0.315866 + 0.948804i \(0.602295\pi\)
\(128\) 0 0
\(129\) −13.2770 −1.16897
\(130\) 0 0
\(131\) 18.7961 1.64222 0.821109 0.570771i \(-0.193356\pi\)
0.821109 + 0.570771i \(0.193356\pi\)
\(132\) 0 0
\(133\) −8.04232 −0.697357
\(134\) 0 0
\(135\) 10.7259 0.923140
\(136\) 0 0
\(137\) 9.08018 0.775772 0.387886 0.921707i \(-0.373205\pi\)
0.387886 + 0.921707i \(0.373205\pi\)
\(138\) 0 0
\(139\) 7.21379 0.611866 0.305933 0.952053i \(-0.401032\pi\)
0.305933 + 0.952053i \(0.401032\pi\)
\(140\) 0 0
\(141\) 14.9246 1.25688
\(142\) 0 0
\(143\) −1.70079 −0.142227
\(144\) 0 0
\(145\) 16.6370 1.38163
\(146\) 0 0
\(147\) 21.1817 1.74704
\(148\) 0 0
\(149\) 3.02654 0.247944 0.123972 0.992286i \(-0.460437\pi\)
0.123972 + 0.992286i \(0.460437\pi\)
\(150\) 0 0
\(151\) 17.8973 1.45646 0.728231 0.685332i \(-0.240343\pi\)
0.728231 + 0.685332i \(0.240343\pi\)
\(152\) 0 0
\(153\) −6.65152 −0.537744
\(154\) 0 0
\(155\) 2.99938 0.240916
\(156\) 0 0
\(157\) −18.6516 −1.48856 −0.744278 0.667870i \(-0.767206\pi\)
−0.744278 + 0.667870i \(0.767206\pi\)
\(158\) 0 0
\(159\) 15.3123 1.21435
\(160\) 0 0
\(161\) −15.5456 −1.22516
\(162\) 0 0
\(163\) 2.08328 0.163175 0.0815876 0.996666i \(-0.474001\pi\)
0.0815876 + 0.996666i \(0.474001\pi\)
\(164\) 0 0
\(165\) 6.46798 0.503531
\(166\) 0 0
\(167\) −19.3445 −1.49692 −0.748461 0.663179i \(-0.769207\pi\)
−0.748461 + 0.663179i \(0.769207\pi\)
\(168\) 0 0
\(169\) −12.5575 −0.965964
\(170\) 0 0
\(171\) 2.08107 0.159143
\(172\) 0 0
\(173\) 0.688871 0.0523739 0.0261869 0.999657i \(-0.491663\pi\)
0.0261869 + 0.999657i \(0.491663\pi\)
\(174\) 0 0
\(175\) −6.53661 −0.494121
\(176\) 0 0
\(177\) −12.4314 −0.934399
\(178\) 0 0
\(179\) −1.42163 −0.106257 −0.0531287 0.998588i \(-0.516919\pi\)
−0.0531287 + 0.998588i \(0.516919\pi\)
\(180\) 0 0
\(181\) 9.05657 0.673170 0.336585 0.941653i \(-0.390728\pi\)
0.336585 + 0.941653i \(0.390728\pi\)
\(182\) 0 0
\(183\) −18.3016 −1.35289
\(184\) 0 0
\(185\) 14.3163 1.05256
\(186\) 0 0
\(187\) −13.7144 −1.00289
\(188\) 0 0
\(189\) −26.9569 −1.96083
\(190\) 0 0
\(191\) 14.2733 1.03278 0.516390 0.856353i \(-0.327275\pi\)
0.516390 + 0.856353i \(0.327275\pi\)
\(192\) 0 0
\(193\) 18.4088 1.32510 0.662549 0.749019i \(-0.269475\pi\)
0.662549 + 0.749019i \(0.269475\pi\)
\(194\) 0 0
\(195\) −1.68267 −0.120498
\(196\) 0 0
\(197\) 4.91118 0.349907 0.174953 0.984577i \(-0.444023\pi\)
0.174953 + 0.984577i \(0.444023\pi\)
\(198\) 0 0
\(199\) −16.8155 −1.19202 −0.596011 0.802976i \(-0.703249\pi\)
−0.596011 + 0.802976i \(0.703249\pi\)
\(200\) 0 0
\(201\) −12.4930 −0.881191
\(202\) 0 0
\(203\) −41.8128 −2.93469
\(204\) 0 0
\(205\) −19.2697 −1.34586
\(206\) 0 0
\(207\) 4.02265 0.279594
\(208\) 0 0
\(209\) 4.29083 0.296803
\(210\) 0 0
\(211\) 8.27971 0.569999 0.284999 0.958528i \(-0.408007\pi\)
0.284999 + 0.958528i \(0.408007\pi\)
\(212\) 0 0
\(213\) −10.5016 −0.719556
\(214\) 0 0
\(215\) 19.0840 1.30151
\(216\) 0 0
\(217\) −7.53819 −0.511726
\(218\) 0 0
\(219\) −1.32619 −0.0896157
\(220\) 0 0
\(221\) 3.56784 0.239999
\(222\) 0 0
\(223\) −2.80832 −0.188059 −0.0940296 0.995569i \(-0.529975\pi\)
−0.0940296 + 0.995569i \(0.529975\pi\)
\(224\) 0 0
\(225\) 1.69145 0.112763
\(226\) 0 0
\(227\) 23.1808 1.53857 0.769283 0.638908i \(-0.220613\pi\)
0.769283 + 0.638908i \(0.220613\pi\)
\(228\) 0 0
\(229\) −11.9513 −0.789767 −0.394884 0.918731i \(-0.629215\pi\)
−0.394884 + 0.918731i \(0.629215\pi\)
\(230\) 0 0
\(231\) −16.2556 −1.06954
\(232\) 0 0
\(233\) 7.77158 0.509133 0.254567 0.967055i \(-0.418067\pi\)
0.254567 + 0.967055i \(0.418067\pi\)
\(234\) 0 0
\(235\) −21.4523 −1.39939
\(236\) 0 0
\(237\) 4.74691 0.308345
\(238\) 0 0
\(239\) −7.70866 −0.498632 −0.249316 0.968422i \(-0.580206\pi\)
−0.249316 + 0.968422i \(0.580206\pi\)
\(240\) 0 0
\(241\) −8.42632 −0.542787 −0.271393 0.962468i \(-0.587484\pi\)
−0.271393 + 0.962468i \(0.587484\pi\)
\(242\) 0 0
\(243\) 11.9109 0.764084
\(244\) 0 0
\(245\) −30.4460 −1.94512
\(246\) 0 0
\(247\) −1.11628 −0.0710269
\(248\) 0 0
\(249\) −6.46354 −0.409610
\(250\) 0 0
\(251\) −7.97037 −0.503085 −0.251543 0.967846i \(-0.580938\pi\)
−0.251543 + 0.967846i \(0.580938\pi\)
\(252\) 0 0
\(253\) 8.29406 0.521443
\(254\) 0 0
\(255\) −13.5683 −0.849678
\(256\) 0 0
\(257\) −11.2507 −0.701799 −0.350900 0.936413i \(-0.614124\pi\)
−0.350900 + 0.936413i \(0.614124\pi\)
\(258\) 0 0
\(259\) −35.9805 −2.23572
\(260\) 0 0
\(261\) 10.8197 0.669723
\(262\) 0 0
\(263\) −21.7761 −1.34277 −0.671385 0.741108i \(-0.734300\pi\)
−0.671385 + 0.741108i \(0.734300\pi\)
\(264\) 0 0
\(265\) −22.0095 −1.35204
\(266\) 0 0
\(267\) −9.99969 −0.611971
\(268\) 0 0
\(269\) −26.4280 −1.61134 −0.805672 0.592362i \(-0.798196\pi\)
−0.805672 + 0.592362i \(0.798196\pi\)
\(270\) 0 0
\(271\) −20.7795 −1.26227 −0.631133 0.775675i \(-0.717410\pi\)
−0.631133 + 0.775675i \(0.717410\pi\)
\(272\) 0 0
\(273\) 4.22896 0.255949
\(274\) 0 0
\(275\) 3.48749 0.210303
\(276\) 0 0
\(277\) −27.3774 −1.64495 −0.822474 0.568802i \(-0.807407\pi\)
−0.822474 + 0.568802i \(0.807407\pi\)
\(278\) 0 0
\(279\) 1.95062 0.116781
\(280\) 0 0
\(281\) −16.8364 −1.00437 −0.502187 0.864759i \(-0.667471\pi\)
−0.502187 + 0.864759i \(0.667471\pi\)
\(282\) 0 0
\(283\) 33.4332 1.98740 0.993699 0.112077i \(-0.0357504\pi\)
0.993699 + 0.112077i \(0.0357504\pi\)
\(284\) 0 0
\(285\) 4.24512 0.251459
\(286\) 0 0
\(287\) 48.4296 2.85871
\(288\) 0 0
\(289\) 11.7694 0.692320
\(290\) 0 0
\(291\) −19.9508 −1.16954
\(292\) 0 0
\(293\) −2.23097 −0.130335 −0.0651674 0.997874i \(-0.520758\pi\)
−0.0651674 + 0.997874i \(0.520758\pi\)
\(294\) 0 0
\(295\) 17.8685 1.04035
\(296\) 0 0
\(297\) 14.3824 0.834549
\(298\) 0 0
\(299\) −2.15773 −0.124785
\(300\) 0 0
\(301\) −47.9627 −2.76453
\(302\) 0 0
\(303\) −3.38242 −0.194315
\(304\) 0 0
\(305\) 26.3063 1.50629
\(306\) 0 0
\(307\) −20.6489 −1.17849 −0.589247 0.807953i \(-0.700575\pi\)
−0.589247 + 0.807953i \(0.700575\pi\)
\(308\) 0 0
\(309\) 8.92052 0.507471
\(310\) 0 0
\(311\) −5.49843 −0.311787 −0.155894 0.987774i \(-0.549826\pi\)
−0.155894 + 0.987774i \(0.549826\pi\)
\(312\) 0 0
\(313\) 14.2701 0.806592 0.403296 0.915070i \(-0.367865\pi\)
0.403296 + 0.915070i \(0.367865\pi\)
\(314\) 0 0
\(315\) 11.3323 0.638504
\(316\) 0 0
\(317\) −8.38968 −0.471211 −0.235606 0.971849i \(-0.575707\pi\)
−0.235606 + 0.971849i \(0.575707\pi\)
\(318\) 0 0
\(319\) 22.3085 1.24904
\(320\) 0 0
\(321\) 5.66041 0.315933
\(322\) 0 0
\(323\) −9.00114 −0.500837
\(324\) 0 0
\(325\) −0.907283 −0.0503270
\(326\) 0 0
\(327\) 2.36974 0.131047
\(328\) 0 0
\(329\) 53.9148 2.97242
\(330\) 0 0
\(331\) −0.900231 −0.0494812 −0.0247406 0.999694i \(-0.507876\pi\)
−0.0247406 + 0.999694i \(0.507876\pi\)
\(332\) 0 0
\(333\) 9.31050 0.510212
\(334\) 0 0
\(335\) 17.9572 0.981105
\(336\) 0 0
\(337\) −19.6876 −1.07245 −0.536227 0.844074i \(-0.680151\pi\)
−0.536227 + 0.844074i \(0.680151\pi\)
\(338\) 0 0
\(339\) −16.6369 −0.903594
\(340\) 0 0
\(341\) 4.02186 0.217796
\(342\) 0 0
\(343\) 42.9718 2.32026
\(344\) 0 0
\(345\) 8.20571 0.441781
\(346\) 0 0
\(347\) 16.2797 0.873939 0.436970 0.899476i \(-0.356052\pi\)
0.436970 + 0.899476i \(0.356052\pi\)
\(348\) 0 0
\(349\) 19.0899 1.02186 0.510928 0.859623i \(-0.329302\pi\)
0.510928 + 0.859623i \(0.329302\pi\)
\(350\) 0 0
\(351\) −3.74162 −0.199713
\(352\) 0 0
\(353\) 34.0955 1.81472 0.907360 0.420355i \(-0.138095\pi\)
0.907360 + 0.420355i \(0.138095\pi\)
\(354\) 0 0
\(355\) 15.0947 0.801142
\(356\) 0 0
\(357\) 34.1004 1.80479
\(358\) 0 0
\(359\) −30.4237 −1.60570 −0.802850 0.596181i \(-0.796684\pi\)
−0.802850 + 0.596181i \(0.796684\pi\)
\(360\) 0 0
\(361\) −16.1838 −0.851779
\(362\) 0 0
\(363\) −5.91985 −0.310712
\(364\) 0 0
\(365\) 1.90623 0.0997768
\(366\) 0 0
\(367\) −28.2337 −1.47379 −0.736894 0.676008i \(-0.763708\pi\)
−0.736894 + 0.676008i \(0.763708\pi\)
\(368\) 0 0
\(369\) −12.5319 −0.652384
\(370\) 0 0
\(371\) 55.3155 2.87184
\(372\) 0 0
\(373\) 12.2737 0.635506 0.317753 0.948174i \(-0.397072\pi\)
0.317753 + 0.948174i \(0.397072\pi\)
\(374\) 0 0
\(375\) 16.0985 0.831325
\(376\) 0 0
\(377\) −5.80363 −0.298902
\(378\) 0 0
\(379\) −12.6268 −0.648593 −0.324297 0.945955i \(-0.605128\pi\)
−0.324297 + 0.945955i \(0.605128\pi\)
\(380\) 0 0
\(381\) −9.44451 −0.483857
\(382\) 0 0
\(383\) −0.325768 −0.0166459 −0.00832297 0.999965i \(-0.502649\pi\)
−0.00832297 + 0.999965i \(0.502649\pi\)
\(384\) 0 0
\(385\) 23.3654 1.19081
\(386\) 0 0
\(387\) 12.4111 0.630891
\(388\) 0 0
\(389\) 8.44660 0.428260 0.214130 0.976805i \(-0.431308\pi\)
0.214130 + 0.976805i \(0.431308\pi\)
\(390\) 0 0
\(391\) −17.3990 −0.879903
\(392\) 0 0
\(393\) 24.9351 1.25781
\(394\) 0 0
\(395\) −6.82308 −0.343306
\(396\) 0 0
\(397\) 11.6227 0.583326 0.291663 0.956521i \(-0.405791\pi\)
0.291663 + 0.956521i \(0.405791\pi\)
\(398\) 0 0
\(399\) −10.6690 −0.534121
\(400\) 0 0
\(401\) −27.1895 −1.35778 −0.678889 0.734241i \(-0.737538\pi\)
−0.678889 + 0.734241i \(0.737538\pi\)
\(402\) 0 0
\(403\) −1.04630 −0.0521200
\(404\) 0 0
\(405\) 7.13515 0.354549
\(406\) 0 0
\(407\) 19.1967 0.951547
\(408\) 0 0
\(409\) −17.0754 −0.844325 −0.422162 0.906520i \(-0.638729\pi\)
−0.422162 + 0.906520i \(0.638729\pi\)
\(410\) 0 0
\(411\) 12.0459 0.594180
\(412\) 0 0
\(413\) −44.9080 −2.20978
\(414\) 0 0
\(415\) 9.29052 0.456054
\(416\) 0 0
\(417\) 9.56991 0.468641
\(418\) 0 0
\(419\) −5.51491 −0.269421 −0.134710 0.990885i \(-0.543010\pi\)
−0.134710 + 0.990885i \(0.543010\pi\)
\(420\) 0 0
\(421\) 18.0908 0.881690 0.440845 0.897583i \(-0.354679\pi\)
0.440845 + 0.897583i \(0.354679\pi\)
\(422\) 0 0
\(423\) −13.9513 −0.678334
\(424\) 0 0
\(425\) −7.31591 −0.354874
\(426\) 0 0
\(427\) −66.1142 −3.19949
\(428\) 0 0
\(429\) −2.25629 −0.108935
\(430\) 0 0
\(431\) 38.2763 1.84371 0.921853 0.387540i \(-0.126675\pi\)
0.921853 + 0.387540i \(0.126675\pi\)
\(432\) 0 0
\(433\) 24.2629 1.16600 0.583001 0.812471i \(-0.301878\pi\)
0.583001 + 0.812471i \(0.301878\pi\)
\(434\) 0 0
\(435\) 22.0708 1.05822
\(436\) 0 0
\(437\) 5.44364 0.260404
\(438\) 0 0
\(439\) −8.37304 −0.399624 −0.199812 0.979834i \(-0.564033\pi\)
−0.199812 + 0.979834i \(0.564033\pi\)
\(440\) 0 0
\(441\) −19.8003 −0.942870
\(442\) 0 0
\(443\) 32.2412 1.53182 0.765912 0.642945i \(-0.222288\pi\)
0.765912 + 0.642945i \(0.222288\pi\)
\(444\) 0 0
\(445\) 14.3733 0.681359
\(446\) 0 0
\(447\) 4.01505 0.189905
\(448\) 0 0
\(449\) −3.55834 −0.167929 −0.0839643 0.996469i \(-0.526758\pi\)
−0.0839643 + 0.996469i \(0.526758\pi\)
\(450\) 0 0
\(451\) −25.8387 −1.21670
\(452\) 0 0
\(453\) 23.7428 1.11553
\(454\) 0 0
\(455\) −6.07860 −0.284969
\(456\) 0 0
\(457\) −14.5155 −0.679008 −0.339504 0.940605i \(-0.610259\pi\)
−0.339504 + 0.940605i \(0.610259\pi\)
\(458\) 0 0
\(459\) −30.1707 −1.40825
\(460\) 0 0
\(461\) −40.0471 −1.86518 −0.932590 0.360938i \(-0.882457\pi\)
−0.932590 + 0.360938i \(0.882457\pi\)
\(462\) 0 0
\(463\) 1.42164 0.0660694 0.0330347 0.999454i \(-0.489483\pi\)
0.0330347 + 0.999454i \(0.489483\pi\)
\(464\) 0 0
\(465\) 3.97902 0.184523
\(466\) 0 0
\(467\) −8.53745 −0.395066 −0.197533 0.980296i \(-0.563293\pi\)
−0.197533 + 0.980296i \(0.563293\pi\)
\(468\) 0 0
\(469\) −45.1308 −2.08395
\(470\) 0 0
\(471\) −24.7434 −1.14012
\(472\) 0 0
\(473\) 25.5896 1.17661
\(474\) 0 0
\(475\) 2.28894 0.105024
\(476\) 0 0
\(477\) −14.3137 −0.655380
\(478\) 0 0
\(479\) −7.03715 −0.321536 −0.160768 0.986992i \(-0.551397\pi\)
−0.160768 + 0.986992i \(0.551397\pi\)
\(480\) 0 0
\(481\) −4.99410 −0.227711
\(482\) 0 0
\(483\) −20.6230 −0.938378
\(484\) 0 0
\(485\) 28.6768 1.30215
\(486\) 0 0
\(487\) −16.6355 −0.753827 −0.376913 0.926249i \(-0.623015\pi\)
−0.376913 + 0.926249i \(0.623015\pi\)
\(488\) 0 0
\(489\) 2.76371 0.124979
\(490\) 0 0
\(491\) 38.0646 1.71783 0.858915 0.512118i \(-0.171139\pi\)
0.858915 + 0.512118i \(0.171139\pi\)
\(492\) 0 0
\(493\) −46.7978 −2.10767
\(494\) 0 0
\(495\) −6.04615 −0.271754
\(496\) 0 0
\(497\) −37.9367 −1.70169
\(498\) 0 0
\(499\) 11.0886 0.496392 0.248196 0.968710i \(-0.420162\pi\)
0.248196 + 0.968710i \(0.420162\pi\)
\(500\) 0 0
\(501\) −25.6627 −1.14652
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 4.86180 0.216347
\(506\) 0 0
\(507\) −16.6590 −0.739852
\(508\) 0 0
\(509\) −41.8784 −1.85623 −0.928114 0.372296i \(-0.878571\pi\)
−0.928114 + 0.372296i \(0.878571\pi\)
\(510\) 0 0
\(511\) −4.79084 −0.211934
\(512\) 0 0
\(513\) 9.43956 0.416767
\(514\) 0 0
\(515\) −12.8221 −0.565010
\(516\) 0 0
\(517\) −28.7653 −1.26510
\(518\) 0 0
\(519\) 0.913866 0.0401142
\(520\) 0 0
\(521\) 39.8325 1.74510 0.872548 0.488529i \(-0.162466\pi\)
0.872548 + 0.488529i \(0.162466\pi\)
\(522\) 0 0
\(523\) 8.78494 0.384139 0.192069 0.981381i \(-0.438480\pi\)
0.192069 + 0.981381i \(0.438480\pi\)
\(524\) 0 0
\(525\) −8.67155 −0.378458
\(526\) 0 0
\(527\) −8.43690 −0.367517
\(528\) 0 0
\(529\) −12.4776 −0.542504
\(530\) 0 0
\(531\) 11.6206 0.504292
\(532\) 0 0
\(533\) 6.72204 0.291164
\(534\) 0 0
\(535\) −8.13613 −0.351755
\(536\) 0 0
\(537\) −1.88595 −0.0813847
\(538\) 0 0
\(539\) −40.8250 −1.75846
\(540\) 0 0
\(541\) 14.6947 0.631776 0.315888 0.948797i \(-0.397698\pi\)
0.315888 + 0.948797i \(0.397698\pi\)
\(542\) 0 0
\(543\) 12.0146 0.515595
\(544\) 0 0
\(545\) −3.40620 −0.145905
\(546\) 0 0
\(547\) −32.3196 −1.38188 −0.690942 0.722910i \(-0.742804\pi\)
−0.690942 + 0.722910i \(0.742804\pi\)
\(548\) 0 0
\(549\) 17.1080 0.730154
\(550\) 0 0
\(551\) 14.6417 0.623758
\(552\) 0 0
\(553\) 17.1481 0.729211
\(554\) 0 0
\(555\) 18.9922 0.806176
\(556\) 0 0
\(557\) −13.2855 −0.562926 −0.281463 0.959572i \(-0.590820\pi\)
−0.281463 + 0.959572i \(0.590820\pi\)
\(558\) 0 0
\(559\) −6.65724 −0.281571
\(560\) 0 0
\(561\) −18.1937 −0.768137
\(562\) 0 0
\(563\) −18.1298 −0.764080 −0.382040 0.924146i \(-0.624778\pi\)
−0.382040 + 0.924146i \(0.624778\pi\)
\(564\) 0 0
\(565\) 23.9135 1.00605
\(566\) 0 0
\(567\) −17.9324 −0.753091
\(568\) 0 0
\(569\) 19.1648 0.803428 0.401714 0.915765i \(-0.368415\pi\)
0.401714 + 0.915765i \(0.368415\pi\)
\(570\) 0 0
\(571\) 5.80333 0.242862 0.121431 0.992600i \(-0.461252\pi\)
0.121431 + 0.992600i \(0.461252\pi\)
\(572\) 0 0
\(573\) 18.9352 0.791028
\(574\) 0 0
\(575\) 4.42446 0.184513
\(576\) 0 0
\(577\) −42.6964 −1.77748 −0.888738 0.458415i \(-0.848417\pi\)
−0.888738 + 0.458415i \(0.848417\pi\)
\(578\) 0 0
\(579\) 24.4214 1.01492
\(580\) 0 0
\(581\) −23.3494 −0.968696
\(582\) 0 0
\(583\) −29.5126 −1.22229
\(584\) 0 0
\(585\) 1.57293 0.0650326
\(586\) 0 0
\(587\) 30.6861 1.26655 0.633276 0.773926i \(-0.281710\pi\)
0.633276 + 0.773926i \(0.281710\pi\)
\(588\) 0 0
\(589\) 2.63967 0.108766
\(590\) 0 0
\(591\) 6.51523 0.268001
\(592\) 0 0
\(593\) 33.8800 1.39128 0.695642 0.718389i \(-0.255120\pi\)
0.695642 + 0.718389i \(0.255120\pi\)
\(594\) 0 0
\(595\) −49.0150 −2.00942
\(596\) 0 0
\(597\) −22.3077 −0.912995
\(598\) 0 0
\(599\) 1.40726 0.0574991 0.0287496 0.999587i \(-0.490847\pi\)
0.0287496 + 0.999587i \(0.490847\pi\)
\(600\) 0 0
\(601\) −1.20083 −0.0489830 −0.0244915 0.999700i \(-0.507797\pi\)
−0.0244915 + 0.999700i \(0.507797\pi\)
\(602\) 0 0
\(603\) 11.6783 0.475576
\(604\) 0 0
\(605\) 8.50904 0.345942
\(606\) 0 0
\(607\) −8.67375 −0.352057 −0.176028 0.984385i \(-0.556325\pi\)
−0.176028 + 0.984385i \(0.556325\pi\)
\(608\) 0 0
\(609\) −55.4695 −2.24774
\(610\) 0 0
\(611\) 7.48340 0.302746
\(612\) 0 0
\(613\) 6.62694 0.267660 0.133830 0.991004i \(-0.457272\pi\)
0.133830 + 0.991004i \(0.457272\pi\)
\(614\) 0 0
\(615\) −25.5635 −1.03082
\(616\) 0 0
\(617\) 31.1730 1.25498 0.627489 0.778625i \(-0.284083\pi\)
0.627489 + 0.778625i \(0.284083\pi\)
\(618\) 0 0
\(619\) 41.5540 1.67020 0.835098 0.550102i \(-0.185411\pi\)
0.835098 + 0.550102i \(0.185411\pi\)
\(620\) 0 0
\(621\) 18.2464 0.732204
\(622\) 0 0
\(623\) −36.1236 −1.44726
\(624\) 0 0
\(625\) −16.3198 −0.652791
\(626\) 0 0
\(627\) 5.69228 0.227328
\(628\) 0 0
\(629\) −40.2701 −1.60568
\(630\) 0 0
\(631\) 5.75268 0.229011 0.114505 0.993423i \(-0.463472\pi\)
0.114505 + 0.993423i \(0.463472\pi\)
\(632\) 0 0
\(633\) 10.9840 0.436574
\(634\) 0 0
\(635\) 13.5753 0.538719
\(636\) 0 0
\(637\) 10.6208 0.420810
\(638\) 0 0
\(639\) 9.81669 0.388342
\(640\) 0 0
\(641\) −17.8737 −0.705967 −0.352983 0.935630i \(-0.614833\pi\)
−0.352983 + 0.935630i \(0.614833\pi\)
\(642\) 0 0
\(643\) 0.176330 0.00695376 0.00347688 0.999994i \(-0.498893\pi\)
0.00347688 + 0.999994i \(0.498893\pi\)
\(644\) 0 0
\(645\) 25.3170 0.996857
\(646\) 0 0
\(647\) −20.8464 −0.819556 −0.409778 0.912185i \(-0.634394\pi\)
−0.409778 + 0.912185i \(0.634394\pi\)
\(648\) 0 0
\(649\) 23.9599 0.940507
\(650\) 0 0
\(651\) −10.0003 −0.391941
\(652\) 0 0
\(653\) −17.8852 −0.699902 −0.349951 0.936768i \(-0.613802\pi\)
−0.349951 + 0.936768i \(0.613802\pi\)
\(654\) 0 0
\(655\) −35.8410 −1.40043
\(656\) 0 0
\(657\) 1.23970 0.0483653
\(658\) 0 0
\(659\) 42.0752 1.63902 0.819509 0.573066i \(-0.194246\pi\)
0.819509 + 0.573066i \(0.194246\pi\)
\(660\) 0 0
\(661\) 13.0492 0.507557 0.253778 0.967262i \(-0.418327\pi\)
0.253778 + 0.967262i \(0.418327\pi\)
\(662\) 0 0
\(663\) 4.73315 0.183820
\(664\) 0 0
\(665\) 15.3354 0.594682
\(666\) 0 0
\(667\) 28.3020 1.09586
\(668\) 0 0
\(669\) −3.72556 −0.144039
\(670\) 0 0
\(671\) 35.2740 1.36174
\(672\) 0 0
\(673\) 6.30308 0.242966 0.121483 0.992594i \(-0.461235\pi\)
0.121483 + 0.992594i \(0.461235\pi\)
\(674\) 0 0
\(675\) 7.67225 0.295305
\(676\) 0 0
\(677\) 15.7333 0.604678 0.302339 0.953200i \(-0.402232\pi\)
0.302339 + 0.953200i \(0.402232\pi\)
\(678\) 0 0
\(679\) −72.0720 −2.76587
\(680\) 0 0
\(681\) 30.7520 1.17842
\(682\) 0 0
\(683\) 38.0044 1.45420 0.727098 0.686534i \(-0.240869\pi\)
0.727098 + 0.686534i \(0.240869\pi\)
\(684\) 0 0
\(685\) −17.3144 −0.661551
\(686\) 0 0
\(687\) −15.8548 −0.604899
\(688\) 0 0
\(689\) 7.67780 0.292501
\(690\) 0 0
\(691\) 7.05114 0.268238 0.134119 0.990965i \(-0.457180\pi\)
0.134119 + 0.990965i \(0.457180\pi\)
\(692\) 0 0
\(693\) 15.1955 0.577229
\(694\) 0 0
\(695\) −13.7555 −0.521777
\(696\) 0 0
\(697\) 54.2034 2.05310
\(698\) 0 0
\(699\) 10.3099 0.389956
\(700\) 0 0
\(701\) 5.10262 0.192723 0.0963617 0.995346i \(-0.469279\pi\)
0.0963617 + 0.995346i \(0.469279\pi\)
\(702\) 0 0
\(703\) 12.5994 0.475195
\(704\) 0 0
\(705\) −28.4589 −1.07182
\(706\) 0 0
\(707\) −12.2189 −0.459540
\(708\) 0 0
\(709\) 5.76858 0.216644 0.108322 0.994116i \(-0.465452\pi\)
0.108322 + 0.994116i \(0.465452\pi\)
\(710\) 0 0
\(711\) −4.43733 −0.166413
\(712\) 0 0
\(713\) 5.10240 0.191087
\(714\) 0 0
\(715\) 3.24313 0.121286
\(716\) 0 0
\(717\) −10.2264 −0.381912
\(718\) 0 0
\(719\) 8.79042 0.327827 0.163914 0.986475i \(-0.447588\pi\)
0.163914 + 0.986475i \(0.447588\pi\)
\(720\) 0 0
\(721\) 32.2252 1.20013
\(722\) 0 0
\(723\) −11.1785 −0.415732
\(724\) 0 0
\(725\) 11.9004 0.441971
\(726\) 0 0
\(727\) −42.1945 −1.56491 −0.782454 0.622708i \(-0.786033\pi\)
−0.782454 + 0.622708i \(0.786033\pi\)
\(728\) 0 0
\(729\) 27.0268 1.00099
\(730\) 0 0
\(731\) −53.6809 −1.98546
\(732\) 0 0
\(733\) −14.7361 −0.544289 −0.272144 0.962256i \(-0.587733\pi\)
−0.272144 + 0.962256i \(0.587733\pi\)
\(734\) 0 0
\(735\) −40.3901 −1.48981
\(736\) 0 0
\(737\) 24.0787 0.886951
\(738\) 0 0
\(739\) −34.3879 −1.26498 −0.632490 0.774569i \(-0.717967\pi\)
−0.632490 + 0.774569i \(0.717967\pi\)
\(740\) 0 0
\(741\) −1.48087 −0.0544010
\(742\) 0 0
\(743\) 33.5162 1.22959 0.614795 0.788687i \(-0.289239\pi\)
0.614795 + 0.788687i \(0.289239\pi\)
\(744\) 0 0
\(745\) −5.77113 −0.211438
\(746\) 0 0
\(747\) 6.04201 0.221065
\(748\) 0 0
\(749\) 20.4481 0.747158
\(750\) 0 0
\(751\) −5.39197 −0.196756 −0.0983778 0.995149i \(-0.531365\pi\)
−0.0983778 + 0.995149i \(0.531365\pi\)
\(752\) 0 0
\(753\) −10.5736 −0.385323
\(754\) 0 0
\(755\) −34.1273 −1.24202
\(756\) 0 0
\(757\) −5.89577 −0.214285 −0.107143 0.994244i \(-0.534170\pi\)
−0.107143 + 0.994244i \(0.534170\pi\)
\(758\) 0 0
\(759\) 11.0030 0.399384
\(760\) 0 0
\(761\) −25.1241 −0.910749 −0.455375 0.890300i \(-0.650495\pi\)
−0.455375 + 0.890300i \(0.650495\pi\)
\(762\) 0 0
\(763\) 8.56062 0.309915
\(764\) 0 0
\(765\) 12.6834 0.458569
\(766\) 0 0
\(767\) −6.23325 −0.225069
\(768\) 0 0
\(769\) −35.9719 −1.29718 −0.648590 0.761138i \(-0.724641\pi\)
−0.648590 + 0.761138i \(0.724641\pi\)
\(770\) 0 0
\(771\) −14.9253 −0.537523
\(772\) 0 0
\(773\) −26.8023 −0.964013 −0.482007 0.876168i \(-0.660092\pi\)
−0.482007 + 0.876168i \(0.660092\pi\)
\(774\) 0 0
\(775\) 2.14546 0.0770672
\(776\) 0 0
\(777\) −47.7322 −1.71238
\(778\) 0 0
\(779\) −16.9587 −0.607609
\(780\) 0 0
\(781\) 20.2404 0.724259
\(782\) 0 0
\(783\) 49.0773 1.75388
\(784\) 0 0
\(785\) 35.5655 1.26939
\(786\) 0 0
\(787\) 32.5261 1.15943 0.579715 0.814820i \(-0.303164\pi\)
0.579715 + 0.814820i \(0.303164\pi\)
\(788\) 0 0
\(789\) −28.8884 −1.02846
\(790\) 0 0
\(791\) −60.1005 −2.13693
\(792\) 0 0
\(793\) −9.17667 −0.325873
\(794\) 0 0
\(795\) −29.1982 −1.03555
\(796\) 0 0
\(797\) −20.1511 −0.713790 −0.356895 0.934145i \(-0.616165\pi\)
−0.356895 + 0.934145i \(0.616165\pi\)
\(798\) 0 0
\(799\) 60.3427 2.13477
\(800\) 0 0
\(801\) 9.34754 0.330279
\(802\) 0 0
\(803\) 2.55606 0.0902015
\(804\) 0 0
\(805\) 29.6429 1.04478
\(806\) 0 0
\(807\) −35.0598 −1.23416
\(808\) 0 0
\(809\) −49.5524 −1.74217 −0.871084 0.491134i \(-0.836583\pi\)
−0.871084 + 0.491134i \(0.836583\pi\)
\(810\) 0 0
\(811\) −37.6036 −1.32044 −0.660220 0.751072i \(-0.729537\pi\)
−0.660220 + 0.751072i \(0.729537\pi\)
\(812\) 0 0
\(813\) −27.5664 −0.966796
\(814\) 0 0
\(815\) −3.97248 −0.139150
\(816\) 0 0
\(817\) 16.7952 0.587591
\(818\) 0 0
\(819\) −3.95316 −0.138135
\(820\) 0 0
\(821\) 1.78688 0.0623625 0.0311812 0.999514i \(-0.490073\pi\)
0.0311812 + 0.999514i \(0.490073\pi\)
\(822\) 0 0
\(823\) −20.2747 −0.706732 −0.353366 0.935485i \(-0.614963\pi\)
−0.353366 + 0.935485i \(0.614963\pi\)
\(824\) 0 0
\(825\) 4.62655 0.161076
\(826\) 0 0
\(827\) 41.7240 1.45089 0.725443 0.688283i \(-0.241635\pi\)
0.725443 + 0.688283i \(0.241635\pi\)
\(828\) 0 0
\(829\) −21.8918 −0.760334 −0.380167 0.924918i \(-0.624133\pi\)
−0.380167 + 0.924918i \(0.624133\pi\)
\(830\) 0 0
\(831\) −36.3192 −1.25990
\(832\) 0 0
\(833\) 85.6410 2.96728
\(834\) 0 0
\(835\) 36.8869 1.27652
\(836\) 0 0
\(837\) 8.84785 0.305826
\(838\) 0 0
\(839\) 9.82934 0.339346 0.169673 0.985500i \(-0.445729\pi\)
0.169673 + 0.985500i \(0.445729\pi\)
\(840\) 0 0
\(841\) 47.1238 1.62496
\(842\) 0 0
\(843\) −22.3354 −0.769271
\(844\) 0 0
\(845\) 23.9452 0.823740
\(846\) 0 0
\(847\) −21.3853 −0.734809
\(848\) 0 0
\(849\) 44.3530 1.52219
\(850\) 0 0
\(851\) 24.3543 0.834853
\(852\) 0 0
\(853\) 10.7591 0.368383 0.184191 0.982890i \(-0.441033\pi\)
0.184191 + 0.982890i \(0.441033\pi\)
\(854\) 0 0
\(855\) −3.96827 −0.135712
\(856\) 0 0
\(857\) −8.46366 −0.289113 −0.144557 0.989497i \(-0.546176\pi\)
−0.144557 + 0.989497i \(0.546176\pi\)
\(858\) 0 0
\(859\) −48.5553 −1.65668 −0.828342 0.560222i \(-0.810716\pi\)
−0.828342 + 0.560222i \(0.810716\pi\)
\(860\) 0 0
\(861\) 64.2474 2.18954
\(862\) 0 0
\(863\) 10.3752 0.353176 0.176588 0.984285i \(-0.443494\pi\)
0.176588 + 0.984285i \(0.443494\pi\)
\(864\) 0 0
\(865\) −1.31357 −0.0446626
\(866\) 0 0
\(867\) 15.6135 0.530262
\(868\) 0 0
\(869\) −9.14905 −0.310360
\(870\) 0 0
\(871\) −6.26417 −0.212253
\(872\) 0 0
\(873\) 18.6497 0.631197
\(874\) 0 0
\(875\) 58.1556 1.96602
\(876\) 0 0
\(877\) 8.38935 0.283288 0.141644 0.989918i \(-0.454761\pi\)
0.141644 + 0.989918i \(0.454761\pi\)
\(878\) 0 0
\(879\) −2.95964 −0.0998261
\(880\) 0 0
\(881\) −33.7646 −1.13756 −0.568778 0.822491i \(-0.692584\pi\)
−0.568778 + 0.822491i \(0.692584\pi\)
\(882\) 0 0
\(883\) 47.4095 1.59546 0.797728 0.603017i \(-0.206035\pi\)
0.797728 + 0.603017i \(0.206035\pi\)
\(884\) 0 0
\(885\) 23.7046 0.796822
\(886\) 0 0
\(887\) −27.6153 −0.927232 −0.463616 0.886036i \(-0.653448\pi\)
−0.463616 + 0.886036i \(0.653448\pi\)
\(888\) 0 0
\(889\) −34.1181 −1.14428
\(890\) 0 0
\(891\) 9.56751 0.320524
\(892\) 0 0
\(893\) −18.8795 −0.631778
\(894\) 0 0
\(895\) 2.71081 0.0906125
\(896\) 0 0
\(897\) −2.86248 −0.0955753
\(898\) 0 0
\(899\) 13.7239 0.457718
\(900\) 0 0
\(901\) 61.9103 2.06253
\(902\) 0 0
\(903\) −63.6280 −2.11741
\(904\) 0 0
\(905\) −17.2694 −0.574055
\(906\) 0 0
\(907\) 2.91293 0.0967221 0.0483610 0.998830i \(-0.484600\pi\)
0.0483610 + 0.998830i \(0.484600\pi\)
\(908\) 0 0
\(909\) 3.16183 0.104871
\(910\) 0 0
\(911\) −10.6566 −0.353068 −0.176534 0.984295i \(-0.556489\pi\)
−0.176534 + 0.984295i \(0.556489\pi\)
\(912\) 0 0
\(913\) 12.4576 0.412288
\(914\) 0 0
\(915\) 34.8983 1.15370
\(916\) 0 0
\(917\) 90.0775 2.97462
\(918\) 0 0
\(919\) 42.5605 1.40394 0.701970 0.712206i \(-0.252304\pi\)
0.701970 + 0.712206i \(0.252304\pi\)
\(920\) 0 0
\(921\) −27.3931 −0.902633
\(922\) 0 0
\(923\) −5.26562 −0.173320
\(924\) 0 0
\(925\) 10.2405 0.336705
\(926\) 0 0
\(927\) −8.33875 −0.273881
\(928\) 0 0
\(929\) −22.6152 −0.741980 −0.370990 0.928637i \(-0.620982\pi\)
−0.370990 + 0.928637i \(0.620982\pi\)
\(930\) 0 0
\(931\) −26.7946 −0.878158
\(932\) 0 0
\(933\) −7.29429 −0.238804
\(934\) 0 0
\(935\) 26.1511 0.855232
\(936\) 0 0
\(937\) 55.9096 1.82649 0.913244 0.407413i \(-0.133569\pi\)
0.913244 + 0.407413i \(0.133569\pi\)
\(938\) 0 0
\(939\) 18.9309 0.617786
\(940\) 0 0
\(941\) −53.6255 −1.74814 −0.874071 0.485798i \(-0.838529\pi\)
−0.874071 + 0.485798i \(0.838529\pi\)
\(942\) 0 0
\(943\) −32.7807 −1.06749
\(944\) 0 0
\(945\) 51.4025 1.67212
\(946\) 0 0
\(947\) 18.2338 0.592519 0.296259 0.955108i \(-0.404261\pi\)
0.296259 + 0.955108i \(0.404261\pi\)
\(948\) 0 0
\(949\) −0.664969 −0.0215858
\(950\) 0 0
\(951\) −11.1299 −0.360911
\(952\) 0 0
\(953\) 3.09947 0.100402 0.0502009 0.998739i \(-0.484014\pi\)
0.0502009 + 0.998739i \(0.484014\pi\)
\(954\) 0 0
\(955\) −27.2169 −0.880718
\(956\) 0 0
\(957\) 29.5947 0.956662
\(958\) 0 0
\(959\) 43.5155 1.40519
\(960\) 0 0
\(961\) −28.5258 −0.920187
\(962\) 0 0
\(963\) −5.29126 −0.170508
\(964\) 0 0
\(965\) −35.1027 −1.13000
\(966\) 0 0
\(967\) −47.8888 −1.54000 −0.770000 0.638044i \(-0.779744\pi\)
−0.770000 + 0.638044i \(0.779744\pi\)
\(968\) 0 0
\(969\) −11.9410 −0.383601
\(970\) 0 0
\(971\) −13.7794 −0.442202 −0.221101 0.975251i \(-0.570965\pi\)
−0.221101 + 0.975251i \(0.570965\pi\)
\(972\) 0 0
\(973\) 34.5711 1.10830
\(974\) 0 0
\(975\) −1.20361 −0.0385465
\(976\) 0 0
\(977\) 40.1880 1.28573 0.642863 0.765981i \(-0.277746\pi\)
0.642863 + 0.765981i \(0.277746\pi\)
\(978\) 0 0
\(979\) 19.2731 0.615971
\(980\) 0 0
\(981\) −2.21519 −0.0707255
\(982\) 0 0
\(983\) 7.44527 0.237467 0.118734 0.992926i \(-0.462117\pi\)
0.118734 + 0.992926i \(0.462117\pi\)
\(984\) 0 0
\(985\) −9.36482 −0.298388
\(986\) 0 0
\(987\) 71.5242 2.27664
\(988\) 0 0
\(989\) 32.4647 1.03232
\(990\) 0 0
\(991\) −19.4370 −0.617437 −0.308719 0.951153i \(-0.599900\pi\)
−0.308719 + 0.951153i \(0.599900\pi\)
\(992\) 0 0
\(993\) −1.19426 −0.0378987
\(994\) 0 0
\(995\) 32.0645 1.01651
\(996\) 0 0
\(997\) 60.9374 1.92991 0.964953 0.262422i \(-0.0845212\pi\)
0.964953 + 0.262422i \(0.0845212\pi\)
\(998\) 0 0
\(999\) 42.2316 1.33615
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 \(a_p\))