Properties

Label 8016.2.a.bg.1.5
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 0
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8016.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-2.04519\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-2.04519 q^{5}\) \(-1.81275 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-2.04519 q^{5}\) \(-1.81275 q^{7}\) \(+1.00000 q^{9}\) \(+1.62116 q^{11}\) \(-3.43477 q^{13}\) \(+2.04519 q^{15}\) \(-4.77393 q^{17}\) \(-5.04637 q^{19}\) \(+1.81275 q^{21}\) \(-3.71784 q^{23}\) \(-0.817207 q^{25}\) \(-1.00000 q^{27}\) \(+5.69513 q^{29}\) \(-4.23616 q^{31}\) \(-1.62116 q^{33}\) \(+3.70741 q^{35}\) \(-2.11506 q^{37}\) \(+3.43477 q^{39}\) \(+2.68365 q^{41}\) \(-12.6956 q^{43}\) \(-2.04519 q^{45}\) \(+8.44574 q^{47}\) \(-3.71395 q^{49}\) \(+4.77393 q^{51}\) \(-2.62431 q^{53}\) \(-3.31557 q^{55}\) \(+5.04637 q^{57}\) \(-0.400667 q^{59}\) \(+0.131727 q^{61}\) \(-1.81275 q^{63}\) \(+7.02474 q^{65}\) \(-6.63043 q^{67}\) \(+3.71784 q^{69}\) \(-12.2723 q^{71}\) \(+13.2063 q^{73}\) \(+0.817207 q^{75}\) \(-2.93875 q^{77}\) \(-2.93266 q^{79}\) \(+1.00000 q^{81}\) \(-15.4039 q^{83}\) \(+9.76358 q^{85}\) \(-5.69513 q^{87}\) \(+5.43002 q^{89}\) \(+6.22636 q^{91}\) \(+4.23616 q^{93}\) \(+10.3208 q^{95}\) \(+9.62800 q^{97}\) \(+1.62116 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 15q^{17} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 17q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 26q^{49} \) \(\mathstrut -\mathstrut 15q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut -\mathstrut 17q^{71} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 37q^{75} \) \(\mathstrut +\mathstrut 30q^{77} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 3q^{87} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 29q^{91} \) \(\mathstrut -\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −2.04519 −0.914636 −0.457318 0.889303i \(-0.651190\pi\)
−0.457318 + 0.889303i \(0.651190\pi\)
\(6\) 0 0
\(7\) −1.81275 −0.685154 −0.342577 0.939490i \(-0.611300\pi\)
−0.342577 + 0.939490i \(0.611300\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 1.62116 0.488797 0.244398 0.969675i \(-0.421410\pi\)
0.244398 + 0.969675i \(0.421410\pi\)
\(12\) 0 0
\(13\) −3.43477 −0.952633 −0.476316 0.879274i \(-0.658028\pi\)
−0.476316 + 0.879274i \(0.658028\pi\)
\(14\) 0 0
\(15\) 2.04519 0.528065
\(16\) 0 0
\(17\) −4.77393 −1.15785 −0.578924 0.815381i \(-0.696527\pi\)
−0.578924 + 0.815381i \(0.696527\pi\)
\(18\) 0 0
\(19\) −5.04637 −1.15772 −0.578859 0.815428i \(-0.696502\pi\)
−0.578859 + 0.815428i \(0.696502\pi\)
\(20\) 0 0
\(21\) 1.81275 0.395574
\(22\) 0 0
\(23\) −3.71784 −0.775222 −0.387611 0.921823i \(-0.626700\pi\)
−0.387611 + 0.921823i \(0.626700\pi\)
\(24\) 0 0
\(25\) −0.817207 −0.163441
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 5.69513 1.05756 0.528780 0.848759i \(-0.322650\pi\)
0.528780 + 0.848759i \(0.322650\pi\)
\(30\) 0 0
\(31\) −4.23616 −0.760836 −0.380418 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(32\) 0 0
\(33\) −1.62116 −0.282207
\(34\) 0 0
\(35\) 3.70741 0.626666
\(36\) 0 0
\(37\) −2.11506 −0.347714 −0.173857 0.984771i \(-0.555623\pi\)
−0.173857 + 0.984771i \(0.555623\pi\)
\(38\) 0 0
\(39\) 3.43477 0.550003
\(40\) 0 0
\(41\) 2.68365 0.419116 0.209558 0.977796i \(-0.432797\pi\)
0.209558 + 0.977796i \(0.432797\pi\)
\(42\) 0 0
\(43\) −12.6956 −1.93606 −0.968030 0.250834i \(-0.919295\pi\)
−0.968030 + 0.250834i \(0.919295\pi\)
\(44\) 0 0
\(45\) −2.04519 −0.304879
\(46\) 0 0
\(47\) 8.44574 1.23194 0.615969 0.787771i \(-0.288765\pi\)
0.615969 + 0.787771i \(0.288765\pi\)
\(48\) 0 0
\(49\) −3.71395 −0.530564
\(50\) 0 0
\(51\) 4.77393 0.668484
\(52\) 0 0
\(53\) −2.62431 −0.360476 −0.180238 0.983623i \(-0.557687\pi\)
−0.180238 + 0.983623i \(0.557687\pi\)
\(54\) 0 0
\(55\) −3.31557 −0.447071
\(56\) 0 0
\(57\) 5.04637 0.668409
\(58\) 0 0
\(59\) −0.400667 −0.0521624 −0.0260812 0.999660i \(-0.508303\pi\)
−0.0260812 + 0.999660i \(0.508303\pi\)
\(60\) 0 0
\(61\) 0.131727 0.0168660 0.00843298 0.999964i \(-0.497316\pi\)
0.00843298 + 0.999964i \(0.497316\pi\)
\(62\) 0 0
\(63\) −1.81275 −0.228385
\(64\) 0 0
\(65\) 7.02474 0.871312
\(66\) 0 0
\(67\) −6.63043 −0.810036 −0.405018 0.914309i \(-0.632735\pi\)
−0.405018 + 0.914309i \(0.632735\pi\)
\(68\) 0 0
\(69\) 3.71784 0.447575
\(70\) 0 0
\(71\) −12.2723 −1.45646 −0.728228 0.685335i \(-0.759656\pi\)
−0.728228 + 0.685335i \(0.759656\pi\)
\(72\) 0 0
\(73\) 13.2063 1.54568 0.772840 0.634601i \(-0.218836\pi\)
0.772840 + 0.634601i \(0.218836\pi\)
\(74\) 0 0
\(75\) 0.817207 0.0943629
\(76\) 0 0
\(77\) −2.93875 −0.334901
\(78\) 0 0
\(79\) −2.93266 −0.329950 −0.164975 0.986298i \(-0.552754\pi\)
−0.164975 + 0.986298i \(0.552754\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −15.4039 −1.69080 −0.845399 0.534135i \(-0.820637\pi\)
−0.845399 + 0.534135i \(0.820637\pi\)
\(84\) 0 0
\(85\) 9.76358 1.05901
\(86\) 0 0
\(87\) −5.69513 −0.610582
\(88\) 0 0
\(89\) 5.43002 0.575581 0.287791 0.957693i \(-0.407079\pi\)
0.287791 + 0.957693i \(0.407079\pi\)
\(90\) 0 0
\(91\) 6.22636 0.652700
\(92\) 0 0
\(93\) 4.23616 0.439269
\(94\) 0 0
\(95\) 10.3208 1.05889
\(96\) 0 0
\(97\) 9.62800 0.977575 0.488788 0.872403i \(-0.337439\pi\)
0.488788 + 0.872403i \(0.337439\pi\)
\(98\) 0 0
\(99\) 1.62116 0.162932
\(100\) 0 0
\(101\) −11.8915 −1.18325 −0.591625 0.806213i \(-0.701513\pi\)
−0.591625 + 0.806213i \(0.701513\pi\)
\(102\) 0 0
\(103\) −6.78324 −0.668372 −0.334186 0.942507i \(-0.608461\pi\)
−0.334186 + 0.942507i \(0.608461\pi\)
\(104\) 0 0
\(105\) −3.70741 −0.361806
\(106\) 0 0
\(107\) 3.79200 0.366586 0.183293 0.983058i \(-0.441324\pi\)
0.183293 + 0.983058i \(0.441324\pi\)
\(108\) 0 0
\(109\) 13.8797 1.32944 0.664719 0.747093i \(-0.268551\pi\)
0.664719 + 0.747093i \(0.268551\pi\)
\(110\) 0 0
\(111\) 2.11506 0.200753
\(112\) 0 0
\(113\) −19.5403 −1.83820 −0.919099 0.394027i \(-0.871082\pi\)
−0.919099 + 0.394027i \(0.871082\pi\)
\(114\) 0 0
\(115\) 7.60367 0.709046
\(116\) 0 0
\(117\) −3.43477 −0.317544
\(118\) 0 0
\(119\) 8.65393 0.793304
\(120\) 0 0
\(121\) −8.37185 −0.761077
\(122\) 0 0
\(123\) −2.68365 −0.241977
\(124\) 0 0
\(125\) 11.8973 1.06413
\(126\) 0 0
\(127\) 4.29936 0.381507 0.190753 0.981638i \(-0.438907\pi\)
0.190753 + 0.981638i \(0.438907\pi\)
\(128\) 0 0
\(129\) 12.6956 1.11778
\(130\) 0 0
\(131\) −15.0965 −1.31898 −0.659492 0.751712i \(-0.729229\pi\)
−0.659492 + 0.751712i \(0.729229\pi\)
\(132\) 0 0
\(133\) 9.14780 0.793215
\(134\) 0 0
\(135\) 2.04519 0.176022
\(136\) 0 0
\(137\) −1.35974 −0.116170 −0.0580852 0.998312i \(-0.518499\pi\)
−0.0580852 + 0.998312i \(0.518499\pi\)
\(138\) 0 0
\(139\) 19.9242 1.68995 0.844973 0.534808i \(-0.179616\pi\)
0.844973 + 0.534808i \(0.179616\pi\)
\(140\) 0 0
\(141\) −8.44574 −0.711259
\(142\) 0 0
\(143\) −5.56829 −0.465644
\(144\) 0 0
\(145\) −11.6476 −0.967282
\(146\) 0 0
\(147\) 3.71395 0.306321
\(148\) 0 0
\(149\) −7.38010 −0.604601 −0.302301 0.953213i \(-0.597755\pi\)
−0.302301 + 0.953213i \(0.597755\pi\)
\(150\) 0 0
\(151\) −15.5284 −1.26368 −0.631841 0.775098i \(-0.717700\pi\)
−0.631841 + 0.775098i \(0.717700\pi\)
\(152\) 0 0
\(153\) −4.77393 −0.385949
\(154\) 0 0
\(155\) 8.66373 0.695888
\(156\) 0 0
\(157\) 19.4332 1.55094 0.775470 0.631385i \(-0.217513\pi\)
0.775470 + 0.631385i \(0.217513\pi\)
\(158\) 0 0
\(159\) 2.62431 0.208121
\(160\) 0 0
\(161\) 6.73949 0.531147
\(162\) 0 0
\(163\) −9.15822 −0.717327 −0.358664 0.933467i \(-0.616767\pi\)
−0.358664 + 0.933467i \(0.616767\pi\)
\(164\) 0 0
\(165\) 3.31557 0.258117
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −1.20239 −0.0924912
\(170\) 0 0
\(171\) −5.04637 −0.385906
\(172\) 0 0
\(173\) −18.5002 −1.40655 −0.703274 0.710919i \(-0.748279\pi\)
−0.703274 + 0.710919i \(0.748279\pi\)
\(174\) 0 0
\(175\) 1.48139 0.111982
\(176\) 0 0
\(177\) 0.400667 0.0301160
\(178\) 0 0
\(179\) −19.2383 −1.43794 −0.718969 0.695042i \(-0.755386\pi\)
−0.718969 + 0.695042i \(0.755386\pi\)
\(180\) 0 0
\(181\) 26.1135 1.94100 0.970501 0.241098i \(-0.0775076\pi\)
0.970501 + 0.241098i \(0.0775076\pi\)
\(182\) 0 0
\(183\) −0.131727 −0.00973757
\(184\) 0 0
\(185\) 4.32569 0.318031
\(186\) 0 0
\(187\) −7.73929 −0.565953
\(188\) 0 0
\(189\) 1.81275 0.131858
\(190\) 0 0
\(191\) 26.0096 1.88199 0.940993 0.338425i \(-0.109894\pi\)
0.940993 + 0.338425i \(0.109894\pi\)
\(192\) 0 0
\(193\) 6.70727 0.482800 0.241400 0.970426i \(-0.422393\pi\)
0.241400 + 0.970426i \(0.422393\pi\)
\(194\) 0 0
\(195\) −7.02474 −0.503052
\(196\) 0 0
\(197\) −20.2795 −1.44486 −0.722429 0.691445i \(-0.756974\pi\)
−0.722429 + 0.691445i \(0.756974\pi\)
\(198\) 0 0
\(199\) 20.4915 1.45260 0.726301 0.687377i \(-0.241238\pi\)
0.726301 + 0.687377i \(0.241238\pi\)
\(200\) 0 0
\(201\) 6.63043 0.467675
\(202\) 0 0
\(203\) −10.3238 −0.724591
\(204\) 0 0
\(205\) −5.48857 −0.383339
\(206\) 0 0
\(207\) −3.71784 −0.258407
\(208\) 0 0
\(209\) −8.18096 −0.565889
\(210\) 0 0
\(211\) 9.74296 0.670733 0.335366 0.942088i \(-0.391140\pi\)
0.335366 + 0.942088i \(0.391140\pi\)
\(212\) 0 0
\(213\) 12.2723 0.840885
\(214\) 0 0
\(215\) 25.9649 1.77079
\(216\) 0 0
\(217\) 7.67908 0.521290
\(218\) 0 0
\(219\) −13.2063 −0.892398
\(220\) 0 0
\(221\) 16.3973 1.10300
\(222\) 0 0
\(223\) −19.0423 −1.27516 −0.637582 0.770382i \(-0.720065\pi\)
−0.637582 + 0.770382i \(0.720065\pi\)
\(224\) 0 0
\(225\) −0.817207 −0.0544804
\(226\) 0 0
\(227\) −24.0274 −1.59476 −0.797378 0.603480i \(-0.793780\pi\)
−0.797378 + 0.603480i \(0.793780\pi\)
\(228\) 0 0
\(229\) −12.6375 −0.835109 −0.417555 0.908652i \(-0.637113\pi\)
−0.417555 + 0.908652i \(0.637113\pi\)
\(230\) 0 0
\(231\) 2.93875 0.193355
\(232\) 0 0
\(233\) 25.0038 1.63805 0.819027 0.573754i \(-0.194514\pi\)
0.819027 + 0.573754i \(0.194514\pi\)
\(234\) 0 0
\(235\) −17.2731 −1.12677
\(236\) 0 0
\(237\) 2.93266 0.190497
\(238\) 0 0
\(239\) −12.9032 −0.834638 −0.417319 0.908760i \(-0.637030\pi\)
−0.417319 + 0.908760i \(0.637030\pi\)
\(240\) 0 0
\(241\) −10.1834 −0.655972 −0.327986 0.944683i \(-0.606370\pi\)
−0.327986 + 0.944683i \(0.606370\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 7.59572 0.485273
\(246\) 0 0
\(247\) 17.3331 1.10288
\(248\) 0 0
\(249\) 15.4039 0.976183
\(250\) 0 0
\(251\) −0.514670 −0.0324857 −0.0162428 0.999868i \(-0.505170\pi\)
−0.0162428 + 0.999868i \(0.505170\pi\)
\(252\) 0 0
\(253\) −6.02719 −0.378926
\(254\) 0 0
\(255\) −9.76358 −0.611419
\(256\) 0 0
\(257\) 22.3692 1.39535 0.697677 0.716412i \(-0.254217\pi\)
0.697677 + 0.716412i \(0.254217\pi\)
\(258\) 0 0
\(259\) 3.83407 0.238237
\(260\) 0 0
\(261\) 5.69513 0.352520
\(262\) 0 0
\(263\) 15.7692 0.972368 0.486184 0.873857i \(-0.338389\pi\)
0.486184 + 0.873857i \(0.338389\pi\)
\(264\) 0 0
\(265\) 5.36720 0.329705
\(266\) 0 0
\(267\) −5.43002 −0.332312
\(268\) 0 0
\(269\) 14.4917 0.883575 0.441788 0.897120i \(-0.354345\pi\)
0.441788 + 0.897120i \(0.354345\pi\)
\(270\) 0 0
\(271\) 28.2465 1.71585 0.857927 0.513772i \(-0.171752\pi\)
0.857927 + 0.513772i \(0.171752\pi\)
\(272\) 0 0
\(273\) −6.22636 −0.376836
\(274\) 0 0
\(275\) −1.32482 −0.0798896
\(276\) 0 0
\(277\) −5.04261 −0.302981 −0.151490 0.988459i \(-0.548407\pi\)
−0.151490 + 0.988459i \(0.548407\pi\)
\(278\) 0 0
\(279\) −4.23616 −0.253612
\(280\) 0 0
\(281\) −16.8548 −1.00547 −0.502736 0.864440i \(-0.667673\pi\)
−0.502736 + 0.864440i \(0.667673\pi\)
\(282\) 0 0
\(283\) −23.2569 −1.38248 −0.691238 0.722627i \(-0.742934\pi\)
−0.691238 + 0.722627i \(0.742934\pi\)
\(284\) 0 0
\(285\) −10.3208 −0.611350
\(286\) 0 0
\(287\) −4.86478 −0.287159
\(288\) 0 0
\(289\) 5.79041 0.340612
\(290\) 0 0
\(291\) −9.62800 −0.564403
\(292\) 0 0
\(293\) 9.38017 0.547995 0.273998 0.961730i \(-0.411654\pi\)
0.273998 + 0.961730i \(0.411654\pi\)
\(294\) 0 0
\(295\) 0.819440 0.0477096
\(296\) 0 0
\(297\) −1.62116 −0.0940690
\(298\) 0 0
\(299\) 12.7699 0.738502
\(300\) 0 0
\(301\) 23.0139 1.32650
\(302\) 0 0
\(303\) 11.8915 0.683150
\(304\) 0 0
\(305\) −0.269407 −0.0154262
\(306\) 0 0
\(307\) −23.3987 −1.33543 −0.667716 0.744416i \(-0.732728\pi\)
−0.667716 + 0.744416i \(0.732728\pi\)
\(308\) 0 0
\(309\) 6.78324 0.385885
\(310\) 0 0
\(311\) 4.38962 0.248912 0.124456 0.992225i \(-0.460281\pi\)
0.124456 + 0.992225i \(0.460281\pi\)
\(312\) 0 0
\(313\) 30.5307 1.72570 0.862848 0.505464i \(-0.168679\pi\)
0.862848 + 0.505464i \(0.168679\pi\)
\(314\) 0 0
\(315\) 3.70741 0.208889
\(316\) 0 0
\(317\) 23.0063 1.29216 0.646082 0.763268i \(-0.276406\pi\)
0.646082 + 0.763268i \(0.276406\pi\)
\(318\) 0 0
\(319\) 9.23270 0.516932
\(320\) 0 0
\(321\) −3.79200 −0.211649
\(322\) 0 0
\(323\) 24.0910 1.34046
\(324\) 0 0
\(325\) 2.80691 0.155700
\(326\) 0 0
\(327\) −13.8797 −0.767552
\(328\) 0 0
\(329\) −15.3100 −0.844067
\(330\) 0 0
\(331\) −21.5613 −1.18512 −0.592559 0.805527i \(-0.701882\pi\)
−0.592559 + 0.805527i \(0.701882\pi\)
\(332\) 0 0
\(333\) −2.11506 −0.115905
\(334\) 0 0
\(335\) 13.5605 0.740888
\(336\) 0 0
\(337\) −3.17835 −0.173136 −0.0865679 0.996246i \(-0.527590\pi\)
−0.0865679 + 0.996246i \(0.527590\pi\)
\(338\) 0 0
\(339\) 19.5403 1.06128
\(340\) 0 0
\(341\) −6.86747 −0.371894
\(342\) 0 0
\(343\) 19.4217 1.04867
\(344\) 0 0
\(345\) −7.60367 −0.409368
\(346\) 0 0
\(347\) 2.98591 0.160292 0.0801460 0.996783i \(-0.474461\pi\)
0.0801460 + 0.996783i \(0.474461\pi\)
\(348\) 0 0
\(349\) 23.1887 1.24126 0.620631 0.784102i \(-0.286876\pi\)
0.620631 + 0.784102i \(0.286876\pi\)
\(350\) 0 0
\(351\) 3.43477 0.183334
\(352\) 0 0
\(353\) 20.7847 1.10626 0.553128 0.833096i \(-0.313434\pi\)
0.553128 + 0.833096i \(0.313434\pi\)
\(354\) 0 0
\(355\) 25.0992 1.33213
\(356\) 0 0
\(357\) −8.65393 −0.458014
\(358\) 0 0
\(359\) 8.44829 0.445884 0.222942 0.974832i \(-0.428434\pi\)
0.222942 + 0.974832i \(0.428434\pi\)
\(360\) 0 0
\(361\) 6.46589 0.340310
\(362\) 0 0
\(363\) 8.37185 0.439408
\(364\) 0 0
\(365\) −27.0093 −1.41373
\(366\) 0 0
\(367\) −2.08409 −0.108789 −0.0543944 0.998520i \(-0.517323\pi\)
−0.0543944 + 0.998520i \(0.517323\pi\)
\(368\) 0 0
\(369\) 2.68365 0.139705
\(370\) 0 0
\(371\) 4.75721 0.246982
\(372\) 0 0
\(373\) −17.7296 −0.918005 −0.459002 0.888435i \(-0.651793\pi\)
−0.459002 + 0.888435i \(0.651793\pi\)
\(374\) 0 0
\(375\) −11.8973 −0.614373
\(376\) 0 0
\(377\) −19.5614 −1.00747
\(378\) 0 0
\(379\) 20.5594 1.05607 0.528034 0.849223i \(-0.322929\pi\)
0.528034 + 0.849223i \(0.322929\pi\)
\(380\) 0 0
\(381\) −4.29936 −0.220263
\(382\) 0 0
\(383\) 20.1341 1.02880 0.514401 0.857550i \(-0.328014\pi\)
0.514401 + 0.857550i \(0.328014\pi\)
\(384\) 0 0
\(385\) 6.01029 0.306313
\(386\) 0 0
\(387\) −12.6956 −0.645353
\(388\) 0 0
\(389\) −30.1426 −1.52829 −0.764146 0.645043i \(-0.776839\pi\)
−0.764146 + 0.645043i \(0.776839\pi\)
\(390\) 0 0
\(391\) 17.7487 0.897590
\(392\) 0 0
\(393\) 15.0965 0.761516
\(394\) 0 0
\(395\) 5.99784 0.301784
\(396\) 0 0
\(397\) 15.2249 0.764116 0.382058 0.924138i \(-0.375215\pi\)
0.382058 + 0.924138i \(0.375215\pi\)
\(398\) 0 0
\(399\) −9.14780 −0.457963
\(400\) 0 0
\(401\) 11.0171 0.550166 0.275083 0.961421i \(-0.411295\pi\)
0.275083 + 0.961421i \(0.411295\pi\)
\(402\) 0 0
\(403\) 14.5502 0.724797
\(404\) 0 0
\(405\) −2.04519 −0.101626
\(406\) 0 0
\(407\) −3.42884 −0.169961
\(408\) 0 0
\(409\) 18.1892 0.899400 0.449700 0.893180i \(-0.351531\pi\)
0.449700 + 0.893180i \(0.351531\pi\)
\(410\) 0 0
\(411\) 1.35974 0.0670710
\(412\) 0 0
\(413\) 0.726308 0.0357393
\(414\) 0 0
\(415\) 31.5039 1.54646
\(416\) 0 0
\(417\) −19.9242 −0.975691
\(418\) 0 0
\(419\) 19.1465 0.935370 0.467685 0.883895i \(-0.345088\pi\)
0.467685 + 0.883895i \(0.345088\pi\)
\(420\) 0 0
\(421\) 34.1391 1.66384 0.831918 0.554899i \(-0.187243\pi\)
0.831918 + 0.554899i \(0.187243\pi\)
\(422\) 0 0
\(423\) 8.44574 0.410646
\(424\) 0 0
\(425\) 3.90129 0.189240
\(426\) 0 0
\(427\) −0.238788 −0.0115558
\(428\) 0 0
\(429\) 5.56829 0.268840
\(430\) 0 0
\(431\) 37.9439 1.82769 0.913846 0.406061i \(-0.133098\pi\)
0.913846 + 0.406061i \(0.133098\pi\)
\(432\) 0 0
\(433\) 31.0410 1.49174 0.745869 0.666093i \(-0.232035\pi\)
0.745869 + 0.666093i \(0.232035\pi\)
\(434\) 0 0
\(435\) 11.6476 0.558460
\(436\) 0 0
\(437\) 18.7616 0.897488
\(438\) 0 0
\(439\) 13.8058 0.658915 0.329458 0.944170i \(-0.393134\pi\)
0.329458 + 0.944170i \(0.393134\pi\)
\(440\) 0 0
\(441\) −3.71395 −0.176855
\(442\) 0 0
\(443\) −27.9941 −1.33004 −0.665021 0.746825i \(-0.731577\pi\)
−0.665021 + 0.746825i \(0.731577\pi\)
\(444\) 0 0
\(445\) −11.1054 −0.526447
\(446\) 0 0
\(447\) 7.38010 0.349067
\(448\) 0 0
\(449\) 17.3679 0.819644 0.409822 0.912166i \(-0.365591\pi\)
0.409822 + 0.912166i \(0.365591\pi\)
\(450\) 0 0
\(451\) 4.35062 0.204863
\(452\) 0 0
\(453\) 15.5284 0.729587
\(454\) 0 0
\(455\) −12.7341 −0.596983
\(456\) 0 0
\(457\) −41.6155 −1.94669 −0.973345 0.229347i \(-0.926341\pi\)
−0.973345 + 0.229347i \(0.926341\pi\)
\(458\) 0 0
\(459\) 4.77393 0.222828
\(460\) 0 0
\(461\) −4.29941 −0.200243 −0.100122 0.994975i \(-0.531923\pi\)
−0.100122 + 0.994975i \(0.531923\pi\)
\(462\) 0 0
\(463\) 37.3526 1.73592 0.867960 0.496634i \(-0.165431\pi\)
0.867960 + 0.496634i \(0.165431\pi\)
\(464\) 0 0
\(465\) −8.66373 −0.401771
\(466\) 0 0
\(467\) −28.1745 −1.30376 −0.651881 0.758321i \(-0.726020\pi\)
−0.651881 + 0.758321i \(0.726020\pi\)
\(468\) 0 0
\(469\) 12.0193 0.554999
\(470\) 0 0
\(471\) −19.4332 −0.895435
\(472\) 0 0
\(473\) −20.5815 −0.946340
\(474\) 0 0
\(475\) 4.12393 0.189219
\(476\) 0 0
\(477\) −2.62431 −0.120159
\(478\) 0 0
\(479\) 9.39801 0.429406 0.214703 0.976679i \(-0.431122\pi\)
0.214703 + 0.976679i \(0.431122\pi\)
\(480\) 0 0
\(481\) 7.26473 0.331243
\(482\) 0 0
\(483\) −6.73949 −0.306658
\(484\) 0 0
\(485\) −19.6911 −0.894125
\(486\) 0 0
\(487\) −10.5408 −0.477650 −0.238825 0.971063i \(-0.576762\pi\)
−0.238825 + 0.971063i \(0.576762\pi\)
\(488\) 0 0
\(489\) 9.15822 0.414149
\(490\) 0 0
\(491\) 14.3694 0.648482 0.324241 0.945975i \(-0.394891\pi\)
0.324241 + 0.945975i \(0.394891\pi\)
\(492\) 0 0
\(493\) −27.1882 −1.22449
\(494\) 0 0
\(495\) −3.31557 −0.149024
\(496\) 0 0
\(497\) 22.2466 0.997896
\(498\) 0 0
\(499\) 29.1966 1.30702 0.653511 0.756917i \(-0.273296\pi\)
0.653511 + 0.756917i \(0.273296\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) −24.1817 −1.07821 −0.539104 0.842239i \(-0.681237\pi\)
−0.539104 + 0.842239i \(0.681237\pi\)
\(504\) 0 0
\(505\) 24.3204 1.08224
\(506\) 0 0
\(507\) 1.20239 0.0533998
\(508\) 0 0
\(509\) −33.3635 −1.47881 −0.739405 0.673260i \(-0.764893\pi\)
−0.739405 + 0.673260i \(0.764893\pi\)
\(510\) 0 0
\(511\) −23.9397 −1.05903
\(512\) 0 0
\(513\) 5.04637 0.222803
\(514\) 0 0
\(515\) 13.8730 0.611317
\(516\) 0 0
\(517\) 13.6919 0.602167
\(518\) 0 0
\(519\) 18.5002 0.812071
\(520\) 0 0
\(521\) −0.496462 −0.0217504 −0.0108752 0.999941i \(-0.503462\pi\)
−0.0108752 + 0.999941i \(0.503462\pi\)
\(522\) 0 0
\(523\) 23.9410 1.04687 0.523434 0.852066i \(-0.324651\pi\)
0.523434 + 0.852066i \(0.324651\pi\)
\(524\) 0 0
\(525\) −1.48139 −0.0646531
\(526\) 0 0
\(527\) 20.2231 0.880932
\(528\) 0 0
\(529\) −9.17770 −0.399030
\(530\) 0 0
\(531\) −0.400667 −0.0173875
\(532\) 0 0
\(533\) −9.21772 −0.399264
\(534\) 0 0
\(535\) −7.75535 −0.335293
\(536\) 0 0
\(537\) 19.2383 0.830194
\(538\) 0 0
\(539\) −6.02089 −0.259338
\(540\) 0 0
\(541\) −19.0931 −0.820876 −0.410438 0.911889i \(-0.634624\pi\)
−0.410438 + 0.911889i \(0.634624\pi\)
\(542\) 0 0
\(543\) −26.1135 −1.12064
\(544\) 0 0
\(545\) −28.3867 −1.21595
\(546\) 0 0
\(547\) −4.49603 −0.192236 −0.0961181 0.995370i \(-0.530643\pi\)
−0.0961181 + 0.995370i \(0.530643\pi\)
\(548\) 0 0
\(549\) 0.131727 0.00562199
\(550\) 0 0
\(551\) −28.7398 −1.22436
\(552\) 0 0
\(553\) 5.31617 0.226066
\(554\) 0 0
\(555\) −4.32569 −0.183615
\(556\) 0 0
\(557\) −30.0454 −1.27306 −0.636532 0.771250i \(-0.719632\pi\)
−0.636532 + 0.771250i \(0.719632\pi\)
\(558\) 0 0
\(559\) 43.6064 1.84435
\(560\) 0 0
\(561\) 7.73929 0.326753
\(562\) 0 0
\(563\) 32.3325 1.36265 0.681326 0.731980i \(-0.261403\pi\)
0.681326 + 0.731980i \(0.261403\pi\)
\(564\) 0 0
\(565\) 39.9636 1.68128
\(566\) 0 0
\(567\) −1.81275 −0.0761282
\(568\) 0 0
\(569\) 20.1979 0.846738 0.423369 0.905957i \(-0.360847\pi\)
0.423369 + 0.905957i \(0.360847\pi\)
\(570\) 0 0
\(571\) −33.2137 −1.38995 −0.694976 0.719033i \(-0.744585\pi\)
−0.694976 + 0.719033i \(0.744585\pi\)
\(572\) 0 0
\(573\) −26.0096 −1.08657
\(574\) 0 0
\(575\) 3.03824 0.126703
\(576\) 0 0
\(577\) −34.6552 −1.44271 −0.721356 0.692564i \(-0.756481\pi\)
−0.721356 + 0.692564i \(0.756481\pi\)
\(578\) 0 0
\(579\) −6.70727 −0.278745
\(580\) 0 0
\(581\) 27.9234 1.15846
\(582\) 0 0
\(583\) −4.25441 −0.176200
\(584\) 0 0
\(585\) 7.02474 0.290437
\(586\) 0 0
\(587\) −3.82995 −0.158079 −0.0790394 0.996871i \(-0.525185\pi\)
−0.0790394 + 0.996871i \(0.525185\pi\)
\(588\) 0 0
\(589\) 21.3772 0.880833
\(590\) 0 0
\(591\) 20.2795 0.834189
\(592\) 0 0
\(593\) −21.3949 −0.878581 −0.439291 0.898345i \(-0.644770\pi\)
−0.439291 + 0.898345i \(0.644770\pi\)
\(594\) 0 0
\(595\) −17.6989 −0.725584
\(596\) 0 0
\(597\) −20.4915 −0.838660
\(598\) 0 0
\(599\) −8.79373 −0.359302 −0.179651 0.983730i \(-0.557497\pi\)
−0.179651 + 0.983730i \(0.557497\pi\)
\(600\) 0 0
\(601\) −0.891749 −0.0363752 −0.0181876 0.999835i \(-0.505790\pi\)
−0.0181876 + 0.999835i \(0.505790\pi\)
\(602\) 0 0
\(603\) −6.63043 −0.270012
\(604\) 0 0
\(605\) 17.1220 0.696109
\(606\) 0 0
\(607\) 20.2852 0.823353 0.411676 0.911330i \(-0.364943\pi\)
0.411676 + 0.911330i \(0.364943\pi\)
\(608\) 0 0
\(609\) 10.3238 0.418343
\(610\) 0 0
\(611\) −29.0091 −1.17358
\(612\) 0 0
\(613\) 11.1524 0.450441 0.225221 0.974308i \(-0.427690\pi\)
0.225221 + 0.974308i \(0.427690\pi\)
\(614\) 0 0
\(615\) 5.48857 0.221321
\(616\) 0 0
\(617\) −33.1142 −1.33313 −0.666564 0.745447i \(-0.732236\pi\)
−0.666564 + 0.745447i \(0.732236\pi\)
\(618\) 0 0
\(619\) 24.3281 0.977828 0.488914 0.872332i \(-0.337393\pi\)
0.488914 + 0.872332i \(0.337393\pi\)
\(620\) 0 0
\(621\) 3.71784 0.149192
\(622\) 0 0
\(623\) −9.84326 −0.394362
\(624\) 0 0
\(625\) −20.2461 −0.809846
\(626\) 0 0
\(627\) 8.18096 0.326716
\(628\) 0 0
\(629\) 10.0971 0.402599
\(630\) 0 0
\(631\) 20.3393 0.809693 0.404846 0.914385i \(-0.367325\pi\)
0.404846 + 0.914385i \(0.367325\pi\)
\(632\) 0 0
\(633\) −9.74296 −0.387248
\(634\) 0 0
\(635\) −8.79300 −0.348940
\(636\) 0 0
\(637\) 12.7565 0.505433
\(638\) 0 0
\(639\) −12.2723 −0.485485
\(640\) 0 0
\(641\) −12.8194 −0.506338 −0.253169 0.967422i \(-0.581473\pi\)
−0.253169 + 0.967422i \(0.581473\pi\)
\(642\) 0 0
\(643\) 11.5937 0.457211 0.228605 0.973519i \(-0.426583\pi\)
0.228605 + 0.973519i \(0.426583\pi\)
\(644\) 0 0
\(645\) −25.9649 −1.02237
\(646\) 0 0
\(647\) −3.44127 −0.135290 −0.0676452 0.997709i \(-0.521549\pi\)
−0.0676452 + 0.997709i \(0.521549\pi\)
\(648\) 0 0
\(649\) −0.649544 −0.0254968
\(650\) 0 0
\(651\) −7.67908 −0.300967
\(652\) 0 0
\(653\) 23.9286 0.936400 0.468200 0.883622i \(-0.344903\pi\)
0.468200 + 0.883622i \(0.344903\pi\)
\(654\) 0 0
\(655\) 30.8751 1.20639
\(656\) 0 0
\(657\) 13.2063 0.515226
\(658\) 0 0
\(659\) −20.8812 −0.813417 −0.406708 0.913558i \(-0.633323\pi\)
−0.406708 + 0.913558i \(0.633323\pi\)
\(660\) 0 0
\(661\) 29.7368 1.15663 0.578314 0.815814i \(-0.303711\pi\)
0.578314 + 0.815814i \(0.303711\pi\)
\(662\) 0 0
\(663\) −16.3973 −0.636820
\(664\) 0 0
\(665\) −18.7090 −0.725503
\(666\) 0 0
\(667\) −21.1736 −0.819844
\(668\) 0 0
\(669\) 19.0423 0.736217
\(670\) 0 0
\(671\) 0.213551 0.00824403
\(672\) 0 0
\(673\) 4.94319 0.190546 0.0952730 0.995451i \(-0.469628\pi\)
0.0952730 + 0.995451i \(0.469628\pi\)
\(674\) 0 0
\(675\) 0.817207 0.0314543
\(676\) 0 0
\(677\) 14.2784 0.548764 0.274382 0.961621i \(-0.411527\pi\)
0.274382 + 0.961621i \(0.411527\pi\)
\(678\) 0 0
\(679\) −17.4531 −0.669789
\(680\) 0 0
\(681\) 24.0274 0.920733
\(682\) 0 0
\(683\) −23.5913 −0.902694 −0.451347 0.892348i \(-0.649056\pi\)
−0.451347 + 0.892348i \(0.649056\pi\)
\(684\) 0 0
\(685\) 2.78092 0.106254
\(686\) 0 0
\(687\) 12.6375 0.482151
\(688\) 0 0
\(689\) 9.01388 0.343402
\(690\) 0 0
\(691\) −23.3287 −0.887467 −0.443733 0.896159i \(-0.646346\pi\)
−0.443733 + 0.896159i \(0.646346\pi\)
\(692\) 0 0
\(693\) −2.93875 −0.111634
\(694\) 0 0
\(695\) −40.7487 −1.54569
\(696\) 0 0
\(697\) −12.8116 −0.485273
\(698\) 0 0
\(699\) −25.0038 −0.945731
\(700\) 0 0
\(701\) 30.0234 1.13397 0.566984 0.823729i \(-0.308110\pi\)
0.566984 + 0.823729i \(0.308110\pi\)
\(702\) 0 0
\(703\) 10.6734 0.402554
\(704\) 0 0
\(705\) 17.2731 0.650543
\(706\) 0 0
\(707\) 21.5563 0.810709
\(708\) 0 0
\(709\) −15.6410 −0.587410 −0.293705 0.955896i \(-0.594888\pi\)
−0.293705 + 0.955896i \(0.594888\pi\)
\(710\) 0 0
\(711\) −2.93266 −0.109983
\(712\) 0 0
\(713\) 15.7493 0.589817
\(714\) 0 0
\(715\) 11.3882 0.425895
\(716\) 0 0
\(717\) 12.9032 0.481878
\(718\) 0 0
\(719\) −8.66277 −0.323067 −0.161533 0.986867i \(-0.551644\pi\)
−0.161533 + 0.986867i \(0.551644\pi\)
\(720\) 0 0
\(721\) 12.2963 0.457938
\(722\) 0 0
\(723\) 10.1834 0.378726
\(724\) 0 0
\(725\) −4.65410 −0.172849
\(726\) 0 0
\(727\) −24.1368 −0.895183 −0.447592 0.894238i \(-0.647718\pi\)
−0.447592 + 0.894238i \(0.647718\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 60.6079 2.24166
\(732\) 0 0
\(733\) −38.9993 −1.44047 −0.720235 0.693730i \(-0.755966\pi\)
−0.720235 + 0.693730i \(0.755966\pi\)
\(734\) 0 0
\(735\) −7.59572 −0.280172
\(736\) 0 0
\(737\) −10.7490 −0.395943
\(738\) 0 0
\(739\) 30.1884 1.11050 0.555250 0.831684i \(-0.312623\pi\)
0.555250 + 0.831684i \(0.312623\pi\)
\(740\) 0 0
\(741\) −17.3331 −0.636748
\(742\) 0 0
\(743\) −10.1790 −0.373432 −0.186716 0.982414i \(-0.559784\pi\)
−0.186716 + 0.982414i \(0.559784\pi\)
\(744\) 0 0
\(745\) 15.0937 0.552990
\(746\) 0 0
\(747\) −15.4039 −0.563599
\(748\) 0 0
\(749\) −6.87394 −0.251168
\(750\) 0 0
\(751\) −14.6388 −0.534179 −0.267089 0.963672i \(-0.586062\pi\)
−0.267089 + 0.963672i \(0.586062\pi\)
\(752\) 0 0
\(753\) 0.514670 0.0187556
\(754\) 0 0
\(755\) 31.7584 1.15581
\(756\) 0 0
\(757\) −40.6501 −1.47745 −0.738727 0.674004i \(-0.764573\pi\)
−0.738727 + 0.674004i \(0.764573\pi\)
\(758\) 0 0
\(759\) 6.02719 0.218773
\(760\) 0 0
\(761\) −33.7343 −1.22287 −0.611434 0.791295i \(-0.709407\pi\)
−0.611434 + 0.791295i \(0.709407\pi\)
\(762\) 0 0
\(763\) −25.1605 −0.910870
\(764\) 0 0
\(765\) 9.76358 0.353003
\(766\) 0 0
\(767\) 1.37620 0.0496916
\(768\) 0 0
\(769\) −9.28736 −0.334911 −0.167455 0.985880i \(-0.553555\pi\)
−0.167455 + 0.985880i \(0.553555\pi\)
\(770\) 0 0
\(771\) −22.3692 −0.805608
\(772\) 0 0
\(773\) −23.0520 −0.829122 −0.414561 0.910021i \(-0.636065\pi\)
−0.414561 + 0.910021i \(0.636065\pi\)
\(774\) 0 0
\(775\) 3.46181 0.124352
\(776\) 0 0
\(777\) −3.83407 −0.137546
\(778\) 0 0
\(779\) −13.5427 −0.485218
\(780\) 0 0
\(781\) −19.8953 −0.711911
\(782\) 0 0
\(783\) −5.69513 −0.203527
\(784\) 0 0
\(785\) −39.7446 −1.41854
\(786\) 0 0
\(787\) −16.4746 −0.587255 −0.293627 0.955920i \(-0.594863\pi\)
−0.293627 + 0.955920i \(0.594863\pi\)
\(788\) 0 0
\(789\) −15.7692 −0.561397
\(790\) 0 0
\(791\) 35.4216 1.25945
\(792\) 0 0
\(793\) −0.452453 −0.0160671
\(794\) 0 0
\(795\) −5.36720 −0.190355
\(796\) 0 0
\(797\) −44.0201 −1.55927 −0.779636 0.626233i \(-0.784596\pi\)
−0.779636 + 0.626233i \(0.784596\pi\)
\(798\) 0 0
\(799\) −40.3194 −1.42640
\(800\) 0 0
\(801\) 5.43002 0.191860
\(802\) 0 0
\(803\) 21.4095 0.755523
\(804\) 0 0
\(805\) −13.7835 −0.485806
\(806\) 0 0
\(807\) −14.4917 −0.510132
\(808\) 0 0
\(809\) 2.92181 0.102726 0.0513628 0.998680i \(-0.483644\pi\)
0.0513628 + 0.998680i \(0.483644\pi\)
\(810\) 0 0
\(811\) 22.6747 0.796217 0.398109 0.917338i \(-0.369667\pi\)
0.398109 + 0.917338i \(0.369667\pi\)
\(812\) 0 0
\(813\) −28.2465 −0.990649
\(814\) 0 0
\(815\) 18.7303 0.656093
\(816\) 0 0
\(817\) 64.0667 2.24141
\(818\) 0 0
\(819\) 6.22636 0.217567
\(820\) 0 0
\(821\) 11.1758 0.390038 0.195019 0.980799i \(-0.437523\pi\)
0.195019 + 0.980799i \(0.437523\pi\)
\(822\) 0 0
\(823\) −14.9066 −0.519613 −0.259806 0.965661i \(-0.583659\pi\)
−0.259806 + 0.965661i \(0.583659\pi\)
\(824\) 0 0
\(825\) 1.32482 0.0461243
\(826\) 0 0
\(827\) 10.7483 0.373754 0.186877 0.982383i \(-0.440163\pi\)
0.186877 + 0.982383i \(0.440163\pi\)
\(828\) 0 0
\(829\) 42.3443 1.47068 0.735339 0.677700i \(-0.237023\pi\)
0.735339 + 0.677700i \(0.237023\pi\)
\(830\) 0 0
\(831\) 5.04261 0.174926
\(832\) 0 0
\(833\) 17.7301 0.614313
\(834\) 0 0
\(835\) −2.04519 −0.0707766
\(836\) 0 0
\(837\) 4.23616 0.146423
\(838\) 0 0
\(839\) 9.10935 0.314490 0.157245 0.987560i \(-0.449739\pi\)
0.157245 + 0.987560i \(0.449739\pi\)
\(840\) 0 0
\(841\) 3.43453 0.118432
\(842\) 0 0
\(843\) 16.8548 0.580510
\(844\) 0 0
\(845\) 2.45911 0.0845958
\(846\) 0 0
\(847\) 15.1760 0.521455
\(848\) 0 0
\(849\) 23.2569 0.798173
\(850\) 0 0
\(851\) 7.86344 0.269555
\(852\) 0 0
\(853\) −20.1422 −0.689656 −0.344828 0.938666i \(-0.612063\pi\)
−0.344828 + 0.938666i \(0.612063\pi\)
\(854\) 0 0
\(855\) 10.3208 0.352963
\(856\) 0 0
\(857\) 12.3338 0.421316 0.210658 0.977560i \(-0.432439\pi\)
0.210658 + 0.977560i \(0.432439\pi\)
\(858\) 0 0
\(859\) −37.6878 −1.28589 −0.642945 0.765912i \(-0.722288\pi\)
−0.642945 + 0.765912i \(0.722288\pi\)
\(860\) 0 0
\(861\) 4.86478 0.165791
\(862\) 0 0
\(863\) 18.5076 0.630005 0.315003 0.949091i \(-0.397995\pi\)
0.315003 + 0.949091i \(0.397995\pi\)
\(864\) 0 0
\(865\) 37.8365 1.28648
\(866\) 0 0
\(867\) −5.79041 −0.196653
\(868\) 0 0
\(869\) −4.75430 −0.161278
\(870\) 0 0
\(871\) 22.7740 0.771667
\(872\) 0 0
\(873\) 9.62800 0.325858
\(874\) 0 0
\(875\) −21.5668 −0.729090
\(876\) 0 0
\(877\) −2.78287 −0.0939710 −0.0469855 0.998896i \(-0.514961\pi\)
−0.0469855 + 0.998896i \(0.514961\pi\)
\(878\) 0 0
\(879\) −9.38017 −0.316385
\(880\) 0 0
\(881\) −49.2793 −1.66026 −0.830131 0.557568i \(-0.811735\pi\)
−0.830131 + 0.557568i \(0.811735\pi\)
\(882\) 0 0
\(883\) 22.1741 0.746219 0.373110 0.927787i \(-0.378292\pi\)
0.373110 + 0.927787i \(0.378292\pi\)
\(884\) 0 0
\(885\) −0.819440 −0.0275452
\(886\) 0 0
\(887\) 11.7418 0.394250 0.197125 0.980378i \(-0.436840\pi\)
0.197125 + 0.980378i \(0.436840\pi\)
\(888\) 0 0
\(889\) −7.79365 −0.261391
\(890\) 0 0
\(891\) 1.62116 0.0543108
\(892\) 0 0
\(893\) −42.6204 −1.42624
\(894\) 0 0
\(895\) 39.3459 1.31519
\(896\) 0 0
\(897\) −12.7699 −0.426374
\(898\) 0 0
\(899\) −24.1255 −0.804629
\(900\) 0 0
\(901\) 12.5283 0.417377
\(902\) 0 0
\(903\) −23.0139 −0.765855
\(904\) 0 0
\(905\) −53.4070 −1.77531
\(906\) 0 0
\(907\) 27.7655 0.921938 0.460969 0.887416i \(-0.347502\pi\)
0.460969 + 0.887416i \(0.347502\pi\)
\(908\) 0 0
\(909\) −11.8915 −0.394417
\(910\) 0 0
\(911\) 39.1106 1.29579 0.647896 0.761729i \(-0.275649\pi\)
0.647896 + 0.761729i \(0.275649\pi\)
\(912\) 0 0
\(913\) −24.9721 −0.826457
\(914\) 0 0
\(915\) 0.269407 0.00890633
\(916\) 0 0
\(917\) 27.3661 0.903707
\(918\) 0 0
\(919\) −4.66627 −0.153926 −0.0769630 0.997034i \(-0.524522\pi\)
−0.0769630 + 0.997034i \(0.524522\pi\)
\(920\) 0 0
\(921\) 23.3987 0.771012
\(922\) 0 0
\(923\) 42.1525 1.38747
\(924\) 0 0
\(925\) 1.72844 0.0568308
\(926\) 0 0
\(927\) −6.78324 −0.222791
\(928\) 0 0
\(929\) 2.00389 0.0657454 0.0328727 0.999460i \(-0.489534\pi\)
0.0328727 + 0.999460i \(0.489534\pi\)
\(930\) 0 0
\(931\) 18.7420 0.614243
\(932\) 0 0
\(933\) −4.38962 −0.143710
\(934\) 0 0
\(935\) 15.8283 0.517641
\(936\) 0 0
\(937\) 41.0177 1.33999 0.669994 0.742366i \(-0.266297\pi\)
0.669994 + 0.742366i \(0.266297\pi\)
\(938\) 0 0
\(939\) −30.5307 −0.996331
\(940\) 0 0
\(941\) −28.9672 −0.944302 −0.472151 0.881518i \(-0.656522\pi\)
−0.472151 + 0.881518i \(0.656522\pi\)
\(942\) 0 0
\(943\) −9.97738 −0.324908
\(944\) 0 0
\(945\) −3.70741 −0.120602
\(946\) 0 0
\(947\) −56.9248 −1.84981 −0.924905 0.380199i \(-0.875855\pi\)
−0.924905 + 0.380199i \(0.875855\pi\)
\(948\) 0 0
\(949\) −45.3605 −1.47246
\(950\) 0 0
\(951\) −23.0063 −0.746031
\(952\) 0 0
\(953\) 6.31738 0.204640 0.102320 0.994752i \(-0.467373\pi\)
0.102320 + 0.994752i \(0.467373\pi\)
\(954\) 0 0
\(955\) −53.1945 −1.72133
\(956\) 0 0
\(957\) −9.23270 −0.298451
\(958\) 0 0
\(959\) 2.46486 0.0795946
\(960\) 0 0
\(961\) −13.0550 −0.421129
\(962\) 0 0
\(963\) 3.79200 0.122195
\(964\) 0 0
\(965\) −13.7176 −0.441586
\(966\) 0 0
\(967\) −3.63830 −0.117000 −0.0585000 0.998287i \(-0.518632\pi\)
−0.0585000 + 0.998287i \(0.518632\pi\)
\(968\) 0 0
\(969\) −24.0910 −0.773916
\(970\) 0 0
\(971\) 56.4885 1.81280 0.906402 0.422417i \(-0.138818\pi\)
0.906402 + 0.422417i \(0.138818\pi\)
\(972\) 0 0
\(973\) −36.1175 −1.15787
\(974\) 0 0
\(975\) −2.80691 −0.0898932
\(976\) 0 0
\(977\) 29.4542 0.942322 0.471161 0.882047i \(-0.343835\pi\)
0.471161 + 0.882047i \(0.343835\pi\)
\(978\) 0 0
\(979\) 8.80292 0.281342
\(980\) 0 0
\(981\) 13.8797 0.443146
\(982\) 0 0
\(983\) −44.6845 −1.42521 −0.712607 0.701564i \(-0.752486\pi\)
−0.712607 + 0.701564i \(0.752486\pi\)
\(984\) 0 0
\(985\) 41.4755 1.32152
\(986\) 0 0
\(987\) 15.3100 0.487322
\(988\) 0 0
\(989\) 47.2001 1.50088
\(990\) 0 0
\(991\) −53.8233 −1.70975 −0.854877 0.518831i \(-0.826367\pi\)
−0.854877 + 0.518831i \(0.826367\pi\)
\(992\) 0 0
\(993\) 21.5613 0.684229
\(994\) 0 0
\(995\) −41.9089 −1.32860
\(996\) 0 0
\(997\) 32.4015 1.02617 0.513083 0.858339i \(-0.328503\pi\)
0.513083 + 0.858339i \(0.328503\pi\)
\(998\) 0 0
\(999\) 2.11506 0.0669175
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 \(a_p\))