Properties

Label 4.18.a.a.1.1
Level 4
Weight 18
Character 4.1
Self dual Yes
Analytic conductor 7.329
Analytic rank 0
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 18 \)
Character orbit: \([\chi]\) = 4.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(7.32888349378\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{9361}) \)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{7}\cdot 3 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(48.8761\)
Character \(\chi\) = 4.1

$q$-expansion

\(f(q)\) \(=\) \(q-21516.4 q^{3} +970774. q^{5} +1.64068e6 q^{7} +3.33817e8 q^{9} +O(q^{10})\) \(q-21516.4 q^{3} +970774. q^{5} +1.64068e6 q^{7} +3.33817e8 q^{9} -7.82166e7 q^{11} +2.36340e9 q^{13} -2.08876e10 q^{15} -1.04976e10 q^{17} +1.03725e11 q^{19} -3.53015e10 q^{21} +3.30946e11 q^{23} +1.79462e11 q^{25} -4.40391e12 q^{27} +3.69924e12 q^{29} +2.53459e12 q^{31} +1.68294e12 q^{33} +1.59273e12 q^{35} +1.96434e13 q^{37} -5.08519e13 q^{39} -3.32602e13 q^{41} -8.49511e13 q^{43} +3.24061e14 q^{45} +2.18640e12 q^{47} -2.29939e14 q^{49} +2.25872e14 q^{51} -1.81963e13 q^{53} -7.59307e13 q^{55} -2.23179e15 q^{57} +1.24801e15 q^{59} +2.09807e15 q^{61} +5.47686e14 q^{63} +2.29433e15 q^{65} -2.53819e15 q^{67} -7.12077e15 q^{69} +8.39308e15 q^{71} -6.50233e15 q^{73} -3.86138e15 q^{75} -1.28328e14 q^{77} -1.41887e16 q^{79} +5.16473e16 q^{81} +1.76295e16 q^{83} -1.01908e16 q^{85} -7.95945e16 q^{87} +2.17799e16 q^{89} +3.87758e15 q^{91} -5.45352e16 q^{93} +1.00694e17 q^{95} -8.31143e16 q^{97} -2.61100e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 5880q^{3} + 604044q^{5} + 25350160q^{7} + 449174682q^{9} + O(q^{10}) \) \( 2q - 5880q^{3} + 604044q^{5} + 25350160q^{7} + 449174682q^{9} + 1259648280q^{11} - 1320052580q^{13} - 26621930448q^{15} - 27498226140q^{17} + 101133633832q^{19} + 335430207552q^{21} + 134767491120q^{23} - 448986850114q^{25} - 4619416117680q^{27} + 2337155582652q^{29} + 278836113472q^{31} + 22602380058720q^{33} - 7102242382752q^{35} + 20929802888140q^{37} - 108447997173648q^{39} + 4166592315732q^{41} - 111143148534440q^{43} + 281755357404444q^{45} + 196772651157600q^{47} + 99570326741874q^{49} - 39956666918256q^{51} - 487965122736660q^{53} - 566565363246960q^{55} - 2272313631999840q^{57} + 2835904197813624q^{59} - 67544034994436q^{61} + 3282762121966800q^{63} + 3645157343001768q^{65} - 995171321546360q^{67} - 10188302100105024q^{69} + 3882245493215376q^{71} - 12746425881769580q^{73} - 13688080703624712q^{75} + 31591755846002880q^{77} - 14984271534065504q^{79} + 33380230287529458q^{81} + 43899417809893800q^{83} - 3956216991540264q^{85} - 100892756486768400q^{87} + 51909007958846388q^{89} - 83455169400462112q^{91} - 89807116632334080q^{93} + 101643889304423664q^{95} - 49281007789848380q^{97} + 128223271309133880q^{99} + O(q^{100}) \)

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
\(3\) −21516.4 −1.89339 −0.946694 0.322134i \(-0.895600\pi\)
−0.946694 + 0.322134i \(0.895600\pi\)
\(4\) 0 0
\(5\) 970774. 1.11141 0.555703 0.831381i \(-0.312449\pi\)
0.555703 + 0.831381i \(0.312449\pi\)
\(6\) 0 0
\(7\) 1.64068e6 0.107570 0.0537849 0.998553i \(-0.482871\pi\)
0.0537849 + 0.998553i \(0.482871\pi\)
\(8\) 0 0
\(9\) 3.33817e8 2.58492
\(10\) 0 0
\(11\) −7.82166e7 −0.110017 −0.0550087 0.998486i \(-0.517519\pi\)
−0.0550087 + 0.998486i \(0.517519\pi\)
\(12\) 0 0
\(13\) 2.36340e9 0.803561 0.401780 0.915736i \(-0.368392\pi\)
0.401780 + 0.915736i \(0.368392\pi\)
\(14\) 0 0
\(15\) −2.08876e10 −2.10432
\(16\) 0 0
\(17\) −1.04976e10 −0.364986 −0.182493 0.983207i \(-0.558417\pi\)
−0.182493 + 0.983207i \(0.558417\pi\)
\(18\) 0 0
\(19\) 1.03725e11 1.40113 0.700564 0.713589i \(-0.252932\pi\)
0.700564 + 0.713589i \(0.252932\pi\)
\(20\) 0 0
\(21\) −3.53015e10 −0.203671
\(22\) 0 0
\(23\) 3.30946e11 0.881191 0.440596 0.897706i \(-0.354767\pi\)
0.440596 + 0.897706i \(0.354767\pi\)
\(24\) 0 0
\(25\) 1.79462e11 0.235224
\(26\) 0 0
\(27\) −4.40391e12 −3.00087
\(28\) 0 0
\(29\) 3.69924e12 1.37319 0.686594 0.727041i \(-0.259105\pi\)
0.686594 + 0.727041i \(0.259105\pi\)
\(30\) 0 0
\(31\) 2.53459e12 0.533743 0.266872 0.963732i \(-0.414010\pi\)
0.266872 + 0.963732i \(0.414010\pi\)
\(32\) 0 0
\(33\) 1.68294e12 0.208306
\(34\) 0 0
\(35\) 1.59273e12 0.119554
\(36\) 0 0
\(37\) 1.96434e13 0.919393 0.459697 0.888076i \(-0.347958\pi\)
0.459697 + 0.888076i \(0.347958\pi\)
\(38\) 0 0
\(39\) −5.08519e13 −1.52145
\(40\) 0 0
\(41\) −3.32602e13 −0.650522 −0.325261 0.945624i \(-0.605452\pi\)
−0.325261 + 0.945624i \(0.605452\pi\)
\(42\) 0 0
\(43\) −8.49511e13 −1.10838 −0.554188 0.832392i \(-0.686971\pi\)
−0.554188 + 0.832392i \(0.686971\pi\)
\(44\) 0 0
\(45\) 3.24061e14 2.87290
\(46\) 0 0
\(47\) 2.18640e12 0.0133936 0.00669681 0.999978i \(-0.497868\pi\)
0.00669681 + 0.999978i \(0.497868\pi\)
\(48\) 0 0
\(49\) −2.29939e14 −0.988429
\(50\) 0 0
\(51\) 2.25872e14 0.691060
\(52\) 0 0
\(53\) −1.81963e13 −0.0401456 −0.0200728 0.999799i \(-0.506390\pi\)
−0.0200728 + 0.999799i \(0.506390\pi\)
\(54\) 0 0
\(55\) −7.59307e13 −0.122274
\(56\) 0 0
\(57\) −2.23179e15 −2.65288
\(58\) 0 0
\(59\) 1.24801e15 1.10656 0.553282 0.832994i \(-0.313375\pi\)
0.553282 + 0.832994i \(0.313375\pi\)
\(60\) 0 0
\(61\) 2.09807e15 1.40126 0.700628 0.713527i \(-0.252903\pi\)
0.700628 + 0.713527i \(0.252903\pi\)
\(62\) 0 0
\(63\) 5.47686e14 0.278059
\(64\) 0 0
\(65\) 2.29433e15 0.893083
\(66\) 0 0
\(67\) −2.53819e15 −0.763639 −0.381820 0.924237i \(-0.624702\pi\)
−0.381820 + 0.924237i \(0.624702\pi\)
\(68\) 0 0
\(69\) −7.12077e15 −1.66844
\(70\) 0 0
\(71\) 8.39308e15 1.54250 0.771250 0.636532i \(-0.219632\pi\)
0.771250 + 0.636532i \(0.219632\pi\)
\(72\) 0 0
\(73\) −6.50233e15 −0.943680 −0.471840 0.881684i \(-0.656410\pi\)
−0.471840 + 0.881684i \(0.656410\pi\)
\(74\) 0 0
\(75\) −3.86138e15 −0.445371
\(76\) 0 0
\(77\) −1.28328e14 −0.0118345
\(78\) 0 0
\(79\) −1.41887e16 −1.05223 −0.526116 0.850413i \(-0.676352\pi\)
−0.526116 + 0.850413i \(0.676352\pi\)
\(80\) 0 0
\(81\) 5.16473e16 3.09688
\(82\) 0 0
\(83\) 1.76295e16 0.859165 0.429583 0.903028i \(-0.358661\pi\)
0.429583 + 0.903028i \(0.358661\pi\)
\(84\) 0 0
\(85\) −1.01908e16 −0.405648
\(86\) 0 0
\(87\) −7.95945e16 −2.59998
\(88\) 0 0
\(89\) 2.17799e16 0.586464 0.293232 0.956041i \(-0.405269\pi\)
0.293232 + 0.956041i \(0.405269\pi\)
\(90\) 0 0
\(91\) 3.87758e15 0.0864388
\(92\) 0 0
\(93\) −5.45352e16 −1.01058
\(94\) 0 0
\(95\) 1.00694e17 1.55722
\(96\) 0 0
\(97\) −8.31143e16 −1.07675 −0.538377 0.842704i \(-0.680962\pi\)
−0.538377 + 0.842704i \(0.680962\pi\)
\(98\) 0 0
\(99\) −2.61100e16 −0.284386
\(100\) 0 0
\(101\) 1.52559e17 1.40186 0.700931 0.713229i \(-0.252768\pi\)
0.700931 + 0.713229i \(0.252768\pi\)
\(102\) 0 0
\(103\) 1.07476e17 0.835977 0.417989 0.908452i \(-0.362735\pi\)
0.417989 + 0.908452i \(0.362735\pi\)
\(104\) 0 0
\(105\) −3.42698e16 −0.226362
\(106\) 0 0
\(107\) 1.26948e17 0.714274 0.357137 0.934052i \(-0.383753\pi\)
0.357137 + 0.934052i \(0.383753\pi\)
\(108\) 0 0
\(109\) −1.60767e17 −0.772807 −0.386404 0.922330i \(-0.626283\pi\)
−0.386404 + 0.922330i \(0.626283\pi\)
\(110\) 0 0
\(111\) −4.22655e17 −1.74077
\(112\) 0 0
\(113\) −4.76977e17 −1.68784 −0.843919 0.536471i \(-0.819757\pi\)
−0.843919 + 0.536471i \(0.819757\pi\)
\(114\) 0 0
\(115\) 3.21273e17 0.979362
\(116\) 0 0
\(117\) 7.88943e17 2.07714
\(118\) 0 0
\(119\) −1.72233e16 −0.0392614
\(120\) 0 0
\(121\) −4.99329e17 −0.987896
\(122\) 0 0
\(123\) 7.15641e17 1.23169
\(124\) 0 0
\(125\) −5.66425e17 −0.849977
\(126\) 0 0
\(127\) 8.84957e16 0.116035 0.0580177 0.998316i \(-0.481522\pi\)
0.0580177 + 0.998316i \(0.481522\pi\)
\(128\) 0 0
\(129\) 1.82784e18 2.09859
\(130\) 0 0
\(131\) −9.61186e17 −0.968281 −0.484141 0.874990i \(-0.660868\pi\)
−0.484141 + 0.874990i \(0.660868\pi\)
\(132\) 0 0
\(133\) 1.70179e17 0.150719
\(134\) 0 0
\(135\) −4.27520e18 −3.33518
\(136\) 0 0
\(137\) 1.92685e17 0.132655 0.0663273 0.997798i \(-0.478872\pi\)
0.0663273 + 0.997798i \(0.478872\pi\)
\(138\) 0 0
\(139\) 1.69703e18 1.03292 0.516458 0.856313i \(-0.327250\pi\)
0.516458 + 0.856313i \(0.327250\pi\)
\(140\) 0 0
\(141\) −4.70436e16 −0.0253593
\(142\) 0 0
\(143\) −1.84857e17 −0.0884057
\(144\) 0 0
\(145\) 3.59113e18 1.52617
\(146\) 0 0
\(147\) 4.94746e18 1.87148
\(148\) 0 0
\(149\) −5.35576e18 −1.80608 −0.903042 0.429551i \(-0.858672\pi\)
−0.903042 + 0.429551i \(0.858672\pi\)
\(150\) 0 0
\(151\) 4.78142e17 0.143964 0.0719819 0.997406i \(-0.477068\pi\)
0.0719819 + 0.997406i \(0.477068\pi\)
\(152\) 0 0
\(153\) −3.50429e18 −0.943458
\(154\) 0 0
\(155\) 2.46051e18 0.593206
\(156\) 0 0
\(157\) −8.86680e17 −0.191699 −0.0958495 0.995396i \(-0.530557\pi\)
−0.0958495 + 0.995396i \(0.530557\pi\)
\(158\) 0 0
\(159\) 3.91519e17 0.0760112
\(160\) 0 0
\(161\) 5.42976e17 0.0947895
\(162\) 0 0
\(163\) −9.72864e18 −1.52918 −0.764588 0.644519i \(-0.777058\pi\)
−0.764588 + 0.644519i \(0.777058\pi\)
\(164\) 0 0
\(165\) 1.63376e18 0.231512
\(166\) 0 0
\(167\) −1.04608e19 −1.33805 −0.669027 0.743238i \(-0.733289\pi\)
−0.669027 + 0.743238i \(0.733289\pi\)
\(168\) 0 0
\(169\) −3.06476e18 −0.354290
\(170\) 0 0
\(171\) 3.46252e19 3.62180
\(172\) 0 0
\(173\) 1.50783e19 1.42876 0.714381 0.699756i \(-0.246708\pi\)
0.714381 + 0.699756i \(0.246708\pi\)
\(174\) 0 0
\(175\) 2.94439e17 0.0253030
\(176\) 0 0
\(177\) −2.68528e19 −2.09515
\(178\) 0 0
\(179\) 4.59833e18 0.326099 0.163049 0.986618i \(-0.447867\pi\)
0.163049 + 0.986618i \(0.447867\pi\)
\(180\) 0 0
\(181\) 8.29716e18 0.535379 0.267690 0.963505i \(-0.413740\pi\)
0.267690 + 0.963505i \(0.413740\pi\)
\(182\) 0 0
\(183\) −4.51431e19 −2.65312
\(184\) 0 0
\(185\) 1.90693e19 1.02182
\(186\) 0 0
\(187\) 8.21090e17 0.0401548
\(188\) 0 0
\(189\) −7.22540e18 −0.322802
\(190\) 0 0
\(191\) 1.62722e19 0.664756 0.332378 0.943146i \(-0.392149\pi\)
0.332378 + 0.943146i \(0.392149\pi\)
\(192\) 0 0
\(193\) −7.66981e18 −0.286779 −0.143390 0.989666i \(-0.545800\pi\)
−0.143390 + 0.989666i \(0.545800\pi\)
\(194\) 0 0
\(195\) −4.93657e19 −1.69095
\(196\) 0 0
\(197\) 4.94003e19 1.55155 0.775776 0.631008i \(-0.217359\pi\)
0.775776 + 0.631008i \(0.217359\pi\)
\(198\) 0 0
\(199\) −5.51277e18 −0.158898 −0.0794491 0.996839i \(-0.525316\pi\)
−0.0794491 + 0.996839i \(0.525316\pi\)
\(200\) 0 0
\(201\) 5.46128e19 1.44587
\(202\) 0 0
\(203\) 6.06927e18 0.147713
\(204\) 0 0
\(205\) −3.22881e19 −0.722994
\(206\) 0 0
\(207\) 1.10475e20 2.27781
\(208\) 0 0
\(209\) −8.11303e18 −0.154149
\(210\) 0 0
\(211\) −3.73068e19 −0.653712 −0.326856 0.945074i \(-0.605989\pi\)
−0.326856 + 0.945074i \(0.605989\pi\)
\(212\) 0 0
\(213\) −1.80589e20 −2.92055
\(214\) 0 0
\(215\) −8.24683e19 −1.23186
\(216\) 0 0
\(217\) 4.15844e18 0.0574146
\(218\) 0 0
\(219\) 1.39907e20 1.78675
\(220\) 0 0
\(221\) −2.48101e19 −0.293288
\(222\) 0 0
\(223\) 7.68538e19 0.841538 0.420769 0.907168i \(-0.361760\pi\)
0.420769 + 0.907168i \(0.361760\pi\)
\(224\) 0 0
\(225\) 5.99074e19 0.608036
\(226\) 0 0
\(227\) −7.77271e19 −0.731733 −0.365867 0.930667i \(-0.619227\pi\)
−0.365867 + 0.930667i \(0.619227\pi\)
\(228\) 0 0
\(229\) 3.74051e19 0.326835 0.163418 0.986557i \(-0.447748\pi\)
0.163418 + 0.986557i \(0.447748\pi\)
\(230\) 0 0
\(231\) 2.76117e18 0.0224074
\(232\) 0 0
\(233\) −6.95476e19 −0.524514 −0.262257 0.964998i \(-0.584467\pi\)
−0.262257 + 0.964998i \(0.584467\pi\)
\(234\) 0 0
\(235\) 2.12250e18 0.0148858
\(236\) 0 0
\(237\) 3.05290e20 1.99228
\(238\) 0 0
\(239\) 1.27125e20 0.772410 0.386205 0.922413i \(-0.373786\pi\)
0.386205 + 0.922413i \(0.373786\pi\)
\(240\) 0 0
\(241\) 4.16245e19 0.235616 0.117808 0.993036i \(-0.462413\pi\)
0.117808 + 0.993036i \(0.462413\pi\)
\(242\) 0 0
\(243\) −5.42544e20 −2.86274
\(244\) 0 0
\(245\) −2.23218e20 −1.09855
\(246\) 0 0
\(247\) 2.45144e20 1.12589
\(248\) 0 0
\(249\) −3.79324e20 −1.62673
\(250\) 0 0
\(251\) −6.23721e18 −0.0249899 −0.0124949 0.999922i \(-0.503977\pi\)
−0.0124949 + 0.999922i \(0.503977\pi\)
\(252\) 0 0
\(253\) −2.58855e19 −0.0969464
\(254\) 0 0
\(255\) 2.19270e20 0.768048
\(256\) 0 0
\(257\) 1.25865e20 0.412547 0.206274 0.978494i \(-0.433866\pi\)
0.206274 + 0.978494i \(0.433866\pi\)
\(258\) 0 0
\(259\) 3.22284e19 0.0988989
\(260\) 0 0
\(261\) 1.23487e21 3.54958
\(262\) 0 0
\(263\) −5.68084e20 −1.53034 −0.765171 0.643827i \(-0.777345\pi\)
−0.765171 + 0.643827i \(0.777345\pi\)
\(264\) 0 0
\(265\) −1.76645e19 −0.0446181
\(266\) 0 0
\(267\) −4.68626e20 −1.11040
\(268\) 0 0
\(269\) −1.43474e20 −0.319066 −0.159533 0.987193i \(-0.550999\pi\)
−0.159533 + 0.987193i \(0.550999\pi\)
\(270\) 0 0
\(271\) 3.74752e20 0.782537 0.391269 0.920277i \(-0.372036\pi\)
0.391269 + 0.920277i \(0.372036\pi\)
\(272\) 0 0
\(273\) −8.34317e19 −0.163662
\(274\) 0 0
\(275\) −1.40369e19 −0.0258788
\(276\) 0 0
\(277\) −8.63656e20 −1.49714 −0.748571 0.663055i \(-0.769259\pi\)
−0.748571 + 0.663055i \(0.769259\pi\)
\(278\) 0 0
\(279\) 8.46087e20 1.37968
\(280\) 0 0
\(281\) 6.30753e20 0.967956 0.483978 0.875080i \(-0.339191\pi\)
0.483978 + 0.875080i \(0.339191\pi\)
\(282\) 0 0
\(283\) −6.12217e20 −0.884546 −0.442273 0.896880i \(-0.645828\pi\)
−0.442273 + 0.896880i \(0.645828\pi\)
\(284\) 0 0
\(285\) −2.16657e21 −2.94843
\(286\) 0 0
\(287\) −5.45693e19 −0.0699765
\(288\) 0 0
\(289\) −7.17040e20 −0.866785
\(290\) 0 0
\(291\) 1.78832e21 2.03871
\(292\) 0 0
\(293\) 1.44992e21 1.55945 0.779723 0.626125i \(-0.215360\pi\)
0.779723 + 0.626125i \(0.215360\pi\)
\(294\) 0 0
\(295\) 1.21154e21 1.22984
\(296\) 0 0
\(297\) 3.44459e20 0.330147
\(298\) 0 0
\(299\) 7.82157e20 0.708091
\(300\) 0 0
\(301\) −1.39377e20 −0.119228
\(302\) 0 0
\(303\) −3.28252e21 −2.65427
\(304\) 0 0
\(305\) 2.03675e21 1.55736
\(306\) 0 0
\(307\) −2.06695e19 −0.0149505 −0.00747523 0.999972i \(-0.502379\pi\)
−0.00747523 + 0.999972i \(0.502379\pi\)
\(308\) 0 0
\(309\) −2.31250e21 −1.58283
\(310\) 0 0
\(311\) −1.75766e21 −1.13886 −0.569431 0.822039i \(-0.692837\pi\)
−0.569431 + 0.822039i \(0.692837\pi\)
\(312\) 0 0
\(313\) 7.56307e20 0.464057 0.232028 0.972709i \(-0.425464\pi\)
0.232028 + 0.972709i \(0.425464\pi\)
\(314\) 0 0
\(315\) 5.31679e20 0.309037
\(316\) 0 0
\(317\) 1.98212e21 1.09176 0.545880 0.837864i \(-0.316196\pi\)
0.545880 + 0.837864i \(0.316196\pi\)
\(318\) 0 0
\(319\) −2.89342e20 −0.151075
\(320\) 0 0
\(321\) −2.73147e21 −1.35240
\(322\) 0 0
\(323\) −1.08887e21 −0.511392
\(324\) 0 0
\(325\) 4.24140e20 0.189017
\(326\) 0 0
\(327\) 3.45913e21 1.46322
\(328\) 0 0
\(329\) 3.58718e18 0.00144075
\(330\) 0 0
\(331\) −3.67582e21 −1.40222 −0.701109 0.713054i \(-0.747312\pi\)
−0.701109 + 0.713054i \(0.747312\pi\)
\(332\) 0 0
\(333\) 6.55729e21 2.37656
\(334\) 0 0
\(335\) −2.46401e21 −0.848714
\(336\) 0 0
\(337\) −5.16622e20 −0.169168 −0.0845842 0.996416i \(-0.526956\pi\)
−0.0845842 + 0.996416i \(0.526956\pi\)
\(338\) 0 0
\(339\) 1.02628e22 3.19573
\(340\) 0 0
\(341\) −1.98247e20 −0.0587211
\(342\) 0 0
\(343\) −7.58927e20 −0.213895
\(344\) 0 0
\(345\) −6.91266e21 −1.85431
\(346\) 0 0
\(347\) −6.31869e21 −1.61371 −0.806857 0.590747i \(-0.798833\pi\)
−0.806857 + 0.590747i \(0.798833\pi\)
\(348\) 0 0
\(349\) −9.48315e20 −0.230641 −0.115320 0.993328i \(-0.536789\pi\)
−0.115320 + 0.993328i \(0.536789\pi\)
\(350\) 0 0
\(351\) −1.04082e22 −2.41138
\(352\) 0 0
\(353\) 3.35256e21 0.740101 0.370051 0.929012i \(-0.379340\pi\)
0.370051 + 0.929012i \(0.379340\pi\)
\(354\) 0 0
\(355\) 8.14778e21 1.71434
\(356\) 0 0
\(357\) 3.70583e20 0.0743371
\(358\) 0 0
\(359\) −4.50173e21 −0.861146 −0.430573 0.902556i \(-0.641689\pi\)
−0.430573 + 0.902556i \(0.641689\pi\)
\(360\) 0 0
\(361\) 5.27850e21 0.963162
\(362\) 0 0
\(363\) 1.07438e22 1.87047
\(364\) 0 0
\(365\) −6.31229e21 −1.04881
\(366\) 0 0
\(367\) 6.01056e21 0.953353 0.476676 0.879079i \(-0.341841\pi\)
0.476676 + 0.879079i \(0.341841\pi\)
\(368\) 0 0
\(369\) −1.11028e22 −1.68155
\(370\) 0 0
\(371\) −2.98542e19 −0.00431845
\(372\) 0 0
\(373\) −4.77088e21 −0.659285 −0.329643 0.944106i \(-0.606928\pi\)
−0.329643 + 0.944106i \(0.606928\pi\)
\(374\) 0 0
\(375\) 1.21874e22 1.60934
\(376\) 0 0
\(377\) 8.74279e21 1.10344
\(378\) 0 0
\(379\) 4.74004e21 0.571938 0.285969 0.958239i \(-0.407685\pi\)
0.285969 + 0.958239i \(0.407685\pi\)
\(380\) 0 0
\(381\) −1.90411e21 −0.219700
\(382\) 0 0
\(383\) 1.20992e21 0.133526 0.0667631 0.997769i \(-0.478733\pi\)
0.0667631 + 0.997769i \(0.478733\pi\)
\(384\) 0 0
\(385\) −1.24578e20 −0.0131530
\(386\) 0 0
\(387\) −2.83581e22 −2.86506
\(388\) 0 0
\(389\) −4.86368e21 −0.470320 −0.235160 0.971957i \(-0.575561\pi\)
−0.235160 + 0.971957i \(0.575561\pi\)
\(390\) 0 0
\(391\) −3.47415e21 −0.321622
\(392\) 0 0
\(393\) 2.06813e22 1.83333
\(394\) 0 0
\(395\) −1.37740e22 −1.16946
\(396\) 0 0
\(397\) −2.33860e22 −1.90212 −0.951058 0.309013i \(-0.900001\pi\)
−0.951058 + 0.309013i \(0.900001\pi\)
\(398\) 0 0
\(399\) −3.66165e21 −0.285370
\(400\) 0 0
\(401\) 1.49882e22 1.11949 0.559746 0.828664i \(-0.310899\pi\)
0.559746 + 0.828664i \(0.310899\pi\)
\(402\) 0 0
\(403\) 5.99024e21 0.428895
\(404\) 0 0
\(405\) 5.01378e22 3.44190
\(406\) 0 0
\(407\) −1.53644e21 −0.101149
\(408\) 0 0
\(409\) −6.71662e21 −0.424134 −0.212067 0.977255i \(-0.568019\pi\)
−0.212067 + 0.977255i \(0.568019\pi\)
\(410\) 0 0
\(411\) −4.14589e21 −0.251167
\(412\) 0 0
\(413\) 2.04758e21 0.119033
\(414\) 0 0
\(415\) 1.71143e22 0.954882
\(416\) 0 0
\(417\) −3.65141e22 −1.95571
\(418\) 0 0
\(419\) 1.38192e22 0.710663 0.355331 0.934740i \(-0.384368\pi\)
0.355331 + 0.934740i \(0.384368\pi\)
\(420\) 0 0
\(421\) −2.06280e22 −1.01873 −0.509366 0.860550i \(-0.670120\pi\)
−0.509366 + 0.860550i \(0.670120\pi\)
\(422\) 0 0
\(423\) 7.29858e20 0.0346214
\(424\) 0 0
\(425\) −1.88393e21 −0.0858536
\(426\) 0 0
\(427\) 3.44226e21 0.150733
\(428\) 0 0
\(429\) 3.97747e21 0.167386
\(430\) 0 0
\(431\) 2.30892e22 0.934011 0.467005 0.884254i \(-0.345333\pi\)
0.467005 + 0.884254i \(0.345333\pi\)
\(432\) 0 0
\(433\) 1.35763e22 0.527999 0.263999 0.964523i \(-0.414958\pi\)
0.263999 + 0.964523i \(0.414958\pi\)
\(434\) 0 0
\(435\) −7.72683e22 −2.88963
\(436\) 0 0
\(437\) 3.43274e22 1.23466
\(438\) 0 0
\(439\) −4.41799e22 −1.52854 −0.764268 0.644898i \(-0.776900\pi\)
−0.764268 + 0.644898i \(0.776900\pi\)
\(440\) 0 0
\(441\) −7.67574e22 −2.55501
\(442\) 0 0
\(443\) 1.93958e22 0.621263 0.310632 0.950530i \(-0.399459\pi\)
0.310632 + 0.950530i \(0.399459\pi\)
\(444\) 0 0
\(445\) 2.11434e22 0.651800
\(446\) 0 0
\(447\) 1.15237e23 3.41962
\(448\) 0 0
\(449\) 3.18755e22 0.910676 0.455338 0.890319i \(-0.349518\pi\)
0.455338 + 0.890319i \(0.349518\pi\)
\(450\) 0 0
\(451\) 2.60150e21 0.0715687
\(452\) 0 0
\(453\) −1.02879e22 −0.272579
\(454\) 0 0
\(455\) 3.76425e21 0.0960687
\(456\) 0 0
\(457\) 2.48900e22 0.611981 0.305990 0.952035i \(-0.401012\pi\)
0.305990 + 0.952035i \(0.401012\pi\)
\(458\) 0 0
\(459\) 4.62307e22 1.09527
\(460\) 0 0
\(461\) −5.46414e22 −1.24757 −0.623784 0.781597i \(-0.714405\pi\)
−0.623784 + 0.781597i \(0.714405\pi\)
\(462\) 0 0
\(463\) −2.58506e22 −0.568894 −0.284447 0.958692i \(-0.591810\pi\)
−0.284447 + 0.958692i \(0.591810\pi\)
\(464\) 0 0
\(465\) −5.29414e22 −1.12317
\(466\) 0 0
\(467\) −5.73610e22 −1.17334 −0.586669 0.809827i \(-0.699561\pi\)
−0.586669 + 0.809827i \(0.699561\pi\)
\(468\) 0 0
\(469\) −4.16435e21 −0.0821445
\(470\) 0 0
\(471\) 1.90782e22 0.362961
\(472\) 0 0
\(473\) 6.64459e21 0.121941
\(474\) 0 0
\(475\) 1.86147e22 0.329580
\(476\) 0 0
\(477\) −6.07423e21 −0.103773
\(478\) 0 0
\(479\) −4.01692e22 −0.662280 −0.331140 0.943582i \(-0.607433\pi\)
−0.331140 + 0.943582i \(0.607433\pi\)
\(480\) 0 0
\(481\) 4.64251e22 0.738788
\(482\) 0 0
\(483\) −1.16829e22 −0.179473
\(484\) 0 0
\(485\) −8.06852e22 −1.19671
\(486\) 0 0
\(487\) −2.24546e22 −0.321595 −0.160798 0.986987i \(-0.551407\pi\)
−0.160798 + 0.986987i \(0.551407\pi\)
\(488\) 0 0
\(489\) 2.09326e23 2.89532
\(490\) 0 0
\(491\) −5.70054e22 −0.761593 −0.380797 0.924659i \(-0.624350\pi\)
−0.380797 + 0.924659i \(0.624350\pi\)
\(492\) 0 0
\(493\) −3.88333e22 −0.501194
\(494\) 0 0
\(495\) −2.53469e22 −0.316068
\(496\) 0 0
\(497\) 1.37703e22 0.165926
\(498\) 0 0
\(499\) −4.00593e22 −0.466497 −0.233249 0.972417i \(-0.574936\pi\)
−0.233249 + 0.972417i \(0.574936\pi\)
\(500\) 0 0
\(501\) 2.25078e23 2.53345
\(502\) 0 0
\(503\) 1.64428e22 0.178915 0.0894576 0.995991i \(-0.471487\pi\)
0.0894576 + 0.995991i \(0.471487\pi\)
\(504\) 0 0
\(505\) 1.48100e23 1.55804
\(506\) 0 0
\(507\) 6.59426e22 0.670809
\(508\) 0 0
\(509\) −1.17557e23 −1.15651 −0.578254 0.815857i \(-0.696266\pi\)
−0.578254 + 0.815857i \(0.696266\pi\)
\(510\) 0 0
\(511\) −1.06682e22 −0.101511
\(512\) 0 0
\(513\) −4.56796e23 −4.20460
\(514\) 0 0
\(515\) 1.04335e23 0.929110
\(516\) 0 0
\(517\) −1.71013e20 −0.00147353
\(518\) 0 0
\(519\) −3.24431e23 −2.70520
\(520\) 0 0
\(521\) 1.01491e23 0.819043 0.409522 0.912300i \(-0.365696\pi\)
0.409522 + 0.912300i \(0.365696\pi\)
\(522\) 0 0
\(523\) 1.28745e23 1.00570 0.502849 0.864374i \(-0.332285\pi\)
0.502849 + 0.864374i \(0.332285\pi\)
\(524\) 0 0
\(525\) −6.33528e21 −0.0479084
\(526\) 0 0
\(527\) −2.66072e22 −0.194809
\(528\) 0 0
\(529\) −3.15249e22 −0.223502
\(530\) 0 0
\(531\) 4.16607e23 2.86038
\(532\) 0 0
\(533\) −7.86071e22 −0.522734
\(534\) 0 0
\(535\) 1.23238e23 0.793848
\(536\) 0 0
\(537\) −9.89396e22 −0.617431
\(538\) 0 0
\(539\) 1.79850e22 0.108744
\(540\) 0 0
\(541\) −4.58302e21 −0.0268519 −0.0134259 0.999910i \(-0.504274\pi\)
−0.0134259 + 0.999910i \(0.504274\pi\)
\(542\) 0 0
\(543\) −1.78525e23 −1.01368
\(544\) 0 0
\(545\) −1.56068e23 −0.858903
\(546\) 0 0
\(547\) −1.73760e23 −0.926955 −0.463477 0.886109i \(-0.653399\pi\)
−0.463477 + 0.886109i \(0.653399\pi\)
\(548\) 0 0
\(549\) 7.00372e23 3.62213
\(550\) 0 0
\(551\) 3.83704e23 1.92401
\(552\) 0 0
\(553\) −2.32790e22 −0.113188
\(554\) 0 0
\(555\) −4.10303e23 −1.93470
\(556\) 0 0
\(557\) −3.13961e22 −0.143584 −0.0717922 0.997420i \(-0.522872\pi\)
−0.0717922 + 0.997420i \(0.522872\pi\)
\(558\) 0 0
\(559\) −2.00773e23 −0.890647
\(560\) 0 0
\(561\) −1.76669e22 −0.0760286
\(562\) 0 0
\(563\) 2.59071e23 1.08168 0.540839 0.841126i \(-0.318107\pi\)
0.540839 + 0.841126i \(0.318107\pi\)
\(564\) 0 0
\(565\) −4.63037e23 −1.87587
\(566\) 0 0
\(567\) 8.47366e22 0.333131
\(568\) 0 0
\(569\) −2.43221e23 −0.927998 −0.463999 0.885836i \(-0.653586\pi\)
−0.463999 + 0.885836i \(0.653586\pi\)
\(570\) 0 0
\(571\) −1.84280e23 −0.682452 −0.341226 0.939981i \(-0.610842\pi\)
−0.341226 + 0.939981i \(0.610842\pi\)
\(572\) 0 0
\(573\) −3.50119e23 −1.25864
\(574\) 0 0
\(575\) 5.93922e22 0.207278
\(576\) 0 0
\(577\) 2.30483e23 0.780987 0.390493 0.920606i \(-0.372304\pi\)
0.390493 + 0.920606i \(0.372304\pi\)
\(578\) 0 0
\(579\) 1.65027e23 0.542984
\(580\) 0 0
\(581\) 2.89244e22 0.0924202
\(582\) 0 0
\(583\) 1.42325e21 0.00441671
\(584\) 0 0
\(585\) 7.65885e23 2.30855
\(586\) 0 0
\(587\) 6.23301e23 1.82505 0.912524 0.409024i \(-0.134131\pi\)
0.912524 + 0.409024i \(0.134131\pi\)
\(588\) 0 0
\(589\) 2.62900e23 0.747843
\(590\) 0 0
\(591\) −1.06292e24 −2.93769
\(592\) 0 0
\(593\) 3.24824e23 0.872334 0.436167 0.899866i \(-0.356336\pi\)
0.436167 + 0.899866i \(0.356336\pi\)
\(594\) 0 0
\(595\) −1.67199e22 −0.0436354
\(596\) 0 0
\(597\) 1.18615e23 0.300856
\(598\) 0 0
\(599\) −5.52096e22 −0.136109 −0.0680544 0.997682i \(-0.521679\pi\)
−0.0680544 + 0.997682i \(0.521679\pi\)
\(600\) 0 0
\(601\) 1.14994e23 0.275576 0.137788 0.990462i \(-0.456001\pi\)
0.137788 + 0.990462i \(0.456001\pi\)
\(602\) 0 0
\(603\) −8.47290e23 −1.97395
\(604\) 0 0
\(605\) −4.84736e23 −1.09795
\(606\) 0 0
\(607\) 3.28819e23 0.724190 0.362095 0.932141i \(-0.382062\pi\)
0.362095 + 0.932141i \(0.382062\pi\)
\(608\) 0 0
\(609\) −1.30589e23 −0.279679
\(610\) 0 0
\(611\) 5.16734e21 0.0107626
\(612\) 0 0
\(613\) 8.48661e23 1.71918 0.859588 0.510988i \(-0.170720\pi\)
0.859588 + 0.510988i \(0.170720\pi\)
\(614\) 0 0
\(615\) 6.94725e23 1.36891
\(616\) 0 0
\(617\) 1.44331e22 0.0276652 0.0138326 0.999904i \(-0.495597\pi\)
0.0138326 + 0.999904i \(0.495597\pi\)
\(618\) 0 0
\(619\) −8.65832e23 −1.61459 −0.807296 0.590146i \(-0.799070\pi\)
−0.807296 + 0.590146i \(0.799070\pi\)
\(620\) 0 0
\(621\) −1.45746e24 −2.64434
\(622\) 0 0
\(623\) 3.57338e22 0.0630857
\(624\) 0 0
\(625\) −6.86789e23 −1.17989
\(626\) 0 0
\(627\) 1.74563e23 0.291863
\(628\) 0 0
\(629\) −2.06209e23 −0.335566
\(630\) 0 0
\(631\) 9.17406e23 1.45316 0.726578 0.687084i \(-0.241110\pi\)
0.726578 + 0.687084i \(0.241110\pi\)
\(632\) 0 0
\(633\) 8.02709e23 1.23773
\(634\) 0 0
\(635\) 8.59093e22 0.128962
\(636\) 0 0
\(637\) −5.43437e23 −0.794263
\(638\) 0 0
\(639\) 2.80175e24 3.98724
\(640\) 0 0
\(641\) −1.04783e24 −1.45210 −0.726050 0.687642i \(-0.758646\pi\)
−0.726050 + 0.687642i \(0.758646\pi\)
\(642\) 0 0
\(643\) 9.84086e22 0.132813 0.0664064 0.997793i \(-0.478847\pi\)
0.0664064 + 0.997793i \(0.478847\pi\)
\(644\) 0 0
\(645\) 1.77442e24 2.33238
\(646\) 0 0
\(647\) −1.49070e24 −1.90855 −0.954273 0.298937i \(-0.903368\pi\)
−0.954273 + 0.298937i \(0.903368\pi\)
\(648\) 0 0
\(649\) −9.76153e22 −0.121741
\(650\) 0 0
\(651\) −8.94748e22 −0.108708
\(652\) 0 0
\(653\) 8.28026e23 0.980126 0.490063 0.871687i \(-0.336974\pi\)
0.490063 + 0.871687i \(0.336974\pi\)
\(654\) 0 0
\(655\) −9.33094e23 −1.07615
\(656\) 0 0
\(657\) −2.17059e24 −2.43934
\(658\) 0 0
\(659\) −1.75140e24 −1.91805 −0.959025 0.283320i \(-0.908564\pi\)
−0.959025 + 0.283320i \(0.908564\pi\)
\(660\) 0 0
\(661\) 1.25523e24 1.33971 0.669856 0.742491i \(-0.266356\pi\)
0.669856 + 0.742491i \(0.266356\pi\)
\(662\) 0 0
\(663\) 5.33825e23 0.555308
\(664\) 0 0
\(665\) 1.65206e23 0.167510
\(666\) 0 0
\(667\) 1.22425e24 1.21004
\(668\) 0 0
\(669\) −1.65362e24 −1.59336
\(670\) 0 0
\(671\) −1.64104e23 −0.154162
\(672\) 0 0
\(673\) 4.30567e23 0.394378 0.197189 0.980365i \(-0.436819\pi\)
0.197189 + 0.980365i \(0.436819\pi\)
\(674\) 0 0
\(675\) −7.90335e23 −0.705877
\(676\) 0 0
\(677\) 4.23476e23 0.368829 0.184415 0.982849i \(-0.440961\pi\)
0.184415 + 0.982849i \(0.440961\pi\)
\(678\) 0 0
\(679\) −1.36364e23 −0.115826
\(680\) 0 0
\(681\) 1.67241e24 1.38546
\(682\) 0 0
\(683\) 1.08746e23 0.0878690 0.0439345 0.999034i \(-0.486011\pi\)
0.0439345 + 0.999034i \(0.486011\pi\)
\(684\) 0 0
\(685\) 1.87053e23 0.147433
\(686\) 0 0
\(687\) −8.04824e23 −0.618826
\(688\) 0 0
\(689\) −4.30051e22 −0.0322594
\(690\) 0 0
\(691\) −1.21387e24 −0.888404 −0.444202 0.895927i \(-0.646513\pi\)
−0.444202 + 0.895927i \(0.646513\pi\)
\(692\) 0 0
\(693\) −4.28382e22 −0.0305913
\(694\) 0 0
\(695\) 1.64744e24 1.14799
\(696\) 0 0
\(697\) 3.49154e23 0.237431
\(698\) 0 0
\(699\) 1.49642e24 0.993109
\(700\) 0 0
\(701\) 2.16022e24 1.39925 0.699625 0.714510i \(-0.253350\pi\)
0.699625 + 0.714510i \(0.253350\pi\)
\(702\) 0 0
\(703\) 2.03751e24 1.28819
\(704\) 0 0
\(705\) −4.56687e22 −0.0281845
\(706\) 0 0
\(707\) 2.50300e23 0.150798
\(708\) 0 0
\(709\) −3.06732e24 −1.80412 −0.902062 0.431606i \(-0.857947\pi\)
−0.902062 + 0.431606i \(0.857947\pi\)
\(710\) 0 0
\(711\) −4.73642e24 −2.71993
\(712\) 0 0
\(713\) 8.38810e23 0.470330
\(714\) 0 0
\(715\) −1.79455e23 −0.0982546
\(716\) 0 0
\(717\) −2.73527e24 −1.46247
\(718\) 0 0
\(719\) −1.12483e24 −0.587343 −0.293671 0.955906i \(-0.594877\pi\)
−0.293671 + 0.955906i \(0.594877\pi\)
\(720\) 0 0
\(721\) 1.76333e23 0.0899258
\(722\) 0 0
\(723\) −8.95611e23 −0.446112
\(724\) 0 0
\(725\) 6.63874e23 0.323007
\(726\) 0 0
\(727\) −3.37960e24 −1.60629 −0.803144 0.595785i \(-0.796841\pi\)
−0.803144 + 0.595785i \(0.796841\pi\)
\(728\) 0 0
\(729\) 5.00387e24 2.32339
\(730\) 0 0
\(731\) 8.91786e23 0.404541
\(732\) 0 0
\(733\) 1.47640e24 0.654365 0.327183 0.944961i \(-0.393901\pi\)
0.327183 + 0.944961i \(0.393901\pi\)
\(734\) 0 0
\(735\) 4.80286e24 2.07997
\(736\) 0 0
\(737\) 1.98529e23 0.0840136
\(738\) 0 0
\(739\) 2.15072e24 0.889419 0.444709 0.895675i \(-0.353307\pi\)
0.444709 + 0.895675i \(0.353307\pi\)
\(740\) 0 0
\(741\) −5.27462e24 −2.13175
\(742\) 0 0
\(743\) −1.03206e24 −0.407663 −0.203831 0.979006i \(-0.565339\pi\)
−0.203831 + 0.979006i \(0.565339\pi\)
\(744\) 0 0
\(745\) −5.19923e24 −2.00729
\(746\) 0 0
\(747\) 5.88503e24 2.22087
\(748\) 0 0
\(749\) 2.08281e23 0.0768342
\(750\) 0 0
\(751\) 4.96754e23 0.179144 0.0895719 0.995980i \(-0.471450\pi\)
0.0895719 + 0.995980i \(0.471450\pi\)
\(752\) 0 0
\(753\) 1.34203e23 0.0473155
\(754\) 0 0
\(755\) 4.64168e23 0.160002
\(756\) 0 0
\(757\) 3.61087e24 1.21702 0.608509 0.793547i \(-0.291768\pi\)
0.608509 + 0.793547i \(0.291768\pi\)
\(758\) 0 0
\(759\) 5.56963e23 0.183557
\(760\) 0 0
\(761\) −6.85509e23 −0.220924 −0.110462 0.993880i \(-0.535233\pi\)
−0.110462 + 0.993880i \(0.535233\pi\)
\(762\) 0 0
\(763\) −2.63767e23 −0.0831307
\(764\) 0 0
\(765\) −3.40187e24 −1.04857
\(766\) 0 0
\(767\) 2.94955e24 0.889191
\(768\) 0 0
\(769\) −6.43730e24 −1.89815 −0.949074 0.315054i \(-0.897977\pi\)
−0.949074 + 0.315054i \(0.897977\pi\)
\(770\) 0 0
\(771\) −2.70817e24 −0.781112
\(772\) 0 0
\(773\) 4.44679e24 1.25465 0.627323 0.778759i \(-0.284151\pi\)
0.627323 + 0.778759i \(0.284151\pi\)
\(774\) 0 0
\(775\) 4.54862e23 0.125549
\(776\) 0 0
\(777\) −6.93441e23 −0.187254
\(778\) 0 0
\(779\) −3.44991e24 −0.911465
\(780\) 0 0
\(781\) −6.56478e23 −0.169702
\(782\) 0 0
\(783\) −1.62911e25 −4.12075
\(784\) 0 0
\(785\) −8.60765e23 −0.213055
\(786\) 0 0
\(787\) 6.94797e24 1.68296 0.841478 0.540292i \(-0.181686\pi\)
0.841478 + 0.540292i \(0.181686\pi\)
\(788\) 0 0
\(789\) 1.22231e25 2.89753
\(790\) 0 0
\(791\) −7.82566e23 −0.181560
\(792\) 0 0
\(793\) 4.95859e24 1.12599
\(794\) 0 0
\(795\) 3.80076e23 0.0844793
\(796\) 0 0
\(797\) 5.46753e23 0.118958 0.0594792 0.998230i \(-0.481056\pi\)
0.0594792 + 0.998230i \(0.481056\pi\)
\(798\) 0 0
\(799\) −2.29521e22 −0.00488848
\(800\) 0 0
\(801\) 7.27050e24 1.51596
\(802\) 0 0
\(803\) 5.08590e23 0.103821
\(804\) 0 0
\(805\) 5.27106e23 0.105350
\(806\) 0 0
\(807\) 3.08706e24 0.604115
\(808\) 0 0
\(809\) −4.28024e24 −0.820174 −0.410087 0.912046i \(-0.634502\pi\)
−0.410087 + 0.912046i \(0.634502\pi\)
\(810\) 0 0
\(811\) 7.01384e24 1.31607 0.658034 0.752988i \(-0.271388\pi\)
0.658034 + 0.752988i \(0.271388\pi\)
\(812\) 0 0
\(813\) −8.06333e24 −1.48165
\(814\) 0 0
\(815\) −9.44431e24 −1.69954
\(816\) 0 0
\(817\) −8.81156e24 −1.55298
\(818\) 0 0
\(819\) 1.29440e24 0.223437
\(820\) 0 0
\(821\) 1.96574e24 0.332360 0.166180 0.986095i \(-0.446857\pi\)
0.166180 + 0.986095i \(0.446857\pi\)
\(822\) 0 0
\(823\) 4.44335e24 0.735889 0.367944 0.929848i \(-0.380062\pi\)
0.367944 + 0.929848i \(0.380062\pi\)
\(824\) 0 0
\(825\) 3.02024e23 0.0489986
\(826\) 0 0
\(827\) −8.17355e24 −1.29901 −0.649507 0.760355i \(-0.725025\pi\)
−0.649507 + 0.760355i \(0.725025\pi\)
\(828\) 0 0
\(829\) 5.09518e24 0.793316 0.396658 0.917966i \(-0.370170\pi\)
0.396658 + 0.917966i \(0.370170\pi\)
\(830\) 0 0
\(831\) 1.85828e25 2.83467
\(832\) 0 0
\(833\) 2.41381e24 0.360762
\(834\) 0 0
\(835\) −1.01550e25 −1.48712
\(836\) 0 0
\(837\) −1.11621e25 −1.60169
\(838\) 0 0
\(839\) −1.09555e25 −1.54048 −0.770239 0.637755i \(-0.779863\pi\)
−0.770239 + 0.637755i \(0.779863\pi\)
\(840\) 0 0
\(841\) 6.42726e24 0.885646
\(842\) 0 0
\(843\) −1.35716e25 −1.83272
\(844\) 0 0
\(845\) −2.97519e24 −0.393760
\(846\) 0 0
\(847\) −8.19238e23 −0.106268
\(848\) 0 0
\(849\) 1.31727e25 1.67479
\(850\) 0 0
\(851\) 6.50089e24 0.810162
\(852\) 0 0
\(853\) −1.17613e25 −1.43677 −0.718386 0.695644i \(-0.755119\pi\)
−0.718386 + 0.695644i \(0.755119\pi\)
\(854\) 0 0
\(855\) 3.36132e25 4.02530
\(856\) 0 0
\(857\) −1.55161e24 −0.182157 −0.0910787 0.995844i \(-0.529031\pi\)
−0.0910787 + 0.995844i \(0.529031\pi\)
\(858\) 0 0
\(859\) −1.15282e25 −1.32685 −0.663424 0.748244i \(-0.730897\pi\)
−0.663424 + 0.748244i \(0.730897\pi\)
\(860\) 0 0
\(861\) 1.17414e24 0.132493
\(862\) 0 0
\(863\) 7.30526e24 0.808246 0.404123 0.914705i \(-0.367577\pi\)
0.404123 + 0.914705i \(0.367577\pi\)
\(864\) 0 0
\(865\) 1.46376e25 1.58794
\(866\) 0 0
\(867\) 1.54281e25 1.64116
\(868\) 0 0
\(869\) 1.10979e24 0.115764
\(870\) 0 0
\(871\) −5.99876e24 −0.613631
\(872\) 0 0
\(873\) −2.77450e25 −2.78332
\(874\) 0 0
\(875\) −9.29320e23 −0.0914317
\(876\) 0 0
\(877\) 8.83912e24 0.852928 0.426464 0.904504i \(-0.359759\pi\)
0.426464 + 0.904504i \(0.359759\pi\)
\(878\) 0 0
\(879\) −3.11972e25 −2.95264
\(880\) 0 0
\(881\) 5.00598e24 0.464722 0.232361 0.972630i \(-0.425355\pi\)
0.232361 + 0.972630i \(0.425355\pi\)
\(882\) 0 0
\(883\) 9.42478e24 0.858233 0.429117 0.903249i \(-0.358825\pi\)
0.429117 + 0.903249i \(0.358825\pi\)
\(884\) 0 0
\(885\) −2.60679e25 −2.32857
\(886\) 0 0
\(887\) 1.59100e25 1.39418 0.697090 0.716983i \(-0.254478\pi\)
0.697090 + 0.716983i \(0.254478\pi\)
\(888\) 0 0
\(889\) 1.45193e23 0.0124819
\(890\) 0 0
\(891\) −4.03968e24 −0.340711
\(892\) 0 0
\(893\) 2.26785e23 0.0187662
\(894\) 0 0
\(895\) 4.46393e24 0.362428
\(896\) 0 0
\(897\) −1.68292e25 −1.34069
\(898\) 0 0
\(899\) 9.37605e24 0.732930
\(900\) 0 0
\(901\) 1.91018e23 0.0146526
\(902\) 0 0
\(903\) 2.99890e24 0.225744
\(904\) 0 0
\(905\) 8.05467e24 0.595024
\(906\) 0 0
\(907\) −1.39294e25 −1.00988 −0.504942 0.863153i \(-0.668486\pi\)
−0.504942 + 0.863153i \(0.668486\pi\)
\(908\) 0 0
\(909\) 5.09267e25 3.62370
\(910\) 0 0
\(911\) −4.99198e24 −0.348632 −0.174316 0.984690i \(-0.555771\pi\)
−0.174316 + 0.984690i \(0.555771\pi\)
\(912\) 0 0
\(913\) −1.37892e24 −0.0945231
\(914\) 0 0
\(915\) −4.38237e25 −2.94869
\(916\) 0 0
\(917\) −1.57700e24 −0.104158
\(918\) 0 0
\(919\) −3.29906e24 −0.213899 −0.106950 0.994264i \(-0.534108\pi\)
−0.106950 + 0.994264i \(0.534108\pi\)
\(920\) 0 0
\(921\) 4.44735e23 0.0283070
\(922\) 0 0
\(923\) 1.98362e25 1.23949
\(924\) 0 0
\(925\) 3.52524e24 0.216264
\(926\) 0 0
\(927\) 3.58772e25 2.16093
\(928\) 0 0
\(929\) 1.47943e25 0.874903 0.437451 0.899242i \(-0.355881\pi\)
0.437451 + 0.899242i \(0.355881\pi\)
\(930\) 0 0
\(931\) −2.38504e25 −1.38492
\(932\) 0 0
\(933\) 3.78186e25 2.15631
\(934\) 0 0
\(935\) 7.97093e23 0.0446283
\(936\) 0 0
\(937\) −8.80353e24 −0.484028 −0.242014 0.970273i \(-0.577808\pi\)
−0.242014 + 0.970273i \(0.577808\pi\)
\(938\) 0 0
\(939\) −1.62730e25 −0.878640
\(940\) 0 0
\(941\) −2.08706e25 −1.10668 −0.553342 0.832954i \(-0.686648\pi\)
−0.553342 + 0.832954i \(0.686648\pi\)
\(942\) 0 0
\(943\) −1.10073e25 −0.573234
\(944\) 0 0
\(945\) −7.01423e24 −0.358765
\(946\) 0 0
\(947\) 1.52689e24 0.0767067 0.0383533 0.999264i \(-0.487789\pi\)
0.0383533 + 0.999264i \(0.487789\pi\)
\(948\) 0 0
\(949\) −1.53676e25 −0.758304
\(950\) 0 0
\(951\) −4.26482e25 −2.06712
\(952\) 0 0
\(953\) −2.94509e25 −1.40220 −0.701099 0.713064i \(-0.747307\pi\)
−0.701099 + 0.713064i \(0.747307\pi\)
\(954\) 0 0
\(955\) 1.57966e25 0.738814
\(956\) 0 0
\(957\) 6.22562e24 0.286043
\(958\) 0 0
\(959\) 3.16134e23 0.0142696
\(960\) 0 0
\(961\) −1.61260e25 −0.715118
\(962\) 0 0
\(963\) 4.23775e25 1.84634
\(964\) 0 0
\(965\) −7.44565e24 −0.318728
\(966\) 0 0
\(967\) 3.64906e25 1.53481 0.767407 0.641160i \(-0.221547\pi\)
0.767407 + 0.641160i \(0.221547\pi\)
\(968\) 0 0
\(969\) 2.34286e25 0.968264
\(970\) 0 0
\(971\) 4.03378e25 1.63813 0.819065 0.573700i \(-0.194492\pi\)
0.819065 + 0.573700i \(0.194492\pi\)
\(972\) 0 0
\(973\) 2.78429e24 0.111110
\(974\) 0 0
\(975\) −9.12599e24 −0.357883
\(976\) 0 0
\(977\) −1.53014e25 −0.589694 −0.294847 0.955545i \(-0.595269\pi\)
−0.294847 + 0.955545i \(0.595269\pi\)
\(978\) 0 0
\(979\) −1.70355e24 −0.0645212
\(980\) 0 0
\(981\) −5.36667e25 −1.99764
\(982\) 0 0
\(983\) −1.72483e25 −0.631016 −0.315508 0.948923i \(-0.602175\pi\)
−0.315508 + 0.948923i \(0.602175\pi\)
\(984\) 0 0
\(985\) 4.79565e25 1.72441
\(986\) 0 0
\(987\) −7.71834e22 −0.00272790
\(988\) 0 0
\(989\) −2.81142e25 −0.976691
\(990\) 0 0
\(991\) 4.22399e25 1.44244 0.721219 0.692707i \(-0.243582\pi\)
0.721219 + 0.692707i \(0.243582\pi\)
\(992\) 0 0
\(993\) 7.90905e25 2.65494
\(994\) 0 0
\(995\) −5.35165e24 −0.176600
\(996\) 0 0
\(997\) −2.14018e25 −0.694290 −0.347145 0.937812i \(-0.612849\pi\)
−0.347145 + 0.937812i \(0.612849\pi\)
\(998\) 0 0
\(999\) −8.65077e25 −2.75898
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 \(a_p\))