Properties

Label 4680.2.l.h.2809.1
Level $4680$
Weight $2$
Character 4680.2809
Analytic conductor $37.370$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 4680 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4680.l (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(37.3699881460\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \( x^{10} + 13x^{8} + 56x^{6} + 97x^{4} + 61x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 1560)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2809.1
Root \(-1.28447i\) of defining polynomial
Character \(\chi\) \(=\) 4680.2809
Dual form 4680.2.l.h.2809.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.23081 - 0.153266i) q^{5} +3.71215i q^{7} +O(q^{10})\) \(q+(-2.23081 - 0.153266i) q^{5} +3.71215i q^{7} -3.31842 q^{11} +1.00000i q^{13} +1.55706i q^{17} +5.33709 q^{19} -0.442940i q^{23} +(4.95302 + 0.683813i) q^{25} +2.56894 q^{29} +0.613062 q^{31} +(0.568944 - 8.28109i) q^{35} +0.257322i q^{37} +10.6114 q^{41} +12.6935i q^{43} +7.44442i q^{47} -6.78003 q^{49} +5.39521i q^{53} +(7.40275 + 0.508599i) q^{55} -13.1358 q^{59} -5.27452 q^{61} +(0.153266 - 2.23081i) q^{65} -10.5384i q^{67} -0.311845 q^{71} +9.46841i q^{73} -12.3184i q^{77} -16.1871 q^{79} -11.7546i q^{83} +(0.238644 - 3.47350i) q^{85} -4.58762 q^{89} -3.71215 q^{91} +(-11.9060 - 0.817993i) q^{95} -10.8500i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 2 q^{5} - 10 q^{11} - 12 q^{19} + 6 q^{25} + 4 q^{29} - 16 q^{35} + 2 q^{41} - 4 q^{49} + 10 q^{55} + 40 q^{59} - 38 q^{61} - 26 q^{71} - 14 q^{79} + 24 q^{85} + 18 q^{89} + 2 q^{91} - 32 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4680\mathbb{Z}\right)^\times\).

\(n\) \(937\) \(1081\) \(2081\) \(2341\) \(3511\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\) \(1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −2.23081 0.153266i −0.997648 0.0685425i
\(6\) 0 0
\(7\) 3.71215i 1.40306i 0.712640 + 0.701530i \(0.247499\pi\)
−0.712640 + 0.701530i \(0.752501\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.31842 −1.00054 −0.500270 0.865869i \(-0.666766\pi\)
−0.500270 + 0.865869i \(0.666766\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.55706i 0.377642i 0.982011 + 0.188821i \(0.0604667\pi\)
−0.982011 + 0.188821i \(0.939533\pi\)
\(18\) 0 0
\(19\) 5.33709 1.22441 0.612207 0.790698i \(-0.290282\pi\)
0.612207 + 0.790698i \(0.290282\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.442940i 0.0923594i −0.998933 0.0461797i \(-0.985295\pi\)
0.998933 0.0461797i \(-0.0147047\pi\)
\(24\) 0 0
\(25\) 4.95302 + 0.683813i 0.990604 + 0.136763i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.56894 0.477041 0.238521 0.971137i \(-0.423338\pi\)
0.238521 + 0.971137i \(0.423338\pi\)
\(30\) 0 0
\(31\) 0.613062 0.110109 0.0550546 0.998483i \(-0.482467\pi\)
0.0550546 + 0.998483i \(0.482467\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.568944 8.28109i 0.0961692 1.39976i
\(36\) 0 0
\(37\) 0.257322i 0.0423034i 0.999776 + 0.0211517i \(0.00673331\pi\)
−0.999776 + 0.0211517i \(0.993267\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 10.6114 1.65722 0.828611 0.559826i \(-0.189132\pi\)
0.828611 + 0.559826i \(0.189132\pi\)
\(42\) 0 0
\(43\) 12.6935i 1.93574i 0.251450 + 0.967870i \(0.419093\pi\)
−0.251450 + 0.967870i \(0.580907\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 7.44442i 1.08588i 0.839771 + 0.542940i \(0.182689\pi\)
−0.839771 + 0.542940i \(0.817311\pi\)
\(48\) 0 0
\(49\) −6.78003 −0.968576
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 5.39521i 0.741089i 0.928815 + 0.370545i \(0.120829\pi\)
−0.928815 + 0.370545i \(0.879171\pi\)
\(54\) 0 0
\(55\) 7.40275 + 0.508599i 0.998187 + 0.0685795i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −13.1358 −1.71014 −0.855068 0.518516i \(-0.826485\pi\)
−0.855068 + 0.518516i \(0.826485\pi\)
\(60\) 0 0
\(61\) −5.27452 −0.675333 −0.337667 0.941266i \(-0.609638\pi\)
−0.337667 + 0.941266i \(0.609638\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.153266 2.23081i 0.0190103 0.276698i
\(66\) 0 0
\(67\) 10.5384i 1.28747i −0.765248 0.643736i \(-0.777383\pi\)
0.765248 0.643736i \(-0.222617\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.311845 −0.0370092 −0.0185046 0.999829i \(-0.505891\pi\)
−0.0185046 + 0.999829i \(0.505891\pi\)
\(72\) 0 0
\(73\) 9.46841i 1.10819i 0.832452 + 0.554097i \(0.186936\pi\)
−0.832452 + 0.554097i \(0.813064\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 12.3184i 1.40382i
\(78\) 0 0
\(79\) −16.1871 −1.82119 −0.910597 0.413295i \(-0.864378\pi\)
−0.910597 + 0.413295i \(0.864378\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 11.7546i 1.29023i −0.764084 0.645117i \(-0.776809\pi\)
0.764084 0.645117i \(-0.223191\pi\)
\(84\) 0 0
\(85\) 0.238644 3.47350i 0.0258845 0.376754i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.58762 −0.486287 −0.243144 0.969990i \(-0.578179\pi\)
−0.243144 + 0.969990i \(0.578179\pi\)
\(90\) 0 0
\(91\) −3.71215 −0.389139
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −11.9060 0.817993i −1.22153 0.0839243i
\(96\) 0 0
\(97\) 10.8500i 1.10165i −0.834619 0.550827i \(-0.814312\pi\)
0.834619 0.550827i \(-0.185688\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.68306 −0.167471 −0.0837356 0.996488i \(-0.526685\pi\)
−0.0837356 + 0.996488i \(0.526685\pi\)
\(102\) 0 0
\(103\) 1.78535i 0.175916i 0.996124 + 0.0879578i \(0.0280341\pi\)
−0.996124 + 0.0879578i \(0.971966\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.11943i 0.108220i 0.998535 + 0.0541098i \(0.0172321\pi\)
−0.998535 + 0.0541098i \(0.982768\pi\)
\(108\) 0 0
\(109\) 0.914914 0.0876329 0.0438164 0.999040i \(-0.486048\pi\)
0.0438164 + 0.999040i \(0.486048\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.41386i 0.227077i −0.993534 0.113538i \(-0.963782\pi\)
0.993534 0.113538i \(-0.0362185\pi\)
\(114\) 0 0
\(115\) −0.0678875 + 0.988115i −0.00633054 + 0.0921422i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −5.78003 −0.529855
\(120\) 0 0
\(121\) 0.0118848 0.00108043
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −10.9444 2.28458i −0.978900 0.204339i
\(126\) 0 0
\(127\) 14.0418i 1.24601i 0.782218 + 0.623005i \(0.214088\pi\)
−0.782218 + 0.623005i \(0.785912\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −13.7650 −1.20265 −0.601327 0.799003i \(-0.705361\pi\)
−0.601327 + 0.799003i \(0.705361\pi\)
\(132\) 0 0
\(133\) 19.8121i 1.71792i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.50470i 0.555734i −0.960620 0.277867i \(-0.910373\pi\)
0.960620 0.277867i \(-0.0896275\pi\)
\(138\) 0 0
\(139\) −9.78003 −0.829532 −0.414766 0.909928i \(-0.636137\pi\)
−0.414766 + 0.909928i \(0.636137\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.31842i 0.277500i
\(144\) 0 0
\(145\) −5.73082 0.393731i −0.475919 0.0326976i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.93148 −0.485926 −0.242963 0.970036i \(-0.578119\pi\)
−0.242963 + 0.970036i \(0.578119\pi\)
\(150\) 0 0
\(151\) −0.272818 −0.0222016 −0.0111008 0.999938i \(-0.503534\pi\)
−0.0111008 + 0.999938i \(0.503534\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −1.36763 0.0939614i −0.109850 0.00754716i
\(156\) 0 0
\(157\) 14.6561i 1.16969i −0.811146 0.584844i \(-0.801156\pi\)
0.811146 0.584844i \(-0.198844\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.64426 0.129586
\(162\) 0 0
\(163\) 3.48345i 0.272845i −0.990651 0.136422i \(-0.956440\pi\)
0.990651 0.136422i \(-0.0435604\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.69135i 0.363028i 0.983388 + 0.181514i \(0.0580998\pi\)
−0.983388 + 0.181514i \(0.941900\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3.26475i 0.248214i −0.992269 0.124107i \(-0.960393\pi\)
0.992269 0.124107i \(-0.0396067\pi\)
\(174\) 0 0
\(175\) −2.53841 + 18.3863i −0.191886 + 1.38988i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 19.7204 1.47397 0.736987 0.675907i \(-0.236248\pi\)
0.736987 + 0.675907i \(0.236248\pi\)
\(180\) 0 0
\(181\) −22.0558 −1.63940 −0.819698 0.572796i \(-0.805859\pi\)
−0.819698 + 0.572796i \(0.805859\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.0394386 0.574036i 0.00289958 0.0422040i
\(186\) 0 0
\(187\) 5.16697i 0.377846i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −22.2729 −1.61161 −0.805805 0.592182i \(-0.798267\pi\)
−0.805805 + 0.592182i \(0.798267\pi\)
\(192\) 0 0
\(193\) 15.7733i 1.13539i −0.823241 0.567693i \(-0.807836\pi\)
0.823241 0.567693i \(-0.192164\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.72871i 0.194413i −0.995264 0.0972063i \(-0.969009\pi\)
0.995264 0.0972063i \(-0.0309907\pi\)
\(198\) 0 0
\(199\) 22.1029 1.56684 0.783418 0.621495i \(-0.213474\pi\)
0.783418 + 0.621495i \(0.213474\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 9.53630i 0.669317i
\(204\) 0 0
\(205\) −23.6720 1.62636i −1.65332 0.113590i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −17.7107 −1.22507
\(210\) 0 0
\(211\) 1.01720 0.0700268 0.0350134 0.999387i \(-0.488853\pi\)
0.0350134 + 0.999387i \(0.488853\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.94548 28.3168i 0.132680 1.93119i
\(216\) 0 0
\(217\) 2.27578i 0.154490i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.55706 −0.104739
\(222\) 0 0
\(223\) 6.85535i 0.459068i −0.973301 0.229534i \(-0.926280\pi\)
0.973301 0.229534i \(-0.0737202\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.88224i 0.191301i 0.995415 + 0.0956504i \(0.0304931\pi\)
−0.995415 + 0.0956504i \(0.969507\pi\)
\(228\) 0 0
\(229\) −14.1857 −0.937416 −0.468708 0.883353i \(-0.655280\pi\)
−0.468708 + 0.883353i \(0.655280\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.429354i 0.0281279i −0.999901 0.0140639i \(-0.995523\pi\)
0.999901 0.0140639i \(-0.00447684\pi\)
\(234\) 0 0
\(235\) 1.14097 16.6071i 0.0744289 1.08333i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 19.7255 1.27594 0.637969 0.770062i \(-0.279775\pi\)
0.637969 + 0.770062i \(0.279775\pi\)
\(240\) 0 0
\(241\) 19.6598 1.26640 0.633200 0.773988i \(-0.281741\pi\)
0.633200 + 0.773988i \(0.281741\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 15.1250 + 1.03915i 0.966298 + 0.0663886i
\(246\) 0 0
\(247\) 5.33709i 0.339591i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −23.4175 −1.47810 −0.739051 0.673650i \(-0.764726\pi\)
−0.739051 + 0.673650i \(0.764726\pi\)
\(252\) 0 0
\(253\) 1.46986i 0.0924093i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 30.7987i 1.92117i 0.277981 + 0.960586i \(0.410335\pi\)
−0.277981 + 0.960586i \(0.589665\pi\)
\(258\) 0 0
\(259\) −0.955216 −0.0593543
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 24.1471i 1.48897i 0.667638 + 0.744486i \(0.267305\pi\)
−0.667638 + 0.744486i \(0.732695\pi\)
\(264\) 0 0
\(265\) 0.826900 12.0357i 0.0507961 0.739346i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 12.7557 0.777726 0.388863 0.921295i \(-0.372868\pi\)
0.388863 + 0.921295i \(0.372868\pi\)
\(270\) 0 0
\(271\) −10.4222 −0.633102 −0.316551 0.948575i \(-0.602525\pi\)
−0.316551 + 0.948575i \(0.602525\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −16.4362 2.26918i −0.991139 0.136836i
\(276\) 0 0
\(277\) 19.9404i 1.19810i −0.800710 0.599052i \(-0.795544\pi\)
0.800710 0.599052i \(-0.204456\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −28.5272 −1.70179 −0.850895 0.525336i \(-0.823940\pi\)
−0.850895 + 0.525336i \(0.823940\pi\)
\(282\) 0 0
\(283\) 19.1888i 1.14066i 0.821416 + 0.570329i \(0.193184\pi\)
−0.821416 + 0.570329i \(0.806816\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 39.3910i 2.32518i
\(288\) 0 0
\(289\) 14.5756 0.857386
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 11.9828i 0.700045i 0.936741 + 0.350022i \(0.113826\pi\)
−0.936741 + 0.350022i \(0.886174\pi\)
\(294\) 0 0
\(295\) 29.3035 + 2.01327i 1.70611 + 0.117217i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.442940 0.0256159
\(300\) 0 0
\(301\) −47.1201 −2.71596
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 11.7664 + 0.808403i 0.673745 + 0.0462890i
\(306\) 0 0
\(307\) 25.0299i 1.42853i −0.699874 0.714267i \(-0.746760\pi\)
0.699874 0.714267i \(-0.253240\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −27.6360 −1.56710 −0.783548 0.621331i \(-0.786592\pi\)
−0.783548 + 0.621331i \(0.786592\pi\)
\(312\) 0 0
\(313\) 14.5441i 0.822083i 0.911617 + 0.411042i \(0.134835\pi\)
−0.911617 + 0.411042i \(0.865165\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8.00364i 0.449529i 0.974413 + 0.224765i \(0.0721613\pi\)
−0.974413 + 0.224765i \(0.927839\pi\)
\(318\) 0 0
\(319\) −8.52483 −0.477299
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.31017i 0.462390i
\(324\) 0 0
\(325\) −0.683813 + 4.95302i −0.0379311 + 0.274744i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −27.6348 −1.52355
\(330\) 0 0
\(331\) 5.59929 0.307765 0.153882 0.988089i \(-0.450822\pi\)
0.153882 + 0.988089i \(0.450822\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.61518 + 23.5092i −0.0882465 + 1.28444i
\(336\) 0 0
\(337\) 34.5802i 1.88370i −0.336027 0.941852i \(-0.609083\pi\)
0.336027 0.941852i \(-0.390917\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.03440 −0.110169
\(342\) 0 0
\(343\) 0.816545i 0.0440893i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 31.0537i 1.66705i 0.552482 + 0.833525i \(0.313681\pi\)
−0.552482 + 0.833525i \(0.686319\pi\)
\(348\) 0 0
\(349\) −2.94804 −0.157805 −0.0789026 0.996882i \(-0.525142\pi\)
−0.0789026 + 0.996882i \(0.525142\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.80547i 0.0960957i −0.998845 0.0480478i \(-0.984700\pi\)
0.998845 0.0480478i \(-0.0153000\pi\)
\(354\) 0 0
\(355\) 0.695666 + 0.0477951i 0.0369221 + 0.00253670i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9.29216 −0.490422 −0.245211 0.969470i \(-0.578857\pi\)
−0.245211 + 0.969470i \(0.578857\pi\)
\(360\) 0 0
\(361\) 9.48457 0.499188
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.45118 21.1222i 0.0759583 1.10559i
\(366\) 0 0
\(367\) 18.0955i 0.944579i 0.881444 + 0.472289i \(0.156572\pi\)
−0.881444 + 0.472289i \(0.843428\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −20.0278 −1.03979
\(372\) 0 0
\(373\) 29.4689i 1.52584i −0.646491 0.762922i \(-0.723764\pi\)
0.646491 0.762922i \(-0.276236\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.56894i 0.132307i
\(378\) 0 0
\(379\) 21.2489 1.09148 0.545740 0.837954i \(-0.316249\pi\)
0.545740 + 0.837954i \(0.316249\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 8.19163i 0.418573i 0.977854 + 0.209286i \(0.0671141\pi\)
−0.977854 + 0.209286i \(0.932886\pi\)
\(384\) 0 0
\(385\) −1.88799 + 27.4801i −0.0962211 + 1.40052i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −24.4557 −1.23995 −0.619976 0.784621i \(-0.712858\pi\)
−0.619976 + 0.784621i \(0.712858\pi\)
\(390\) 0 0
\(391\) 0.689684 0.0348788
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 36.1104 + 2.48093i 1.81691 + 0.124829i
\(396\) 0 0
\(397\) 34.4916i 1.73108i −0.500837 0.865541i \(-0.666975\pi\)
0.500837 0.865541i \(-0.333025\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 16.9434 0.846114 0.423057 0.906103i \(-0.360957\pi\)
0.423057 + 0.906103i \(0.360957\pi\)
\(402\) 0 0
\(403\) 0.613062i 0.0305388i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.853901i 0.0423263i
\(408\) 0 0
\(409\) 3.05299 0.150961 0.0754804 0.997147i \(-0.475951\pi\)
0.0754804 + 0.997147i \(0.475951\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 48.7620i 2.39942i
\(414\) 0 0
\(415\) −1.80158 + 26.2223i −0.0884358 + 1.28720i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 20.9567 1.02380 0.511902 0.859044i \(-0.328941\pi\)
0.511902 + 0.859044i \(0.328941\pi\)
\(420\) 0 0
\(421\) −37.4462 −1.82502 −0.912508 0.409059i \(-0.865857\pi\)
−0.912508 + 0.409059i \(0.865857\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.06474 + 7.71215i −0.0516473 + 0.374094i
\(426\) 0 0
\(427\) 19.5798i 0.947533i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 27.2671 1.31341 0.656706 0.754147i \(-0.271949\pi\)
0.656706 + 0.754147i \(0.271949\pi\)
\(432\) 0 0
\(433\) 12.5679i 0.603975i 0.953312 + 0.301988i \(0.0976501\pi\)
−0.953312 + 0.301988i \(0.902350\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.36401i 0.113086i
\(438\) 0 0
\(439\) −14.7241 −0.702742 −0.351371 0.936236i \(-0.614284\pi\)
−0.351371 + 0.936236i \(0.614284\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8.65996i 0.411447i −0.978610 0.205724i \(-0.934045\pi\)
0.978610 0.205724i \(-0.0659548\pi\)
\(444\) 0 0
\(445\) 10.2341 + 0.703125i 0.485143 + 0.0333313i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −21.5690 −1.01791 −0.508953 0.860795i \(-0.669967\pi\)
−0.508953 + 0.860795i \(0.669967\pi\)
\(450\) 0 0
\(451\) −35.2130 −1.65812
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 8.28109 + 0.568944i 0.388224 + 0.0266725i
\(456\) 0 0
\(457\) 0.192394i 0.00899982i 0.999990 + 0.00449991i \(0.00143237\pi\)
−0.999990 + 0.00449991i \(0.998568\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 12.0821 0.562720 0.281360 0.959602i \(-0.409215\pi\)
0.281360 + 0.959602i \(0.409215\pi\)
\(462\) 0 0
\(463\) 25.7245i 1.19552i 0.801676 + 0.597759i \(0.203942\pi\)
−0.801676 + 0.597759i \(0.796058\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 18.4317i 0.852918i 0.904507 + 0.426459i \(0.140239\pi\)
−0.904507 + 0.426459i \(0.859761\pi\)
\(468\) 0 0
\(469\) 39.1201 1.80640
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 42.1223i 1.93679i
\(474\) 0 0
\(475\) 26.4347 + 3.64957i 1.21291 + 0.167454i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 25.5826 1.16890 0.584450 0.811430i \(-0.301310\pi\)
0.584450 + 0.811430i \(0.301310\pi\)
\(480\) 0 0
\(481\) −0.257322 −0.0117329
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.66294 + 24.2044i −0.0755101 + 1.09906i
\(486\) 0 0
\(487\) 30.1997i 1.36848i 0.729258 + 0.684239i \(0.239866\pi\)
−0.729258 + 0.684239i \(0.760134\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 10.7256 0.484039 0.242020 0.970271i \(-0.422190\pi\)
0.242020 + 0.970271i \(0.422190\pi\)
\(492\) 0 0
\(493\) 4.00000i 0.180151i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.15761i 0.0519260i
\(498\) 0 0
\(499\) −7.01044 −0.313830 −0.156915 0.987612i \(-0.550155\pi\)
−0.156915 + 0.987612i \(0.550155\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 32.2604i 1.43842i 0.694793 + 0.719210i \(0.255496\pi\)
−0.694793 + 0.719210i \(0.744504\pi\)
\(504\) 0 0
\(505\) 3.75459 + 0.257956i 0.167077 + 0.0114789i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 17.3631 0.769604 0.384802 0.922999i \(-0.374270\pi\)
0.384802 + 0.922999i \(0.374270\pi\)
\(510\) 0 0
\(511\) −35.1481 −1.55486
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.273632 3.98277i 0.0120577 0.175502i
\(516\) 0 0
\(517\) 24.7037i 1.08647i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −27.6513 −1.21142 −0.605712 0.795684i \(-0.707112\pi\)
−0.605712 + 0.795684i \(0.707112\pi\)
\(522\) 0 0
\(523\) 7.49745i 0.327840i −0.986474 0.163920i \(-0.947586\pi\)
0.986474 0.163920i \(-0.0524140\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.954575i 0.0415819i
\(528\) 0 0
\(529\) 22.8038 0.991470
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 10.6114i 0.459630i
\(534\) 0 0
\(535\) 0.171571 2.49724i 0.00741764 0.107965i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 22.4990 0.969099
\(540\) 0 0
\(541\) 18.8836 0.811871 0.405936 0.913902i \(-0.366946\pi\)
0.405936 + 0.913902i \(0.366946\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.04100 0.140225i −0.0874268 0.00600658i
\(546\) 0 0
\(547\) 21.3808i 0.914178i 0.889421 + 0.457089i \(0.151108\pi\)
−0.889421 + 0.457089i \(0.848892\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 13.7107 0.584095
\(552\) 0 0
\(553\) 60.0890i 2.55524i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3.80681i 0.161300i 0.996743 + 0.0806498i \(0.0256995\pi\)
−0.996743 + 0.0806498i \(0.974300\pi\)
\(558\) 0 0
\(559\) −12.6935 −0.536878
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 29.3983i 1.23899i −0.785001 0.619495i \(-0.787338\pi\)
0.785001 0.619495i \(-0.212662\pi\)
\(564\) 0 0
\(565\) −0.369961 + 5.38486i −0.0155644 + 0.226543i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 12.4014 0.519892 0.259946 0.965623i \(-0.416295\pi\)
0.259946 + 0.965623i \(0.416295\pi\)
\(570\) 0 0
\(571\) −4.56899 −0.191206 −0.0956032 0.995420i \(-0.530478\pi\)
−0.0956032 + 0.995420i \(0.530478\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.302888 2.19389i 0.0126313 0.0914916i
\(576\) 0 0
\(577\) 27.4496i 1.14274i −0.820692 0.571370i \(-0.806412\pi\)
0.820692 0.571370i \(-0.193588\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 43.6348 1.81028
\(582\) 0 0
\(583\) 17.9036i 0.741489i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 19.5191i 0.805641i −0.915279 0.402820i \(-0.868030\pi\)
0.915279 0.402820i \(-0.131970\pi\)
\(588\) 0 0
\(589\) 3.27197 0.134819
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14.8539i 0.609975i 0.952356 + 0.304987i \(0.0986523\pi\)
−0.952356 + 0.304987i \(0.901348\pi\)
\(594\) 0 0
\(595\) 12.8942 + 0.885881i 0.528609 + 0.0363176i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −42.6098 −1.74099 −0.870494 0.492178i \(-0.836201\pi\)
−0.870494 + 0.492178i \(0.836201\pi\)
\(600\) 0 0
\(601\) 34.4960 1.40712 0.703561 0.710635i \(-0.251592\pi\)
0.703561 + 0.710635i \(0.251592\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.0265126 0.00182153i −0.00107789 7.40555e-5i
\(606\) 0 0
\(607\) 44.0061i 1.78615i 0.449906 + 0.893076i \(0.351457\pi\)
−0.449906 + 0.893076i \(0.648543\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −7.44442 −0.301169
\(612\) 0 0
\(613\) 11.4907i 0.464104i 0.972703 + 0.232052i \(0.0745439\pi\)
−0.972703 + 0.232052i \(0.925456\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 47.2506i 1.90224i −0.308823 0.951120i \(-0.599935\pi\)
0.308823 0.951120i \(-0.400065\pi\)
\(618\) 0 0
\(619\) −25.5964 −1.02881 −0.514403 0.857549i \(-0.671986\pi\)
−0.514403 + 0.857549i \(0.671986\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 17.0299i 0.682290i
\(624\) 0 0
\(625\) 24.0648 + 6.77388i 0.962592 + 0.270955i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −0.400665 −0.0159756
\(630\) 0 0
\(631\) 6.54777 0.260663 0.130331 0.991470i \(-0.458396\pi\)
0.130331 + 0.991470i \(0.458396\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.15213 31.3246i 0.0854046 1.24308i
\(636\) 0 0
\(637\) 6.78003i 0.268635i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.899023 0.0355093 0.0177546 0.999842i \(-0.494348\pi\)
0.0177546 + 0.999842i \(0.494348\pi\)
\(642\) 0 0
\(643\) 2.48862i 0.0981416i −0.998795 0.0490708i \(-0.984374\pi\)
0.998795 0.0490708i \(-0.0156260\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.773002i 0.0303898i −0.999885 0.0151949i \(-0.995163\pi\)
0.999885 0.0151949i \(-0.00483688\pi\)
\(648\) 0 0
\(649\) 43.5901 1.71106
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 43.1740i 1.68953i 0.535139 + 0.844764i \(0.320259\pi\)
−0.535139 + 0.844764i \(0.679741\pi\)
\(654\) 0 0
\(655\) 30.7071 + 2.10970i 1.19983 + 0.0824328i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −39.3552 −1.53306 −0.766530 0.642208i \(-0.778019\pi\)
−0.766530 + 0.642208i \(0.778019\pi\)
\(660\) 0 0
\(661\) −20.7673 −0.807756 −0.403878 0.914813i \(-0.632338\pi\)
−0.403878 + 0.914813i \(0.632338\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.03651 44.1970i 0.117751 1.71388i
\(666\) 0 0
\(667\) 1.13789i 0.0440592i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 17.5031 0.675698
\(672\) 0 0
\(673\) 49.6479i 1.91379i −0.290439 0.956893i \(-0.593801\pi\)
0.290439 0.956893i \(-0.406199\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 30.5884i 1.17561i −0.809004 0.587803i \(-0.799993\pi\)
0.809004 0.587803i \(-0.200007\pi\)
\(678\) 0 0
\(679\) 40.2769 1.54569
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 28.9405i 1.10738i −0.832724 0.553688i \(-0.813220\pi\)
0.832724 0.553688i \(-0.186780\pi\)
\(684\) 0 0
\(685\) −0.996947 + 14.5107i −0.0380914 + 0.554427i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −5.39521 −0.205541
\(690\) 0 0
\(691\) −31.9739 −1.21635 −0.608173 0.793805i \(-0.708097\pi\)
−0.608173 + 0.793805i \(0.708097\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 21.8174 + 1.49894i 0.827581 + 0.0568581i
\(696\) 0 0
\(697\) 16.5226i 0.625837i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −4.51673 −0.170595 −0.0852973 0.996356i \(-0.527184\pi\)
−0.0852973 + 0.996356i \(0.527184\pi\)
\(702\) 0 0
\(703\) 1.37335i 0.0517969i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.24778i 0.234972i
\(708\) 0 0
\(709\) 29.7979 1.11908 0.559542 0.828802i \(-0.310977\pi\)
0.559542 + 0.828802i \(0.310977\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0.271550i 0.0101696i
\(714\) 0 0
\(715\) −0.508599 + 7.40275i −0.0190205 + 0.276847i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 41.8431 1.56049 0.780243 0.625477i \(-0.215096\pi\)
0.780243 + 0.625477i \(0.215096\pi\)
\(720\) 0 0
\(721\) −6.62747 −0.246820
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 12.7240 + 1.75668i 0.472559 + 0.0652413i
\(726\) 0 0
\(727\) 15.4317i 0.572330i −0.958180 0.286165i \(-0.907619\pi\)
0.958180 0.286165i \(-0.0923806\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −19.7645 −0.731018
\(732\) 0 0
\(733\) 39.1794i 1.44712i 0.690260 + 0.723561i \(0.257496\pi\)
−0.690260 + 0.723561i \(0.742504\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 34.9708i 1.28817i
\(738\) 0 0
\(739\) −32.5361 −1.19686 −0.598430 0.801175i \(-0.704209\pi\)
−0.598430 + 0.801175i \(0.704209\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 8.13346i 0.298388i −0.988808 0.149194i \(-0.952332\pi\)
0.988808 0.149194i \(-0.0476679\pi\)
\(744\) 0 0
\(745\) 13.2320 + 0.909092i 0.484783 + 0.0333065i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −4.15550 −0.151839
\(750\) 0 0
\(751\) −48.9359 −1.78570 −0.892848 0.450358i \(-0.851296\pi\)
−0.892848 + 0.450358i \(0.851296\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.608605 + 0.0418136i 0.0221494 + 0.00152175i
\(756\) 0 0
\(757\) 3.54775i 0.128945i 0.997919 + 0.0644726i \(0.0205365\pi\)
−0.997919 + 0.0644726i \(0.979463\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −40.8645 −1.48134 −0.740669 0.671870i \(-0.765491\pi\)
−0.740669 + 0.671870i \(0.765491\pi\)
\(762\) 0 0
\(763\) 3.39630i 0.122954i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 13.1358i 0.474306i
\(768\) 0 0
\(769\) 42.6263 1.53714 0.768571 0.639764i \(-0.220968\pi\)
0.768571 + 0.639764i \(0.220968\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 36.3873i 1.30876i −0.756166 0.654379i \(-0.772930\pi\)
0.756166 0.654379i \(-0.227070\pi\)
\(774\) 0 0
\(775\) 3.03651 + 0.419220i 0.109075 + 0.0150588i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 56.6340 2.02912
\(780\) 0 0
\(781\) 1.03483 0.0370291
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.24628 + 32.6951i −0.0801733 + 1.16694i
\(786\) 0 0
\(787\) 12.7280i 0.453705i −0.973929 0.226853i \(-0.927156\pi\)
0.973929 0.226853i \(-0.0728436\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 8.96059 0.318602
\(792\) 0 0
\(793\) 5.27452i 0.187304i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 20.3707i 0.721566i 0.932650 + 0.360783i \(0.117490\pi\)
−0.932650 + 0.360783i \(0.882510\pi\)
\(798\) 0 0
\(799\) −11.5914 −0.410074
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 31.4201i 1.10879i
\(804\) 0 0
\(805\) −3.66803 0.252008i −0.129281 0.00888213i
\(806\) 0