Properties

Label 804.2.ba.a.113.1
Level 804
Weight 2
Character 804.113
Analytic conductor 6.420
Analytic rank 0
Dimension 20
CM discriminant -3
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{33})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{66}]$

Embedding invariants

Embedding label 113.1
Root \(-0.995472 + 0.0950560i\)
Character \(\chi\) = 804.113
Dual form 804.2.ba.a.185.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.57553 + 0.719520i) q^{3} +(3.27565 + 1.13371i) q^{7} +(1.96458 + 2.26725i) q^{9} +O(q^{10})\) \(q+(1.57553 + 0.719520i) q^{3} +(3.27565 + 1.13371i) q^{7} +(1.96458 + 2.26725i) q^{9} +(-0.172289 - 0.334195i) q^{13} +(0.0563415 + 0.162788i) q^{19} +(4.34515 + 4.14309i) q^{21} +(-4.20627 - 2.70320i) q^{25} +(1.46393 + 4.98567i) q^{27} +(0.658548 - 1.27741i) q^{31} +(-2.33343 + 4.04162i) q^{37} +(-0.0309871 - 0.650499i) q^{39} +(8.39906 - 1.20760i) q^{43} +(3.94220 + 3.10018i) q^{49} +(-0.0283616 + 0.297016i) q^{57} +(5.40915 + 1.31225i) q^{61} +(3.86487 + 9.65398i) q^{63} +(-1.34943 - 8.07335i) q^{67} +(-0.548063 + 2.25915i) q^{73} +(-4.68209 - 7.28547i) q^{75} +(-17.2085 - 0.819741i) q^{79} +(-1.28083 + 8.90839i) q^{81} +(-0.185479 - 1.29003i) q^{91} +(1.95668 - 1.53875i) q^{93} +(-2.91553 - 1.68328i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 6q^{7} + 6q^{9} + O(q^{10}) \) \( 20q + 6q^{7} + 6q^{9} + 9q^{13} - 8q^{19} + 6q^{21} + 10q^{25} - 3q^{31} + 10q^{37} - 9q^{39} - 5q^{49} + 141q^{57} + 27q^{61} + 147q^{63} + 11q^{67} - 180q^{73} - 166q^{79} - 18q^{81} - 36q^{91} - 3q^{93} + 33q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{29}{66}\right)\) \(1\)

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
\(3\) 1.57553 + 0.719520i 0.909632 + 0.415415i
\(4\) 0 0
\(5\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(6\) 0 0
\(7\) 3.27565 + 1.13371i 1.23808 + 0.428503i 0.866162 0.499763i \(-0.166579\pi\)
0.371917 + 0.928266i \(0.378701\pi\)
\(8\) 0 0
\(9\) 1.96458 + 2.26725i 0.654861 + 0.755750i
\(10\) 0 0
\(11\) 0 0 0.971812 0.235759i \(-0.0757576\pi\)
−0.971812 + 0.235759i \(0.924242\pi\)
\(12\) 0 0
\(13\) −0.172289 0.334195i −0.0477845 0.0926889i 0.863734 0.503948i \(-0.168120\pi\)
−0.911519 + 0.411259i \(0.865089\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(18\) 0 0
\(19\) 0.0563415 + 0.162788i 0.0129256 + 0.0373462i 0.951279 0.308331i \(-0.0997704\pi\)
−0.938353 + 0.345677i \(0.887649\pi\)
\(20\) 0 0
\(21\) 4.34515 + 4.14309i 0.948190 + 0.904097i
\(22\) 0 0
\(23\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(24\) 0 0
\(25\) −4.20627 2.70320i −0.841254 0.540641i
\(26\) 0 0
\(27\) 1.46393 + 4.98567i 0.281733 + 0.959493i
\(28\) 0 0
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 0 0
\(31\) 0.658548 1.27741i 0.118279 0.229429i −0.822262 0.569109i \(-0.807288\pi\)
0.940541 + 0.339680i \(0.110319\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.33343 + 4.04162i −0.383614 + 0.664439i −0.991576 0.129527i \(-0.958654\pi\)
0.607962 + 0.793966i \(0.291987\pi\)
\(38\) 0 0
\(39\) −0.0309871 0.650499i −0.00496191 0.104163i
\(40\) 0 0
\(41\) 0 0 −0.618159 0.786053i \(-0.712121\pi\)
0.618159 + 0.786053i \(0.287879\pi\)
\(42\) 0 0
\(43\) 8.39906 1.20760i 1.28084 0.184158i 0.531909 0.846801i \(-0.321475\pi\)
0.748935 + 0.662644i \(0.230566\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(48\) 0 0
\(49\) 3.94220 + 3.10018i 0.563172 + 0.442883i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −0.0283616 + 0.297016i −0.00375659 + 0.0393408i
\(58\) 0 0
\(59\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(60\) 0 0
\(61\) 5.40915 + 1.31225i 0.692571 + 0.168016i 0.566569 0.824014i \(-0.308270\pi\)
0.126001 + 0.992030i \(0.459786\pi\)
\(62\) 0 0
\(63\) 3.86487 + 9.65398i 0.486928 + 1.21629i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.34943 8.07335i −0.164860 0.986317i
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(72\) 0 0
\(73\) −0.548063 + 2.25915i −0.0641459 + 0.264413i −0.994850 0.101361i \(-0.967680\pi\)
0.930704 + 0.365774i \(0.119196\pi\)
\(74\) 0 0
\(75\) −4.68209 7.28547i −0.540641 0.841254i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −17.2085 0.819741i −1.93610 0.0922280i −0.956325 0.292306i \(-0.905577\pi\)
−0.979780 + 0.200078i \(0.935880\pi\)
\(80\) 0 0
\(81\) −1.28083 + 8.90839i −0.142315 + 0.989821i
\(82\) 0 0
\(83\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(90\) 0 0
\(91\) −0.185479 1.29003i −0.0194434 0.135232i
\(92\) 0 0
\(93\) 1.95668 1.53875i 0.202898 0.159561i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −2.91553 1.68328i −0.296027 0.170911i 0.344630 0.938739i \(-0.388004\pi\)
−0.640657 + 0.767828i \(0.721338\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 0.189251 0.981929i \(-0.439394\pi\)
−0.189251 + 0.981929i \(0.560606\pi\)
\(102\) 0 0
\(103\) −13.9682 7.20113i −1.37633 0.709548i −0.398153 0.917319i \(-0.630349\pi\)
−0.978178 + 0.207771i \(0.933379\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(108\) 0 0
\(109\) 7.38644 11.4935i 0.707492 1.10088i −0.282433 0.959287i \(-0.591141\pi\)
0.989925 0.141592i \(-0.0452222\pi\)
\(110\) 0 0
\(111\) −6.58442 + 4.68874i −0.624965 + 0.445036i
\(112\) 0 0
\(113\) 0 0 0.690079 0.723734i \(-0.257576\pi\)
−0.690079 + 0.723734i \(0.742424\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.419226 1.04718i 0.0387575 0.0968114i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 9.77719 5.04049i 0.888835 0.458227i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −3.08389 + 8.91031i −0.273651 + 0.790663i 0.721510 + 0.692404i \(0.243448\pi\)
−0.995161 + 0.0982585i \(0.968673\pi\)
\(128\) 0 0
\(129\) 14.1018 + 4.14068i 1.24160 + 0.364566i
\(130\) 0 0
\(131\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(132\) 0 0
\(133\) 0.597112i 0.0517762i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(138\) 0 0
\(139\) 6.50241 22.1452i 0.551528 1.87833i 0.0793066 0.996850i \(-0.474729\pi\)
0.472221 0.881480i \(-0.343452\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 3.98041 + 7.72092i 0.328299 + 0.636811i
\(148\) 0 0
\(149\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(150\) 0 0
\(151\) −22.7526 9.10878i −1.85158 0.741262i −0.953460 0.301518i \(-0.902507\pi\)
−0.898123 0.439744i \(-0.855069\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 3.79352 + 5.32725i 0.302756 + 0.425161i 0.937726 0.347375i \(-0.112927\pi\)
−0.634970 + 0.772537i \(0.718988\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0.792696 + 1.37299i 0.0620887 + 0.107541i 0.895399 0.445265i \(-0.146890\pi\)
−0.833310 + 0.552806i \(0.813557\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(168\) 0 0
\(169\) 7.45874 10.4743i 0.573749 0.805718i
\(170\) 0 0
\(171\) −0.258394 + 0.447551i −0.0197599 + 0.0342251i
\(172\) 0 0
\(173\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(174\) 0 0
\(175\) −10.7136 13.6235i −0.809872 1.02984i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(180\) 0 0
\(181\) −9.39520 + 0.897132i −0.698339 + 0.0666833i −0.438186 0.898884i \(-0.644379\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 7.57808 + 5.95947i 0.560188 + 0.440537i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −0.857016 + 17.9910i −0.0623388 + 1.30865i
\(190\) 0 0
\(191\) 0 0 0.0950560 0.995472i \(-0.469697\pi\)
−0.0950560 + 0.995472i \(0.530303\pi\)
\(192\) 0 0
\(193\) 6.06421 3.89723i 0.436511 0.280529i −0.303873 0.952713i \(-0.598280\pi\)
0.740384 + 0.672184i \(0.234643\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 −0.371662 0.928368i \(-0.621212\pi\)
0.371662 + 0.928368i \(0.378788\pi\)
\(198\) 0 0
\(199\) −19.5091 + 3.76007i −1.38296 + 0.266544i −0.825848 0.563892i \(-0.809303\pi\)
−0.557114 + 0.830436i \(0.688091\pi\)
\(200\) 0 0
\(201\) 3.68287 13.6907i 0.259769 0.965671i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −28.1851 2.69135i −1.94034 0.185280i −0.948875 0.315652i \(-0.897777\pi\)
−0.991465 + 0.130372i \(0.958383\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3.60538 3.43773i 0.244749 0.233368i
\(218\) 0 0
\(219\) −2.48899 + 3.16501i −0.168190 + 0.213871i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −10.2636 22.4742i −0.687303 1.50498i −0.854715 0.519097i \(-0.826268\pi\)
0.167412 0.985887i \(-0.446459\pi\)
\(224\) 0 0
\(225\) −2.13472 14.8473i −0.142315 0.989821i
\(226\) 0 0
\(227\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(228\) 0 0
\(229\) −8.38361 + 0.399360i −0.554004 + 0.0263905i −0.322718 0.946495i \(-0.604597\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.814576 0.580057i \(-0.803030\pi\)
0.814576 + 0.580057i \(0.196970\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −26.5226 13.6734i −1.72283 0.888180i
\(238\) 0 0
\(239\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(240\) 0 0
\(241\) −0.244718 + 0.0718558i −0.0157637 + 0.00462864i −0.289605 0.957146i \(-0.593524\pi\)
0.273841 + 0.961775i \(0.411706\pi\)
\(242\) 0 0
\(243\) −8.42776 + 13.1138i −0.540641 + 0.841254i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0.0446959 0.0468757i 0.00284393 0.00298263i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.371662 0.928368i \(-0.378788\pi\)
−0.371662 + 0.928368i \(0.621212\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(258\) 0 0
\(259\) −12.2256 + 10.5935i −0.759659 + 0.658248i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) −10.6504 4.86387i −0.646966 0.295459i 0.0647769 0.997900i \(-0.479366\pi\)
−0.711742 + 0.702440i \(0.752094\pi\)
\(272\) 0 0
\(273\) 0.635977 2.16594i 0.0384911 0.131088i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 10.7480 + 12.4039i 0.645787 + 0.745278i 0.980387 0.197082i \(-0.0631466\pi\)
−0.334600 + 0.942360i \(0.608601\pi\)
\(278\) 0 0
\(279\) 4.18997 1.01648i 0.250847 0.0608548i
\(280\) 0 0
\(281\) 0 0 −0.458227 0.888835i \(-0.651515\pi\)
0.458227 + 0.888835i \(0.348485\pi\)
\(282\) 0 0
\(283\) 22.0240 25.4171i 1.30919 1.51089i 0.633125 0.774050i \(-0.281772\pi\)
0.676068 0.736839i \(-0.263682\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 12.3035 + 11.7313i 0.723734 + 0.690079i
\(290\) 0 0
\(291\) −3.38234 4.74983i −0.198276 0.278440i
\(292\) 0 0
\(293\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 28.8814 + 5.56644i 1.66470 + 0.320844i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.51544 + 31.8131i 0.0864909 + 1.81567i 0.459867 + 0.887988i \(0.347897\pi\)
−0.373376 + 0.927680i \(0.621800\pi\)
\(308\) 0 0
\(309\) −16.8260 21.3960i −0.957198 1.21718i
\(310\) 0 0
\(311\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(312\) 0 0
\(313\) 1.38404 0.632072i 0.0782308 0.0357268i −0.375915 0.926654i \(-0.622672\pi\)
0.454146 + 0.890927i \(0.349944\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −0.178701 + 1.87145i −0.00991257 + 0.103809i
\(326\) 0 0
\(327\) 19.9074 12.7937i 1.10088 0.707492i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 7.53875 + 18.8309i 0.414367 + 1.03504i 0.977924 + 0.208962i \(0.0670085\pi\)
−0.563556 + 0.826078i \(0.690567\pi\)
\(332\) 0 0
\(333\) −13.7476 + 2.64963i −0.753363 + 0.145199i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 6.30248 + 32.7004i 0.343318 + 1.78130i 0.585089 + 0.810969i \(0.301059\pi\)
−0.241771 + 0.970333i \(0.577728\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −3.71958 5.78778i −0.200839 0.312511i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 −0.998867 0.0475819i \(-0.984848\pi\)
0.998867 + 0.0475819i \(0.0151515\pi\)
\(348\) 0 0
\(349\) −5.31044 + 36.9349i −0.284261 + 1.97708i −0.0917948 + 0.995778i \(0.529260\pi\)
−0.192467 + 0.981304i \(0.561649\pi\)
\(350\) 0 0
\(351\) 1.41397 1.34821i 0.0754719 0.0719624i
\(352\) 0 0
\(353\) 0 0 0.618159 0.786053i \(-0.287879\pi\)
−0.618159 + 0.786053i \(0.712121\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(360\) 0 0
\(361\) 14.9117 11.7267i 0.784825 0.617194i
\(362\) 0 0
\(363\) 19.0310 0.906557i 0.998867 0.0475819i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 30.7002 + 21.8615i 1.60254 + 1.14116i 0.905691 + 0.423938i \(0.139353\pi\)
0.696844 + 0.717222i \(0.254587\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0.336490 0.194273i 0.0174228 0.0100591i −0.491263 0.871011i \(-0.663465\pi\)
0.508686 + 0.860952i \(0.330131\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 29.2453 20.8255i 1.50223 1.06973i 0.526653 0.850081i \(-0.323447\pi\)
0.975578 0.219653i \(-0.0704926\pi\)
\(380\) 0 0
\(381\) −11.2699 + 11.8195i −0.577375 + 0.605533i
\(382\) 0 0
\(383\) 0 0 0.945001 0.327068i \(-0.106061\pi\)
−0.945001 + 0.327068i \(0.893939\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 19.2386 + 16.6703i 0.977951 + 0.847400i
\(388\) 0 0
\(389\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 13.3155 + 3.90978i 0.668284 + 0.196226i 0.598239 0.801318i \(-0.295867\pi\)
0.0700455 + 0.997544i \(0.477686\pi\)
\(398\) 0 0
\(399\) −0.429634 + 0.940767i −0.0215086 + 0.0470973i
\(400\) 0 0
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) −0.540363 −0.0269174
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 22.6809 + 7.84995i 1.12150 + 0.388155i 0.824013 0.566571i \(-0.191730\pi\)
0.297487 + 0.954726i \(0.403852\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 26.1786 30.2118i 1.28197 1.47948i
\(418\) 0 0
\(419\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(420\) 0 0
\(421\) 10.9748 + 31.7095i 0.534877 + 1.54543i 0.811444 + 0.584431i \(0.198682\pi\)
−0.276567 + 0.960995i \(0.589197\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 16.2308 + 10.4309i 0.785462 + 0.504786i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(432\) 0 0
\(433\) 15.5288 30.1217i 0.746268 1.44756i −0.142786 0.989754i \(-0.545606\pi\)
0.889053 0.457804i \(-0.151364\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −18.7908 + 32.5466i −0.896836 + 1.55337i −0.0653196 + 0.997864i \(0.520807\pi\)
−0.831516 + 0.555501i \(0.812527\pi\)
\(440\) 0 0
\(441\) 0.715896 + 15.0285i 0.0340903 + 0.715644i
\(442\) 0 0
\(443\) 0 0 −0.618159 0.786053i \(-0.712121\pi\)
0.618159 + 0.786053i \(0.287879\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −29.2935 30.7221i −1.37633 1.44345i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.71353 + 35.9715i −0.0801557 + 1.68267i 0.498334 + 0.866985i \(0.333945\pi\)
−0.578490 + 0.815690i \(0.696358\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(462\) 0 0
\(463\) −38.9391 9.44652i −1.80965 0.439017i −0.818812 0.574061i \(-0.805367\pi\)
−0.990840 + 0.135044i \(0.956882\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(468\) 0 0
\(469\) 4.73260 27.9753i 0.218531 1.29178i
\(470\) 0 0
\(471\) 2.14374 + 11.1228i 0.0987781 + 0.512509i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.203062 0.837033i 0.00931713 0.0384057i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(480\) 0 0
\(481\) 1.75272 + 0.0834921i 0.0799169 + 0.00380691i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −8.12087 + 10.3265i −0.367992 + 0.467940i −0.934421 0.356171i \(-0.884082\pi\)
0.566429 + 0.824110i \(0.308325\pi\)
\(488\) 0 0
\(489\) 0.261022 + 2.73355i 0.0118038 + 0.123615i
\(490\) 0 0
\(491\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 37.6965 + 21.7641i 1.68753 + 0.974295i 0.956402 + 0.292052i \(0.0943381\pi\)
0.731126 + 0.682243i \(0.238995\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.189251 0.981929i \(-0.439394\pi\)
−0.189251 + 0.981929i \(0.560606\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 19.2879 11.1359i 0.856608 0.494563i
\(508\) 0 0
\(509\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(510\) 0 0
\(511\) −4.35649 + 6.77882i −0.192720 + 0.299878i
\(512\) 0 0
\(513\) −0.729128 + 0.519210i −0.0321918 + 0.0229237i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(522\) 0 0
\(523\) 25.5940 13.1946i 1.11915 0.576962i 0.203554 0.979064i \(-0.434751\pi\)
0.915595 + 0.402102i \(0.131720\pi\)
\(524\) 0 0
\(525\) −7.07724 29.1728i −0.308876 1.27320i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −7.52256 + 21.7350i −0.327068 + 0.945001i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −6.62871 + 22.5753i −0.284991 + 0.970589i 0.685222 + 0.728334i \(0.259705\pi\)
−0.970213 + 0.242255i \(0.922113\pi\)
\(542\) 0 0
\(543\) −15.4479 5.34657i −0.662933 0.229443i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 7.42972 1.80243i 0.317672 0.0770664i −0.0737527 0.997277i \(-0.523498\pi\)
0.391425 + 0.920210i \(0.371982\pi\)
\(548\) 0 0
\(549\) 7.65153 + 14.8419i 0.326559 + 0.633437i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −55.4396 22.1947i −2.35753 0.943813i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(558\) 0 0
\(559\) −1.85064 2.59886i −0.0782738 0.109920i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −14.2951 + 27.7287i −0.600339 + 1.16449i
\(568\) 0 0
\(569\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(570\) 0 0
\(571\) 11.7219 16.4611i 0.490547 0.688878i −0.492897 0.870088i \(-0.664062\pi\)
0.983444 + 0.181210i \(0.0580014\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −13.4235 17.0694i −0.558827 0.710607i 0.421756 0.906709i \(-0.361414\pi\)
−0.980583 + 0.196102i \(0.937171\pi\)
\(578\) 0 0
\(579\) 12.3585 1.77688i 0.513601 0.0738446i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.690079 0.723734i \(-0.742424\pi\)
0.690079 + 0.723734i \(0.257576\pi\)
\(588\) 0 0
\(589\) 0.245050 + 0.0352329i 0.0100971 + 0.00145175i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.0950560 0.995472i \(-0.469697\pi\)
−0.0950560 + 0.995472i \(0.530303\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −33.4426 8.11308i −1.36871 0.332046i
\(598\) 0 0
\(599\) 0 0 −0.371662 0.928368i \(-0.621212\pi\)
0.371662 + 0.928368i \(0.378788\pi\)
\(600\) 0 0
\(601\) −45.6864 + 8.80533i −1.86359 + 0.359177i −0.991493 0.130163i \(-0.958450\pi\)
−0.872093 + 0.489339i \(0.837238\pi\)
\(602\) 0 0
\(603\) 15.6532 18.9203i 0.637449 0.770493i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 26.1439 10.4665i 1.06115 0.424820i 0.225591 0.974222i \(-0.427569\pi\)
0.835558 + 0.549402i \(0.185144\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −37.6683 3.59689i −1.52141 0.145277i −0.699391 0.714739i \(-0.746545\pi\)
−0.822017 + 0.569462i \(0.807151\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(618\) 0 0
\(619\) −21.3405 + 20.3482i −0.857749 + 0.817862i −0.984738 0.174042i \(-0.944317\pi\)
0.126990 + 0.991904i \(0.459469\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 10.3854 + 22.7408i 0.415415 + 0.909632i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 29.9166 1.42510i 1.19096 0.0567325i 0.557279 0.830326i \(-0.311846\pi\)
0.633683 + 0.773593i \(0.281543\pi\)
\(632\) 0 0
\(633\) −42.4699 24.5200i −1.68803 0.974583i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0.356865 1.85159i 0.0141395 0.0733627i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(642\) 0 0
\(643\) 35.0716 10.2979i 1.38309 0.406111i 0.496245 0.868183i \(-0.334712\pi\)
0.886843 + 0.462072i \(0.152894\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.814576 0.580057i \(-0.196970\pi\)
−0.814576 + 0.580057i \(0.803030\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 8.15390 2.82209i 0.319577 0.110607i
\(652\) 0 0
\(653\) 0 0 0.371662 0.928368i \(-0.378788\pi\)
−0.371662 + 0.928368i \(0.621212\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −6.19876 + 3.19568i −0.241837 + 0.124675i
\(658\) 0 0
\(659\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(660\) 0 0
\(661\) 13.6310 11.8114i 0.530186 0.459408i −0.348160 0.937435i \(-0.613193\pi\)
0.878345 + 0.478027i \(0.158648\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 42.7936i 1.65450i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −41.2280 18.8282i −1.58922 0.725773i −0.592416 0.805632i \(-0.701826\pi\)
−0.996806 + 0.0798590i \(0.974553\pi\)
\(674\) 0 0
\(675\) 7.31963 24.9284i 0.281733 0.959493i
\(676\) 0 0
\(677\) 0 0 −0.945001 0.327068i \(-0.893939\pi\)
0.945001 + 0.327068i \(0.106061\pi\)
\(678\) 0 0
\(679\) −7.64188 8.81920i −0.293269 0.338450i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.458227 0.888835i \(-0.651515\pi\)
0.458227 + 0.888835i \(0.348485\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −13.4960 5.40297i −0.514903 0.206136i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 15.4608 + 14.7418i 0.588155 + 0.560805i 0.924620 0.380891i \(-0.124383\pi\)
−0.336465 + 0.941696i \(0.609231\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 0.458227 0.888835i \(-0.348485\pi\)
−0.458227 + 0.888835i \(0.651515\pi\)
\(702\) 0 0
\(703\) −0.789398 0.152144i −0.0297727 0.00573822i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 2.53392 + 53.1936i 0.0951635 + 1.99773i 0.0501074 + 0.998744i \(0.484044\pi\)
0.0450561 + 0.998984i \(0.485653\pi\)
\(710\) 0 0
\(711\) −31.9489 40.6263i −1.19818 1.52361i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(720\) 0 0
\(721\) −37.5910 39.4243i −1.39996 1.46824i
\(722\) 0 0
\(723\) −0.437262 0.0628688i −0.0162620 0.00233812i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −4.91494 + 51.4716i −0.182285 + 1.90898i 0.191555 + 0.981482i \(0.438647\pi\)
−0.373840 + 0.927493i \(0.621959\pi\)
\(728\) 0 0
\(729\) −22.7138 + 14.5973i −0.841254 + 0.540641i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −8.98548 22.4446i −0.331886 0.829012i −0.996637 0.0819464i \(-0.973886\pi\)
0.664750 0.747065i \(-0.268538\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −5.85808 30.3946i −0.215493 1.11808i −0.914999 0.403456i \(-0.867809\pi\)
0.699506 0.714627i \(-0.253403\pi\)
\(740\) 0 0
\(741\) 0.104148 0.0416944i 0.00382596 0.00153168i
\(742\) 0 0
\(743\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −3.49306 + 24.2948i −0.127464 + 0.886528i 0.821290 + 0.570511i \(0.193255\pi\)
−0.948753 + 0.316017i \(0.897654\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −3.48863 36.5346i −0.126797 1.32787i −0.805121 0.593111i \(-0.797900\pi\)
0.678324 0.734763i \(-0.262706\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(762\) 0 0
\(763\) 37.2257 29.2746i 1.34766 1.05981i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −0.520940 0.370960i −0.0187856 0.0133771i 0.570626 0.821210i \(-0.306701\pi\)
−0.589411 + 0.807833i \(0.700640\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(774\) 0 0
\(775\) −6.22312 + 3.59292i −0.223541 + 0.129061i
\(776\) 0 0
\(777\) −26.8839 + 7.89384i −0.964456 + 0.283190i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −10.1693 + 25.4017i −0.362497 + 0.905474i 0.629243 + 0.777209i \(0.283365\pi\)
−0.991740 + 0.128265i \(0.959059\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −0.493393 2.03380i −0.0175209 0.0722222i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0