Properties

Label 804.2.s.a.161.1
Level 804
Weight 2
Character 804.161
Analytic conductor 6.420
Analytic rank 0
Dimension 20
CM discriminant -3
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.s (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{22})\)
Coefficient field: \(\Q(\zeta_{33})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{22}]$

Embedding invariants

Embedding label 161.1
Root \(-0.786053 - 0.618159i\)
Character \(\chi\) = 804.161
Dual form 804.2.s.a.5.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.57553 - 0.719520i) q^{3} +(-3.36481 + 2.91562i) q^{7} +(1.96458 + 2.26725i) q^{9} +O(q^{10})\) \(q+(-1.57553 - 0.719520i) q^{3} +(-3.36481 + 2.91562i) q^{7} +(1.96458 + 2.26725i) q^{9} +(1.63571 - 2.54522i) q^{13} +(4.23982 - 4.89301i) q^{19} +(7.39920 - 2.17260i) q^{21} +(-4.20627 - 2.70320i) q^{25} +(-1.46393 - 4.98567i) q^{27} +(-6.00018 - 9.33646i) q^{31} +12.1582 q^{37} +(-4.40845 + 2.83314i) q^{39} +(-12.9347 + 1.85973i) q^{43} +(1.82487 - 12.6923i) q^{49} +(-10.2006 + 4.65844i) q^{57} +(-4.39867 - 14.9805i) q^{61} +(-13.2209 - 1.90088i) q^{63} +(5.79361 + 5.78222i) q^{67} +(5.46060 - 1.60338i) q^{73} +(4.68209 + 7.28547i) q^{75} +(9.04681 - 14.0771i) q^{79} +(-1.28083 + 8.90839i) q^{81} +(1.91704 + 13.3333i) q^{91} +(2.73569 + 19.0271i) q^{93} -6.97869i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 6q^{9} + O(q^{10}) \) \( 20q + 6q^{9} + 16q^{19} - 12q^{21} + 10q^{25} - 20q^{37} - 24q^{39} + 10q^{49} - 66q^{57} - 132q^{63} - 16q^{67} + 90q^{73} + 44q^{79} - 18q^{81} + 48q^{91} - 36q^{93} + O(q^{100}) \)

Character values

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

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{17}{22}\right)\) \(1\)

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
\(7\) −3.36481 + 2.91562i −1.27178 + 1.10200i −0.281995 + 0.959416i \(0.590996\pi\)
−0.989782 + 0.142586i \(0.954458\pi\)
\(8\) 0 0
\(9\) 1.96458 + 2.26725i 0.654861 + 0.755750i
\(10\) 0 0
\(11\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(12\) 0 0
\(13\) 1.63571 2.54522i 0.453665 0.705917i −0.536795 0.843712i \(-0.680365\pi\)
0.990461 + 0.137795i \(0.0440016\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(18\) 0 0
\(19\) 4.23982 4.89301i 0.972680 1.12253i −0.0197599 0.999805i \(-0.506290\pi\)
0.992440 0.122728i \(-0.0391644\pi\)
\(20\) 0 0
\(21\) 7.39920 2.17260i 1.61464 0.474100i
\(22\) 0 0
\(23\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(24\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) −6.00018 9.33646i −1.07766 1.67688i −0.607589 0.794252i \(-0.707863\pi\)
−0.470075 0.882626i \(-0.655773\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 12.1582 1.99880 0.999398 0.0346855i \(-0.0110430\pi\)
0.999398 + 0.0346855i \(0.0110430\pi\)
\(38\) 0 0
\(39\) −4.40845 + 2.83314i −0.705917 + 0.453665i
\(40\) 0 0
\(41\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(42\) 0 0
\(43\) −12.9347 + 1.85973i −1.97252 + 0.283606i −0.974198 + 0.225693i \(0.927535\pi\)
−0.998322 + 0.0579125i \(0.981556\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(48\) 0 0
\(49\) 1.82487 12.6923i 0.260696 1.81318i
\(50\) 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
\(57\) −10.2006 + 4.65844i −1.35110 + 0.617026i
\(58\) 0 0
\(59\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(60\) 0 0
\(61\) −4.39867 14.9805i −0.563192 1.91806i −0.311467 0.950257i \(-0.600820\pi\)
−0.251725 0.967799i \(-0.580998\pi\)
\(62\) 0 0
\(63\) −13.2209 1.90088i −1.66567 0.239488i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 5.79361 + 5.78222i 0.707802 + 0.706411i
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(72\) 0 0
\(73\) 5.46060 1.60338i 0.639115 0.187661i 0.0539089 0.998546i \(-0.482832\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 0 0
\(75\) 4.68209 + 7.28547i 0.540641 + 0.841254i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 9.04681 14.0771i 1.01785 1.58380i 0.225018 0.974355i \(-0.427756\pi\)
0.792829 0.609445i \(-0.208608\pi\)
\(80\) 0 0
\(81\) −1.28083 + 8.90839i −0.142315 + 0.989821i
\(82\) 0 0
\(83\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(84\) 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
\(91\) 1.91704 + 13.3333i 0.200960 + 1.39771i
\(92\) 0 0
\(93\) 2.73569 + 19.0271i 0.283677 + 1.97302i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.97869i 0.708578i −0.935136 0.354289i \(-0.884723\pi\)
0.935136 0.354289i \(-0.115277\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(102\) 0 0
\(103\) 8.81568 5.66549i 0.868635 0.558238i −0.0286999 0.999588i \(-0.509137\pi\)
0.897335 + 0.441350i \(0.145500\pi\)
\(104\) 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
\(109\) 10.4772 16.3028i 1.00353 1.56153i 0.188534 0.982067i \(-0.439626\pi\)
0.814999 0.579462i \(-0.196737\pi\)
\(110\) 0 0
\(111\) −19.1556 8.74807i −1.81817 0.830330i
\(112\) 0 0
\(113\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 8.98414 1.29172i 0.830584 0.119420i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −9.25379 5.94705i −0.841254 0.540641i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 7.33874 + 8.46936i 0.651208 + 0.751534i 0.981315 0.192410i \(-0.0616302\pi\)
−0.330107 + 0.943944i \(0.607085\pi\)
\(128\) 0 0
\(129\) 21.7171 + 6.37671i 1.91208 + 0.561438i
\(130\) 0 0
\(131\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(132\) 0 0
\(133\) 28.8257i 2.49951i
\(134\) 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
\(139\) −6.12749 + 20.8683i −0.519727 + 1.77003i 0.110782 + 0.993845i \(0.464665\pi\)
−0.630509 + 0.776182i \(0.717154\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −12.0075 + 18.6840i −0.990360 + 1.54103i
\(148\) 0 0
\(149\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(150\) 0 0
\(151\) 0.426045 + 2.96321i 0.0346711 + 0.241142i 0.999786 0.0206838i \(-0.00658434\pi\)
−0.965115 + 0.261826i \(0.915675\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −10.3339 + 22.6280i −0.824732 + 1.80591i −0.302363 + 0.953193i \(0.597776\pi\)
−0.522369 + 0.852719i \(0.674952\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −25.1404 −1.96915 −0.984575 0.174966i \(-0.944019\pi\)
−0.984575 + 0.174966i \(0.944019\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(168\) 0 0
\(169\) 1.59781 + 3.49871i 0.122908 + 0.269132i
\(170\) 0 0
\(171\) 19.4231 1.48532
\(172\) 0 0
\(173\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(174\) 0 0
\(175\) 22.0348 3.16813i 1.66567 0.239488i
\(176\) 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
\(181\) 1.86882 4.09214i 0.138908 0.304166i −0.827374 0.561651i \(-0.810166\pi\)
0.966282 + 0.257485i \(0.0828937\pi\)
\(182\) 0 0
\(183\) −3.84853 + 26.7671i −0.284492 + 1.97868i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 19.4622 + 12.5076i 1.41566 + 0.909792i
\(190\) 0 0
\(191\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(192\) 0 0
\(193\) −18.7210 + 12.0312i −1.34757 + 0.866028i −0.997498 0.0706968i \(-0.977478\pi\)
−0.350068 + 0.936724i \(0.613841\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(198\) 0 0
\(199\) 0.364085 + 0.420177i 0.0258093 + 0.0297855i 0.768507 0.639841i \(-0.221000\pi\)
−0.742698 + 0.669626i \(0.766454\pi\)
\(200\) 0 0
\(201\) −4.96758 13.2787i −0.350386 0.936605i
\(202\) 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
\(211\) −9.21538 20.1789i −0.634413 1.38917i −0.904558 0.426350i \(-0.859799\pi\)
0.270146 0.962819i \(-0.412928\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 47.4111 + 13.9211i 3.21847 + 0.945029i
\(218\) 0 0
\(219\) −9.75699 1.40284i −0.659316 0.0947954i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −8.75894 19.1794i −0.586542 1.28435i −0.937509 0.347960i \(-0.886874\pi\)
0.350967 0.936388i \(-0.385853\pi\)
\(224\) 0 0
\(225\) −2.13472 14.8473i −0.142315 0.989821i
\(226\) 0 0
\(227\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(228\) 0 0
\(229\) 3.02274 + 4.70347i 0.199748 + 0.310814i 0.926649 0.375929i \(-0.122676\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −24.3823 + 15.6695i −1.58380 + 1.01785i
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 3.07530 0.902989i 0.198097 0.0581666i −0.181179 0.983450i \(-0.557991\pi\)
0.379276 + 0.925284i \(0.376173\pi\)
\(242\) 0 0
\(243\) 8.42776 13.1138i 0.540641 0.841254i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −5.51866 18.7948i −0.351144 1.19589i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(258\) 0 0
\(259\) −40.9100 + 35.4487i −2.54203 + 2.20268i
\(260\) 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
\(271\) 8.93119 + 4.07874i 0.542531 + 0.247766i 0.667779 0.744360i \(-0.267245\pi\)
−0.125247 + 0.992126i \(0.539972\pi\)
\(272\) 0 0
\(273\) 6.57322 22.3863i 0.397830 1.35488i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −15.8956 18.3445i −0.955073 1.10221i −0.994682 0.102998i \(-0.967156\pi\)
0.0396081 0.999215i \(-0.487389\pi\)
\(278\) 0 0
\(279\) 9.38024 31.9461i 0.561580 1.91257i
\(280\) 0 0
\(281\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(282\) 0 0
\(283\) 18.1894 20.9916i 1.08125 1.24782i 0.114135 0.993465i \(-0.463590\pi\)
0.967110 0.254358i \(-0.0818643\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −16.3114 + 4.78945i −0.959493 + 0.281733i
\(290\) 0 0
\(291\) −5.02131 + 10.9951i −0.294354 + 0.644546i
\(292\) 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
\(301\) 38.1005 43.9703i 2.19607 2.53440i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 27.8763 17.9150i 1.59098 1.02246i 0.619610 0.784910i \(-0.287291\pi\)
0.971374 0.237553i \(-0.0763455\pi\)
\(308\) 0 0
\(309\) −17.9658 + 2.58309i −1.02204 + 0.146947i
\(310\) 0 0
\(311\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(312\) 0 0
\(313\) −31.6320 + 14.4459i −1.78795 + 0.816528i −0.817227 + 0.576316i \(0.804490\pi\)
−0.970720 + 0.240212i \(0.922783\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −13.7605 + 6.28421i −0.763295 + 0.348585i
\(326\) 0 0
\(327\) −28.2373 + 18.1470i −1.56153 + 1.00353i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 21.6900 + 3.11855i 1.19219 + 0.171411i 0.709708 0.704496i \(-0.248827\pi\)
0.482481 + 0.875907i \(0.339736\pi\)
\(332\) 0 0
\(333\) 23.8858 + 27.5657i 1.30893 + 1.51059i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −5.08244 + 4.40396i −0.276858 + 0.239899i −0.782211 0.623014i \(-0.785908\pi\)
0.505352 + 0.862913i \(0.331363\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 14.0159 + 21.8092i 0.756789 + 1.17759i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(348\) 0 0
\(349\) −5.03054 + 34.9882i −0.269279 + 1.87287i 0.186034 + 0.982543i \(0.440437\pi\)
−0.455313 + 0.890332i \(0.650472\pi\)
\(350\) 0 0
\(351\) −15.0842 4.42912i −0.805135 0.236409i
\(352\) 0 0
\(353\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(354\) 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
\(361\) −3.26151 22.6843i −0.171658 1.19391i
\(362\) 0 0
\(363\) 10.3006 + 16.0280i 0.540641 + 0.841254i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 32.2325 14.7201i 1.68252 0.768382i 0.683253 0.730182i \(-0.260565\pi\)
0.999270 0.0382006i \(-0.0121626\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 24.1815i 1.25207i 0.779795 + 0.626035i \(0.215323\pi\)
−0.779795 + 0.626035i \(0.784677\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −17.1989 7.85448i −0.883449 0.403458i −0.0785782 0.996908i \(-0.525038\pi\)
−0.804871 + 0.593450i \(0.797765\pi\)
\(380\) 0 0
\(381\) −5.46853 18.6241i −0.280161 0.954141i
\(382\) 0 0
\(383\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −29.6277 25.6726i −1.50606 1.30501i
\(388\) 0 0
\(389\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −15.0970 4.43288i −0.757697 0.222480i −0.120007 0.992773i \(-0.538292\pi\)
−0.637690 + 0.770293i \(0.720110\pi\)
\(398\) 0 0
\(399\) 20.7407 45.4158i 1.03833 2.27363i
\(400\) 0 0
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) −33.5779 −1.67264
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 1.95685 1.69562i 0.0967601 0.0838431i −0.605137 0.796121i \(-0.706882\pi\)
0.701898 + 0.712278i \(0.252336\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 24.6692 28.4698i 1.20806 1.39417i
\(418\) 0 0
\(419\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(420\) 0 0
\(421\) 0.144573 0.166847i 0.00704607 0.00813160i −0.752216 0.658917i \(-0.771015\pi\)
0.759262 + 0.650785i \(0.225560\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 58.4781 + 37.5816i 2.82996 + 1.81870i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) −19.4909 30.3285i −0.936674 1.45749i −0.888617 0.458649i \(-0.848333\pi\)
−0.0480569 0.998845i \(-0.515303\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 26.8748 1.28266 0.641331 0.767264i \(-0.278382\pi\)
0.641331 + 0.767264i \(0.278382\pi\)
\(440\) 0 0
\(441\) 32.3616 20.7976i 1.54103 0.990360i
\(442\) 0 0
\(443\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 1.46084 4.97517i 0.0686363 0.233754i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −20.9197 13.4443i −0.978583 0.628897i −0.0495022 0.998774i \(-0.515763\pi\)
−0.929081 + 0.369877i \(0.879400\pi\)
\(458\) 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
\(463\) −2.77184 9.44002i −0.128818 0.438715i 0.869673 0.493629i \(-0.164330\pi\)
−0.998491 + 0.0549137i \(0.982512\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(468\) 0 0
\(469\) −36.3532 2.56408i −1.67863 0.118398i
\(470\) 0 0
\(471\) 32.5626 28.2157i 1.50041 1.30011i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −31.0606 + 9.12022i −1.42516 + 0.418464i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(480\) 0 0
\(481\) 19.8873 30.9453i 0.906785 1.41098i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −43.5968 6.26828i −1.97556 0.284043i −0.996915 0.0784867i \(-0.974991\pi\)
−0.978645 0.205556i \(-0.934100\pi\)
\(488\) 0 0
\(489\) 39.6094 + 18.0890i 1.79120 + 0.818014i
\(490\) 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
\(499\) 8.92718i 0.399636i 0.979833 + 0.199818i \(0.0640350\pi\)
−0.979833 + 0.199818i \(0.935965\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 6.66198i 0.295869i
\(508\) 0 0
\(509\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(510\) 0 0
\(511\) −13.6990 + 21.3161i −0.606009 + 0.942969i
\(512\) 0 0
\(513\) −30.6017 13.9753i −1.35110 0.617026i
\(514\) 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
\(523\) 33.0384 + 21.2325i 1.44467 + 0.928431i 0.999455 + 0.0330064i \(0.0105082\pi\)
0.445212 + 0.895425i \(0.353128\pi\)
\(524\) 0 0
\(525\) −36.9960 10.8630i −1.61464 0.474100i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −15.0618 17.3822i −0.654861 0.755750i
\(530\) 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
\(541\) 12.5500 42.7414i 0.539567 1.83760i −0.00668980 0.999978i \(-0.502129\pi\)
0.546257 0.837618i \(-0.316052\pi\)
\(542\) 0 0
\(543\) −5.88875 + 5.10263i −0.252710 + 0.218975i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −12.1268 + 41.3002i −0.518506 + 1.76587i 0.116316 + 0.993212i \(0.462891\pi\)
−0.634822 + 0.772658i \(0.718927\pi\)
\(548\) 0 0
\(549\) 25.3230 39.4033i 1.08076 1.68169i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 10.6028 + 73.7439i 0.450876 + 3.13591i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(558\) 0 0
\(559\) −16.4240 + 35.9636i −0.694662 + 1.52110i
\(560\) 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
\(567\) −21.6638 33.7095i −0.909792 1.41566i
\(568\) 0 0
\(569\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(570\) 0 0
\(571\) 14.2558 + 31.2159i 0.596588 + 1.30635i 0.931378 + 0.364054i \(0.118607\pi\)
−0.334790 + 0.942293i \(0.608665\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −0.332013 + 0.0477362i −0.0138219 + 0.00198729i −0.149222 0.988804i \(-0.547677\pi\)
0.135400 + 0.990791i \(0.456768\pi\)
\(578\) 0 0
\(579\) 38.1522 5.48545i 1.58555 0.227968i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(588\) 0 0
\(589\) −71.1230 10.2259i −2.93057 0.421353i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.271301 0.923967i −0.0111036 0.0378155i
\(598\) 0 0
\(599\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(600\) 0 0
\(601\) −8.66735 10.0027i −0.353549 0.408017i 0.550919 0.834559i \(-0.314277\pi\)
−0.904468 + 0.426542i \(0.859732\pi\)
\(602\) 0 0
\(603\) −1.72771 + 24.4952i −0.0703577 + 0.997522i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 6.70746 46.6514i 0.272247 1.89352i −0.152650 0.988280i \(-0.548781\pi\)
0.424897 0.905242i \(-0.360310\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 20.5327 + 44.9603i 0.829308 + 1.81593i 0.469696 + 0.882828i \(0.344364\pi\)
0.359612 + 0.933102i \(0.382909\pi\)
\(614\) 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
\(619\) 39.7606 + 11.6748i 1.59812 + 0.469249i 0.955021 0.296538i \(-0.0958321\pi\)
0.643094 + 0.765787i \(0.277650\pi\)
\(620\) 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
\(631\) −27.0845 42.1444i −1.07822 1.67774i −0.602390 0.798202i \(-0.705785\pi\)
−0.475828 0.879538i \(-0.657851\pi\)
\(632\) 0 0
\(633\) 38.4230i 1.52718i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −29.3197 25.4056i −1.16169 1.00661i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) −24.1475 + 7.09036i −0.952286 + 0.279616i −0.720738 0.693207i \(-0.756197\pi\)
−0.231548 + 0.972824i \(0.574379\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −64.6809 56.0464i −2.53505 2.19663i
\(652\) 0 0
\(653\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 14.3630 + 9.23057i 0.560356 + 0.360119i
\(658\) 0 0
\(659\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(660\) 0 0
\(661\) 32.1520 27.8598i 1.25057 1.08362i 0.257474 0.966285i \(-0.417110\pi\)
0.993092 0.117337i \(-0.0374357\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 36.5199i 1.41194i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 24.9073 + 11.3748i 0.960107 + 0.438466i 0.832908 0.553411i \(-0.186674\pi\)
0.127198 + 0.991877i \(0.459401\pi\)
\(674\) 0 0
\(675\) −7.31963 + 24.9284i −0.281733 + 0.959493i
\(676\) 0 0
\(677\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(678\) 0 0
\(679\) 20.3472 + 23.4819i 0.780855 + 0.901154i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −1.37817 9.58538i −0.0525804 0.365705i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 33.4120 9.81065i 1.27105 0.373215i 0.424455 0.905449i \(-0.360466\pi\)
0.846597 + 0.532234i \(0.178648\pi\)
\(692\) 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 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(702\) 0 0
\(703\) 51.5485 59.4902i 1.94419 2.24372i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −29.4234 + 18.9093i −1.10502 + 0.710153i −0.960202 0.279306i \(-0.909896\pi\)
−0.144817 + 0.989458i \(0.546259\pi\)
\(710\) 0 0
\(711\) 49.6895 7.14428i 1.86350 0.267931i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(720\) 0 0
\(721\) −13.1446 + 44.7665i −0.489532 + 1.66719i
\(722\) 0 0
\(723\) −5.49494 0.790053i −0.204359 0.0293824i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −43.6524 + 19.9354i −1.61898 + 0.739362i −0.998976 0.0452379i \(-0.985595\pi\)
−0.620002 + 0.784600i \(0.712868\pi\)
\(728\) 0 0
\(729\) −22.7138 + 14.5973i −0.841254 + 0.540641i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 50.8753 + 7.31477i 1.87912 + 0.270177i 0.984334 0.176312i \(-0.0564167\pi\)
0.894789 + 0.446489i \(0.147326\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −6.38022 + 5.52850i −0.234700 + 0.203369i −0.764268 0.644899i \(-0.776900\pi\)
0.529568 + 0.848268i \(0.322354\pi\)
\(740\) 0 0
\(741\) −4.82845 + 33.5826i −0.177377 + 1.23369i
\(742\) 0 0
\(743\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 1.38669 9.64466i 0.0506011 0.351939i −0.948753 0.316017i \(-0.897654\pi\)
0.999355 0.0359215i \(-0.0114366\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 35.6648 + 16.2875i 1.29626 + 0.591981i 0.939606 0.342257i \(-0.111191\pi\)
0.356651 + 0.934238i \(0.383919\pi\)
\(758\) 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
\(763\) 12.2792 + 85.4035i 0.444536 + 3.09181i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −41.4298 + 18.9204i −1.49400 + 0.682286i −0.984046 0.177916i \(-0.943064\pi\)
−0.509953 + 0.860202i \(0.670337\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(774\) 0 0
\(775\) 55.4914i 1.99331i
\(776\) 0 0
\(777\) 89.9610 26.4149i 3.22733 0.947630i
\(778\) 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
\(787\) 32.8522 4.72344i 1.17106 0.168372i 0.470784 0.882248i \(-0.343971\pi\)
0.700272 + 0.713876i \(0.253062\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −45.3236 13.3082i −1.60949 0.472589i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\)