Properties

Label 804.2.s.a.209.1
Level 804
Weight 2
Character 804.209
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 209.1
Root \(0.723734 - 0.690079i\)
Character \(\chi\) = 804.209
Dual form 804.2.s.a.377.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.30900 + 1.13425i) q^{3} +(2.17449 + 0.312644i) q^{7} +(0.426945 - 2.96946i) q^{9} +O(q^{10})\) \(q+(-1.30900 + 1.13425i) q^{3} +(2.17449 + 0.312644i) q^{7} +(0.426945 - 2.96946i) q^{9} +(2.69763 - 1.23197i) q^{13} +(-0.372992 - 2.59422i) q^{19} +(-3.20102 + 2.05717i) q^{21} +(-2.07708 - 4.54816i) q^{25} +(2.80925 + 4.37128i) q^{27} +(9.91965 + 4.53015i) q^{31} +10.4563 q^{37} +(-2.13383 + 4.67243i) q^{39} +(3.26646 + 11.1245i) q^{43} +(-2.08579 - 0.612443i) q^{49} +(3.43074 + 2.97275i) q^{57} +(3.26736 + 5.08410i) q^{61} +(1.85677 - 6.32359i) q^{63} +(1.74779 + 7.99658i) q^{67} +(0.774960 - 0.498036i) q^{73} +(7.87764 + 3.59760i) q^{75} +(9.85470 - 4.50049i) q^{79} +(-8.63544 - 2.53559i) q^{81} +(6.25114 - 1.83550i) q^{91} +(-18.1231 + 5.32143i) q^{93} -19.6545i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 6q^{9} + O(q^{10}) \) \( 20q + 6q^{9} + 16q^{19} - 12q^{21} + 10q^{25} - 20q^{37} - 24q^{39} + 10q^{49} - 66q^{57} - 132q^{63} - 16q^{67} + 90q^{73} + 44q^{79} - 18q^{81} + 48q^{91} - 36q^{93} + O(q^{100}) \)

Character values

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

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

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
\(3\) −1.30900 + 1.13425i −0.755750 + 0.654861i
\(4\) 0 0
\(5\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(6\) 0 0
\(7\) 2.17449 + 0.312644i 0.821880 + 0.118169i 0.540410 0.841402i \(-0.318269\pi\)
0.281470 + 0.959570i \(0.409178\pi\)
\(8\) 0 0
\(9\) 0.426945 2.96946i 0.142315 0.989821i
\(10\) 0 0
\(11\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(12\) 0 0
\(13\) 2.69763 1.23197i 0.748188 0.341686i −0.00456441 0.999990i \(-0.501453\pi\)
0.752753 + 0.658303i \(0.228726\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(18\) 0 0
\(19\) −0.372992 2.59422i −0.0855702 0.595154i −0.986816 0.161846i \(-0.948255\pi\)
0.901246 0.433308i \(-0.142654\pi\)
\(20\) 0 0
\(21\) −3.20102 + 2.05717i −0.698519 + 0.448911i
\(22\) 0 0
\(23\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(24\) 0 0
\(25\) −2.07708 4.54816i −0.415415 0.909632i
\(26\) 0 0
\(27\) 2.80925 + 4.37128i 0.540641 + 0.841254i
\(28\) 0 0
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 9.91965 + 4.53015i 1.78162 + 0.813640i 0.974878 + 0.222738i \(0.0714995\pi\)
0.806744 + 0.590901i \(0.201228\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 10.4563 1.71900 0.859500 0.511136i \(-0.170775\pi\)
0.859500 + 0.511136i \(0.170775\pi\)
\(38\) 0 0
\(39\) −2.13383 + 4.67243i −0.341686 + 0.748188i
\(40\) 0 0
\(41\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(42\) 0 0
\(43\) 3.26646 + 11.1245i 0.498130 + 1.69647i 0.697529 + 0.716557i \(0.254283\pi\)
−0.199399 + 0.979918i \(0.563899\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(48\) 0 0
\(49\) −2.08579 0.612443i −0.297970 0.0874919i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 3.43074 + 2.97275i 0.454413 + 0.393751i
\(58\) 0 0
\(59\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(60\) 0 0
\(61\) 3.26736 + 5.08410i 0.418342 + 0.650953i 0.984911 0.173061i \(-0.0553659\pi\)
−0.566569 + 0.824014i \(0.691730\pi\)
\(62\) 0 0
\(63\) 1.85677 6.32359i 0.233931 0.796697i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 1.74779 + 7.99658i 0.213527 + 0.976937i
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(72\) 0 0
\(73\) 0.774960 0.498036i 0.0907022 0.0582907i −0.494504 0.869176i \(-0.664650\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 0 0
\(75\) 7.87764 + 3.59760i 0.909632 + 0.415415i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 9.85470 4.50049i 1.10874 0.506345i 0.225018 0.974355i \(-0.427756\pi\)
0.883723 + 0.468010i \(0.155029\pi\)
\(80\) 0 0
\(81\) −8.63544 2.53559i −0.959493 0.281733i
\(82\) 0 0
\(83\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(90\) 0 0
\(91\) 6.25114 1.83550i 0.655298 0.192413i
\(92\) 0 0
\(93\) −18.1231 + 5.32143i −1.87928 + 0.551807i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 19.6545i 1.99561i −0.0661967 0.997807i \(-0.521086\pi\)
0.0661967 0.997807i \(-0.478914\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(102\) 0 0
\(103\) 2.60679 5.70807i 0.256854 0.562433i −0.736644 0.676281i \(-0.763591\pi\)
0.993498 + 0.113848i \(0.0363178\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(108\) 0 0
\(109\) −14.9215 + 6.81440i −1.42922 + 0.652701i −0.971639 0.236468i \(-0.924010\pi\)
−0.457578 + 0.889170i \(0.651283\pi\)
\(110\) 0 0
\(111\) −13.6872 + 11.8600i −1.29913 + 1.12571i
\(112\) 0 0
\(113\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −2.50654 8.53650i −0.231730 0.789200i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −4.56957 10.0060i −0.415415 0.909632i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −0.162932 + 1.13322i −0.0144579 + 0.100557i −0.995773 0.0918526i \(-0.970721\pi\)
0.981315 + 0.192410i \(0.0616302\pi\)
\(128\) 0 0
\(129\) −16.8938 10.8570i −1.48742 0.955904i
\(130\) 0 0
\(131\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(132\) 0 0
\(133\) 5.75771i 0.499257i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(138\) 0 0
\(139\) 0.405195 0.630496i 0.0343682 0.0534780i −0.823644 0.567107i \(-0.808063\pi\)
0.858013 + 0.513629i \(0.171699\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 3.42496 1.56413i 0.282486 0.129007i
\(148\) 0 0
\(149\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(150\) 0 0
\(151\) −9.35009 + 2.74544i −0.760900 + 0.223420i −0.639089 0.769133i \(-0.720688\pi\)
−0.121811 + 0.992553i \(0.538870\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −12.1677 14.0423i −0.971091 1.12070i −0.992661 0.120931i \(-0.961412\pi\)
0.0215699 0.999767i \(-0.493134\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −0.844292 −0.0661301 −0.0330650 0.999453i \(-0.510527\pi\)
−0.0330650 + 0.999453i \(0.510527\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(168\) 0 0
\(169\) −2.75372 + 3.17796i −0.211825 + 0.244459i
\(170\) 0 0
\(171\) −7.86268 −0.601274
\(172\) 0 0
\(173\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(174\) 0 0
\(175\) −3.09462 10.5393i −0.233931 0.796697i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(180\) 0 0
\(181\) 14.5787 + 16.8248i 1.08363 + 1.25058i 0.966282 + 0.257485i \(0.0828937\pi\)
0.117348 + 0.993091i \(0.462561\pi\)
\(182\) 0 0
\(183\) −10.0436 2.94907i −0.742445 0.218002i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 4.74203 + 10.3836i 0.344932 + 0.755296i
\(190\) 0 0
\(191\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(192\) 0 0
\(193\) 11.2769 24.6930i 0.811729 1.77744i 0.211936 0.977284i \(-0.432023\pi\)
0.599793 0.800155i \(-0.295250\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(198\) 0 0
\(199\) 3.96229 27.5584i 0.280880 1.95356i −0.0197060 0.999806i \(-0.506273\pi\)
0.300586 0.953755i \(-0.402818\pi\)
\(200\) 0 0
\(201\) −11.3580 8.48506i −0.801131 0.598490i
\(202\) 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
\(211\) −17.3996 + 20.0802i −1.19784 + 1.38238i −0.293279 + 0.956027i \(0.594746\pi\)
−0.904558 + 0.426350i \(0.859799\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 20.1539 + 12.9521i 1.36813 + 0.879246i
\(218\) 0 0
\(219\) −0.449521 + 1.53093i −0.0303758 + 0.103451i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −6.86433 + 7.92186i −0.459669 + 0.530487i −0.937509 0.347960i \(-0.886874\pi\)
0.477840 + 0.878447i \(0.341420\pi\)
\(224\) 0 0
\(225\) −14.3924 + 4.22599i −0.959493 + 0.281733i
\(226\) 0 0
\(227\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(228\) 0 0
\(229\) −10.3495 4.72645i −0.683913 0.312333i 0.0429870 0.999076i \(-0.486313\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −7.79508 + 17.0688i −0.506345 + 1.10874i
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −16.3141 + 10.4845i −1.05089 + 0.675363i −0.947656 0.319294i \(-0.896554\pi\)
−0.103230 + 0.994657i \(0.532918\pi\)
\(242\) 0 0
\(243\) 14.1798 6.47568i 0.909632 0.415415i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4.20218 6.53872i −0.267378 0.416049i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(258\) 0 0
\(259\) 22.7370 + 3.26909i 1.41281 + 0.203132i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(264\) 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
\(271\) −22.8085 + 19.7637i −1.38552 + 1.20056i −0.431019 + 0.902343i \(0.641846\pi\)
−0.954499 + 0.298215i \(0.903609\pi\)
\(272\) 0 0
\(273\) −6.10080 + 9.49303i −0.369237 + 0.574544i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −2.71695 + 18.8968i −0.163246 + 1.13540i 0.729219 + 0.684281i \(0.239884\pi\)
−0.892464 + 0.451118i \(0.851025\pi\)
\(278\) 0 0
\(279\) 17.6873 27.5219i 1.05891 1.64769i
\(280\) 0 0
\(281\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(282\) 0 0
\(283\) −3.03154 21.0848i −0.180206 1.25336i −0.856274 0.516522i \(-0.827227\pi\)
0.676068 0.736839i \(-0.263682\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 14.3013 9.19089i 0.841254 0.540641i
\(290\) 0 0
\(291\) 22.2932 + 25.7277i 1.30685 + 1.50818i
\(292\) 0 0
\(293\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 3.62486 + 25.2114i 0.208933 + 1.45316i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2.72859 5.97477i 0.155729 0.340998i −0.815646 0.578551i \(-0.803618\pi\)
0.971374 + 0.237553i \(0.0763455\pi\)
\(308\) 0 0
\(309\) 3.06211 + 10.4286i 0.174197 + 0.593262i
\(310\) 0 0
\(311\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(312\) 0 0
\(313\) 13.4766 + 11.6776i 0.761744 + 0.660055i 0.946491 0.322731i \(-0.104601\pi\)
−0.184747 + 0.982786i \(0.559147\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −11.2064 9.71037i −0.621617 0.538634i
\(326\) 0 0
\(327\) 11.8029 25.8447i 0.652701 1.42922i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −10.0090 + 34.0874i −0.550143 + 1.87361i −0.0676621 + 0.997708i \(0.521554\pi\)
−0.482481 + 0.875907i \(0.660264\pi\)
\(332\) 0 0
\(333\) 4.46425 31.0495i 0.244639 1.70150i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 24.9151 + 3.58225i 1.35721 + 0.195138i 0.782211 0.623014i \(-0.214092\pi\)
0.575002 + 0.818152i \(0.305001\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −18.3323 8.37210i −0.989853 0.452051i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(348\) 0 0
\(349\) 30.9878 + 9.09884i 1.65874 + 0.487050i 0.971034 0.238941i \(-0.0768002\pi\)
0.687705 + 0.725991i \(0.258618\pi\)
\(350\) 0 0
\(351\) 12.9636 + 8.33120i 0.691946 + 0.444687i
\(352\) 0 0
\(353\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(360\) 0 0
\(361\) 11.6395 3.41768i 0.612607 0.179878i
\(362\) 0 0
\(363\) 17.3308 + 7.91472i 0.909632 + 0.415415i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −22.5920 19.5761i −1.17929 1.02186i −0.999270 0.0382006i \(-0.987837\pi\)
−0.180023 0.983662i \(-0.557617\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 38.5992i 1.99859i −0.0375318 0.999295i \(-0.511950\pi\)
0.0375318 0.999295i \(-0.488050\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −10.0828 + 8.73682i −0.517920 + 0.448780i −0.874177 0.485608i \(-0.838598\pi\)
0.356257 + 0.934388i \(0.384053\pi\)
\(380\) 0 0
\(381\) −1.07208 1.66819i −0.0549243 0.0854638i
\(382\) 0 0
\(383\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 34.4285 4.95007i 1.75010 0.251626i
\(388\) 0 0
\(389\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −32.3701 20.8030i −1.62461 1.04407i −0.952911 0.303251i \(-0.901928\pi\)
−0.671700 0.740823i \(-0.734436\pi\)
\(398\) 0 0
\(399\) 6.53069 + 7.53682i 0.326944 + 0.377313i
\(400\) 0 0
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 32.3406 1.61100
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −8.79714 1.26484i −0.434990 0.0625422i −0.0786585 0.996902i \(-0.525064\pi\)
−0.356332 + 0.934359i \(0.615973\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0.184742 + 1.28491i 0.00904687 + 0.0629224i
\(418\) 0 0
\(419\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(420\) 0 0
\(421\) 3.18379 + 22.1437i 0.155168 + 1.07922i 0.907384 + 0.420303i \(0.138076\pi\)
−0.752216 + 0.658917i \(0.771015\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 5.51531 + 12.0769i 0.266905 + 0.584440i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) −17.3628 7.92933i −0.834404 0.381059i −0.0480569 0.998845i \(-0.515303\pi\)
−0.786347 + 0.617785i \(0.788030\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −35.6494 −1.70145 −0.850725 0.525610i \(-0.823837\pi\)
−0.850725 + 0.525610i \(0.823837\pi\)
\(440\) 0 0
\(441\) −2.70914 + 5.93220i −0.129007 + 0.282486i
\(442\) 0 0
\(443\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 9.12523 14.1991i 0.428741 0.667133i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 17.6839 + 38.7224i 0.827218 + 1.81136i 0.498334 + 0.866985i \(0.333945\pi\)
0.328884 + 0.944370i \(0.393327\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(462\) 0 0
\(463\) 13.6346 + 21.2159i 0.633654 + 0.985985i 0.998491 + 0.0549137i \(0.0174884\pi\)
−0.364837 + 0.931071i \(0.618875\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(468\) 0 0
\(469\) 1.30047 + 17.9349i 0.0600501 + 0.828157i
\(470\) 0 0
\(471\) 31.8550 + 4.58006i 1.46780 + 0.211038i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −11.0242 + 7.08481i −0.505824 + 0.325073i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(480\) 0 0
\(481\) 28.2071 12.8818i 1.28614 0.587358i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −2.55600 + 8.70495i −0.115824 + 0.394459i −0.996915 0.0784867i \(-0.974991\pi\)
0.881092 + 0.472946i \(0.156809\pi\)
\(488\) 0 0
\(489\) 1.10518 0.957640i 0.0499778 0.0433060i
\(490\) 0 0
\(491\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 16.1569i 0.723281i −0.932318 0.361640i \(-0.882217\pi\)
0.932318 0.361640i \(-0.117783\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 7.28335i 0.323465i
\(508\) 0 0
\(509\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(510\) 0 0
\(511\) 1.84085 0.840688i 0.0814344 0.0371899i
\(512\) 0 0
\(513\) 10.2922 8.91826i 0.454413 0.393751i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(522\) 0 0
\(523\) −18.0441 39.5112i −0.789015 1.72770i −0.679449 0.733723i \(-0.737781\pi\)
−0.109567 0.993979i \(-0.534946\pi\)
\(524\) 0 0
\(525\) 16.0051 + 10.2858i 0.698519 + 0.448911i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −3.27324 + 22.7659i −0.142315 + 0.989821i
\(530\) 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
\(541\) 10.6005 16.4947i 0.455750 0.709162i −0.535001 0.844851i \(-0.679689\pi\)
0.990751 + 0.135690i \(0.0433251\pi\)
\(542\) 0 0
\(543\) −38.1671 5.48760i −1.63791 0.235495i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 6.48616 10.0927i 0.277328 0.431531i −0.674449 0.738321i \(-0.735619\pi\)
0.951777 + 0.306791i \(0.0992551\pi\)
\(548\) 0 0
\(549\) 16.4920 7.53166i 0.703863 0.321444i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 22.8360 6.70526i 0.971086 0.285137i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(558\) 0 0
\(559\) 22.5167 + 25.9857i 0.952357 + 1.09908i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −17.9849 8.21344i −0.755296 0.344932i
\(568\) 0 0
\(569\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(570\) 0 0
\(571\) −29.1490 + 33.6397i −1.21985 + 1.40778i −0.334790 + 0.942293i \(0.608665\pi\)
−0.885056 + 0.465484i \(0.845880\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 3.72246 + 12.6775i 0.154968 + 0.527772i 0.999976 0.00698200i \(-0.00222246\pi\)
−0.845008 + 0.534754i \(0.820404\pi\)
\(578\) 0 0
\(579\) 13.2466 + 45.1139i 0.550511 + 1.87487i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(588\) 0 0
\(589\) 8.05224 27.4234i 0.331787 1.12996i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 26.0715 + 40.5680i 1.06704 + 1.66034i
\(598\) 0 0
\(599\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(600\) 0 0
\(601\) −0.0855917 + 0.595303i −0.00349136 + 0.0242829i −0.991493 0.130163i \(-0.958450\pi\)
0.988001 + 0.154446i \(0.0493591\pi\)
\(602\) 0 0
\(603\) 24.4918 1.77591i 0.997381 0.0723206i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −40.0383 11.7563i −1.62511 0.477174i −0.662722 0.748866i \(-0.730599\pi\)
−0.962384 + 0.271691i \(0.912417\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 2.66422 3.07467i 0.107607 0.124185i −0.699391 0.714739i \(-0.746545\pi\)
0.806998 + 0.590554i \(0.201091\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(618\) 0 0
\(619\) 39.9775 + 25.6920i 1.60683 + 1.03265i 0.963735 + 0.266860i \(0.0859860\pi\)
0.643094 + 0.765787i \(0.277650\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −16.3715 + 18.8937i −0.654861 + 0.755750i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −15.8034 7.21719i −0.629125 0.287312i 0.0752227 0.997167i \(-0.476033\pi\)
−0.704348 + 0.709855i \(0.748761\pi\)
\(632\) 0 0
\(633\) 46.0204i 1.82915i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −6.38120 + 0.917478i −0.252832 + 0.0363518i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0 0
\(643\) −39.6763 + 25.4984i −1.56468 + 1.00556i −0.583579 + 0.812056i \(0.698348\pi\)
−0.981100 + 0.193502i \(0.938015\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −41.0723 + 5.90530i −1.60975 + 0.231447i
\(652\) 0 0
\(653\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −1.14804 2.51385i −0.0447892 0.0980746i
\(658\) 0 0
\(659\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(660\) 0 0
\(661\) −22.3026 3.20663i −0.867472 0.124724i −0.305812 0.952092i \(-0.598928\pi\)
−0.561660 + 0.827368i \(0.689837\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 18.1556i 0.701935i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −29.2390 + 25.3358i −1.12708 + 0.976622i −0.999884 0.0152551i \(-0.995144\pi\)
−0.127198 + 0.991877i \(0.540599\pi\)
\(674\) 0 0
\(675\) 14.0463 21.8564i 0.540641 0.841254i
\(676\) 0 0
\(677\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(678\) 0 0
\(679\) 6.14487 42.7385i 0.235819 1.64015i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 18.9084 5.55202i 0.721402 0.211823i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −42.5583 + 27.3506i −1.61900 + 1.04047i −0.662356 + 0.749189i \(0.730443\pi\)
−0.956639 + 0.291276i \(0.905920\pi\)
\(692\) 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 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(702\) 0 0
\(703\) −3.90010 27.1258i −0.147095 1.02307i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −21.2106 + 46.4448i −0.796581 + 1.74427i −0.139812 + 0.990178i \(0.544650\pi\)
−0.656770 + 0.754091i \(0.728078\pi\)
\(710\) 0 0
\(711\) −9.15664 31.1847i −0.343401 1.16952i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(720\) 0 0
\(721\) 7.45303 11.5971i 0.277565 0.431900i
\(722\) 0 0
\(723\) 9.46313 32.2285i 0.351938 1.19859i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −13.2391 11.4717i −0.491010 0.425462i 0.373840 0.927493i \(-0.378041\pi\)
−0.864850 + 0.502031i \(0.832586\pi\)
\(728\) 0 0
\(729\) −11.2162 + 24.5601i −0.415415 + 0.909632i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 13.1099 44.6482i 0.484225 1.64912i −0.248529 0.968625i \(-0.579947\pi\)
0.732754 0.680494i \(-0.238235\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −53.8111 7.73687i −1.97947 0.284605i −0.991602 0.129329i \(-0.958718\pi\)
−0.987871 0.155277i \(-0.950373\pi\)
\(740\) 0 0
\(741\) 12.9172 + 3.79283i 0.474525 + 0.139333i
\(742\) 0 0
\(743\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −52.5547 15.4314i −1.91775 0.563101i −0.968994 0.247084i \(-0.920528\pi\)
−0.948753 0.316017i \(-0.897654\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −20.2102 + 17.5123i −0.734553 + 0.636494i −0.939606 0.342257i \(-0.888809\pi\)
0.205053 + 0.978751i \(0.434263\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(762\) 0 0
\(763\) −34.5771 + 10.1527i −1.25177 + 0.367554i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −16.0260 13.8866i −0.577911 0.500762i 0.316150 0.948709i \(-0.397610\pi\)
−0.894060 + 0.447947i \(0.852155\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(774\) 0 0
\(775\) 54.5256i 1.95862i
\(776\) 0 0
\(777\) −33.4707 + 21.5103i −1.20075 + 0.771678i
\(778\) 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
\(787\) −14.7567 50.2567i −0.526020 1.79146i −0.606951 0.794739i \(-0.707607\pi\)
0.0809308 0.996720i \(-0.474211\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 15.0776 + 9.68976i 0.535420 + 0.344094i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\)