Properties

Label 2016.2.s.o.289.1
Level $2016$
Weight $2$
Character 2016.289
Analytic conductor $16.098$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2016.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(16.0978410475\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7})\)
Defining polynomial: \( x^{4} + 7x^{2} + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 224)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.1
Root \(1.32288 + 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 2016.289
Dual form 2016.2.s.o.865.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 + 2.59808i) q^{5} -2.64575 q^{7} +O(q^{10})\) \(q+(-1.50000 + 2.59808i) q^{5} -2.64575 q^{7} +(-1.32288 - 2.29129i) q^{11} -4.00000 q^{13} +(0.500000 + 0.866025i) q^{17} +(3.96863 - 6.87386i) q^{19} +(-1.32288 + 2.29129i) q^{23} +(-2.00000 - 3.46410i) q^{25} +4.00000 q^{29} +(1.32288 + 2.29129i) q^{31} +(3.96863 - 6.87386i) q^{35} +(2.50000 - 4.33013i) q^{37} -8.00000 q^{41} +10.5830 q^{43} +(1.32288 - 2.29129i) q^{47} +7.00000 q^{49} +(3.50000 + 6.06218i) q^{53} +7.93725 q^{55} +(1.32288 + 2.29129i) q^{59} +(2.50000 - 4.33013i) q^{61} +(6.00000 - 10.3923i) q^{65} +(-1.32288 - 2.29129i) q^{67} +(4.50000 + 7.79423i) q^{73} +(3.50000 + 6.06218i) q^{77} +(1.32288 - 2.29129i) q^{79} +10.5830 q^{83} -3.00000 q^{85} +(-4.50000 + 7.79423i) q^{89} +10.5830 q^{91} +(11.9059 + 20.6216i) q^{95} -8.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 6 q^{5} - 16 q^{13} + 2 q^{17} - 8 q^{25} + 16 q^{29} + 10 q^{37} - 32 q^{41} + 28 q^{49} + 14 q^{53} + 10 q^{61} + 24 q^{65} + 18 q^{73} + 14 q^{77} - 12 q^{85} - 18 q^{89} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(1765\) \(1793\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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
\(5\) −1.50000 + 2.59808i −0.670820 + 1.16190i 0.306851 + 0.951757i \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 0 0
\(7\) −2.64575 −1.00000
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.32288 2.29129i −0.398862 0.690849i 0.594724 0.803930i \(-0.297261\pi\)
−0.993586 + 0.113081i \(0.963928\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i 0.920268 0.391289i \(-0.127971\pi\)
−0.799000 + 0.601331i \(0.794637\pi\)
\(18\) 0 0
\(19\) 3.96863 6.87386i 0.910465 1.57697i 0.0970575 0.995279i \(-0.469057\pi\)
0.813408 0.581694i \(-0.197610\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.32288 + 2.29129i −0.275839 + 0.477767i −0.970346 0.241719i \(-0.922289\pi\)
0.694508 + 0.719485i \(0.255622\pi\)
\(24\) 0 0
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) 1.32288 + 2.29129i 0.237595 + 0.411527i 0.960024 0.279918i \(-0.0903074\pi\)
−0.722428 + 0.691446i \(0.756974\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.96863 6.87386i 0.670820 1.16190i
\(36\) 0 0
\(37\) 2.50000 4.33013i 0.410997 0.711868i −0.584002 0.811752i \(-0.698514\pi\)
0.994999 + 0.0998840i \(0.0318472\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.00000 −1.24939 −0.624695 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) 10.5830 1.61389 0.806947 0.590624i \(-0.201119\pi\)
0.806947 + 0.590624i \(0.201119\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.32288 2.29129i 0.192961 0.334219i −0.753269 0.657713i \(-0.771524\pi\)
0.946230 + 0.323494i \(0.104858\pi\)
\(48\) 0 0
\(49\) 7.00000 1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.50000 + 6.06218i 0.480762 + 0.832704i 0.999756 0.0220735i \(-0.00702678\pi\)
−0.518994 + 0.854778i \(0.673693\pi\)
\(54\) 0 0
\(55\) 7.93725 1.07026
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.32288 + 2.29129i 0.172224 + 0.298300i 0.939197 0.343379i \(-0.111571\pi\)
−0.766973 + 0.641679i \(0.778238\pi\)
\(60\) 0 0
\(61\) 2.50000 4.33013i 0.320092 0.554416i −0.660415 0.750901i \(-0.729619\pi\)
0.980507 + 0.196485i \(0.0629528\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 6.00000 10.3923i 0.744208 1.28901i
\(66\) 0 0
\(67\) −1.32288 2.29129i −0.161615 0.279925i 0.773833 0.633390i \(-0.218337\pi\)
−0.935448 + 0.353464i \(0.885004\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 4.50000 + 7.79423i 0.526685 + 0.912245i 0.999517 + 0.0310925i \(0.00989865\pi\)
−0.472831 + 0.881153i \(0.656768\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.50000 + 6.06218i 0.398862 + 0.690849i
\(78\) 0 0
\(79\) 1.32288 2.29129i 0.148835 0.257790i −0.781962 0.623326i \(-0.785781\pi\)
0.930797 + 0.365536i \(0.119114\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 10.5830 1.16164 0.580818 0.814034i \(-0.302733\pi\)
0.580818 + 0.814034i \(0.302733\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.50000 + 7.79423i −0.476999 + 0.826187i −0.999653 0.0263586i \(-0.991609\pi\)
0.522654 + 0.852545i \(0.324942\pi\)
\(90\) 0 0
\(91\) 10.5830 1.10940
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 11.9059 + 20.6216i 1.22152 + 2.11573i
\(96\) 0 0
\(97\) −8.00000 −0.812277 −0.406138 0.913812i \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i \(-0.898506\pi\)
0.203317 0.979113i \(-0.434828\pi\)
\(102\) 0 0
\(103\) 1.32288 2.29129i 0.130347 0.225767i −0.793463 0.608618i \(-0.791724\pi\)
0.923810 + 0.382851i \(0.125058\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.61438 11.4564i 0.639436 1.10754i −0.346121 0.938190i \(-0.612501\pi\)
0.985557 0.169346i \(-0.0541655\pi\)
\(108\) 0 0
\(109\) −0.500000 0.866025i −0.0478913 0.0829502i 0.841086 0.540901i \(-0.181917\pi\)
−0.888977 + 0.457951i \(0.848583\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) −3.96863 6.87386i −0.370076 0.640991i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.32288 2.29129i −0.121268 0.210042i
\(120\) 0 0
\(121\) 2.00000 3.46410i 0.181818 0.314918i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) 21.1660 1.87818 0.939090 0.343672i \(-0.111671\pi\)
0.939090 + 0.343672i \(0.111671\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.96863 6.87386i 0.346741 0.600572i −0.638928 0.769267i \(-0.720622\pi\)
0.985668 + 0.168694i \(0.0539551\pi\)
\(132\) 0 0
\(133\) −10.5000 + 18.1865i −0.910465 + 1.57697i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.500000 + 0.866025i 0.0427179 + 0.0739895i 0.886594 0.462549i \(-0.153065\pi\)
−0.843876 + 0.536538i \(0.819732\pi\)
\(138\) 0 0
\(139\) −10.5830 −0.897639 −0.448819 0.893622i \(-0.648155\pi\)
−0.448819 + 0.893622i \(0.648155\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 5.29150 + 9.16515i 0.442498 + 0.766428i
\(144\) 0 0
\(145\) −6.00000 + 10.3923i −0.498273 + 0.863034i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 10.5000 18.1865i 0.860194 1.48990i −0.0115483 0.999933i \(-0.503676\pi\)
0.871742 0.489966i \(-0.162991\pi\)
\(150\) 0 0
\(151\) 1.32288 + 2.29129i 0.107654 + 0.186462i 0.914819 0.403863i \(-0.132333\pi\)
−0.807165 + 0.590325i \(0.798999\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −7.93725 −0.637536
\(156\) 0 0
\(157\) 4.50000 + 7.79423i 0.359139 + 0.622047i 0.987817 0.155618i \(-0.0497370\pi\)
−0.628678 + 0.777666i \(0.716404\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.50000 6.06218i 0.275839 0.477767i
\(162\) 0 0
\(163\) 6.61438 11.4564i 0.518078 0.897338i −0.481701 0.876335i \(-0.659981\pi\)
0.999779 0.0210021i \(-0.00668568\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.29150 −0.409469 −0.204734 0.978818i \(-0.565633\pi\)
−0.204734 + 0.978818i \(0.565633\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.50000 2.59808i 0.114043 0.197528i −0.803354 0.595502i \(-0.796953\pi\)
0.917397 + 0.397974i \(0.130287\pi\)
\(174\) 0 0
\(175\) 5.29150 + 9.16515i 0.400000 + 0.692820i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −11.9059 20.6216i −0.889887 1.54133i −0.840007 0.542575i \(-0.817449\pi\)
−0.0498798 0.998755i \(-0.515884\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 7.50000 + 12.9904i 0.551411 + 0.955072i
\(186\) 0 0
\(187\) 1.32288 2.29129i 0.0967382 0.167556i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 11.9059 20.6216i 0.861479 1.49213i −0.00902170 0.999959i \(-0.502872\pi\)
0.870501 0.492167i \(-0.163795\pi\)
\(192\) 0 0
\(193\) 3.50000 + 6.06218i 0.251936 + 0.436365i 0.964059 0.265689i \(-0.0855996\pi\)
−0.712123 + 0.702055i \(0.752266\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) −9.26013 16.0390i −0.656433 1.13698i −0.981532 0.191296i \(-0.938731\pi\)
0.325099 0.945680i \(-0.394602\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −10.5830 −0.742781
\(204\) 0 0
\(205\) 12.0000 20.7846i 0.838116 1.45166i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −21.0000 −1.45260
\(210\) 0 0
\(211\) −10.5830 −0.728564 −0.364282 0.931289i \(-0.618686\pi\)
−0.364282 + 0.931289i \(0.618686\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −15.8745 + 27.4955i −1.08263 + 1.87517i
\(216\) 0 0
\(217\) −3.50000 6.06218i −0.237595 0.411527i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.00000 3.46410i −0.134535 0.233021i
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.32288 2.29129i −0.0878023 0.152078i 0.818780 0.574108i \(-0.194651\pi\)
−0.906582 + 0.422030i \(0.861318\pi\)
\(228\) 0 0
\(229\) 5.50000 9.52628i 0.363450 0.629514i −0.625076 0.780564i \(-0.714932\pi\)
0.988526 + 0.151050i \(0.0482653\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.50000 7.79423i 0.294805 0.510617i −0.680135 0.733087i \(-0.738079\pi\)
0.974939 + 0.222470i \(0.0714120\pi\)
\(234\) 0 0
\(235\) 3.96863 + 6.87386i 0.258885 + 0.448401i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −15.8745 −1.02684 −0.513418 0.858138i \(-0.671621\pi\)
−0.513418 + 0.858138i \(0.671621\pi\)
\(240\) 0 0
\(241\) 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i \(-0.156413\pi\)
−0.849472 + 0.527633i \(0.823079\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −10.5000 + 18.1865i −0.670820 + 1.16190i
\(246\) 0 0
\(247\) −15.8745 + 27.4955i −1.01007 + 1.74949i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5.29150 −0.333997 −0.166998 0.985957i \(-0.553407\pi\)
−0.166998 + 0.985957i \(0.553407\pi\)
\(252\) 0 0
\(253\) 7.00000 0.440086
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.50000 14.7224i 0.530215 0.918360i −0.469163 0.883112i \(-0.655444\pi\)
0.999379 0.0352486i \(-0.0112223\pi\)
\(258\) 0 0
\(259\) −6.61438 + 11.4564i −0.410997 + 0.711868i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −9.26013 16.0390i −0.571004 0.989008i −0.996463 0.0840304i \(-0.973221\pi\)
0.425459 0.904978i \(-0.360113\pi\)
\(264\) 0 0
\(265\) −21.0000 −1.29002
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7.50000 + 12.9904i 0.457283 + 0.792038i 0.998816 0.0486418i \(-0.0154893\pi\)
−0.541533 + 0.840679i \(0.682156\pi\)
\(270\) 0 0
\(271\) 1.32288 2.29129i 0.0803590 0.139186i −0.823045 0.567976i \(-0.807727\pi\)
0.903404 + 0.428790i \(0.141060\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.29150 + 9.16515i −0.319090 + 0.552679i
\(276\) 0 0
\(277\) 12.5000 + 21.6506i 0.751052 + 1.30086i 0.947313 + 0.320309i \(0.103787\pi\)
−0.196261 + 0.980552i \(0.562880\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 24.0000 1.43172 0.715860 0.698244i \(-0.246035\pi\)
0.715860 + 0.698244i \(0.246035\pi\)
\(282\) 0 0
\(283\) −9.26013 16.0390i −0.550458 0.953420i −0.998241 0.0592787i \(-0.981120\pi\)
0.447784 0.894142i \(-0.352213\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 21.1660 1.24939
\(288\) 0 0
\(289\) 8.00000 13.8564i 0.470588 0.815083i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 10.0000 0.584206 0.292103 0.956387i \(-0.405645\pi\)
0.292103 + 0.956387i \(0.405645\pi\)
\(294\) 0 0
\(295\) −7.93725 −0.462125
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 5.29150 9.16515i 0.306015 0.530034i
\(300\) 0 0
\(301\) −28.0000 −1.61389
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 7.50000 + 12.9904i 0.429449 + 0.743827i
\(306\) 0 0
\(307\) 10.5830 0.604004 0.302002 0.953307i \(-0.402345\pi\)
0.302002 + 0.953307i \(0.402345\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 11.9059 + 20.6216i 0.675121 + 1.16934i 0.976434 + 0.215818i \(0.0692417\pi\)
−0.301313 + 0.953525i \(0.597425\pi\)
\(312\) 0 0
\(313\) 8.50000 14.7224i 0.480448 0.832161i −0.519300 0.854592i \(-0.673807\pi\)
0.999748 + 0.0224310i \(0.00714060\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6.50000 + 11.2583i −0.365076 + 0.632331i −0.988788 0.149323i \(-0.952290\pi\)
0.623712 + 0.781654i \(0.285624\pi\)
\(318\) 0 0
\(319\) −5.29150 9.16515i −0.296267 0.513150i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 7.93725 0.441641
\(324\) 0 0
\(325\) 8.00000 + 13.8564i 0.443760 + 0.768615i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3.50000 + 6.06218i −0.192961 + 0.334219i
\(330\) 0 0
\(331\) −3.96863 + 6.87386i −0.218135 + 0.377822i −0.954238 0.299048i \(-0.903331\pi\)
0.736102 + 0.676870i \(0.236664\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7.93725 0.433659
\(336\) 0 0
\(337\) 24.0000 1.30736 0.653682 0.756770i \(-0.273224\pi\)
0.653682 + 0.756770i \(0.273224\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.50000 6.06218i 0.189536 0.328285i
\(342\) 0 0
\(343\) −18.5203 −1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 11.9059 + 20.6216i 0.639141 + 1.10702i 0.985622 + 0.168968i \(0.0540434\pi\)
−0.346480 + 0.938057i \(0.612623\pi\)
\(348\) 0 0
\(349\) 20.0000 1.07058 0.535288 0.844670i \(-0.320203\pi\)
0.535288 + 0.844670i \(0.320203\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4.50000 + 7.79423i 0.239511 + 0.414845i 0.960574 0.278024i \(-0.0896796\pi\)
−0.721063 + 0.692869i \(0.756346\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −9.26013 + 16.0390i −0.488731 + 0.846507i −0.999916 0.0129639i \(-0.995873\pi\)
0.511185 + 0.859471i \(0.329207\pi\)
\(360\) 0 0
\(361\) −22.0000 38.1051i −1.15789 2.00553i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −27.0000 −1.41324
\(366\) 0 0
\(367\) 9.26013 + 16.0390i 0.483375 + 0.837230i 0.999818 0.0190919i \(-0.00607750\pi\)
−0.516443 + 0.856322i \(0.672744\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −9.26013 16.0390i −0.480762 0.832704i
\(372\) 0 0
\(373\) 10.5000 18.1865i 0.543669 0.941663i −0.455020 0.890481i \(-0.650368\pi\)
0.998689 0.0511818i \(-0.0162988\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −16.0000 −0.824042
\(378\) 0 0
\(379\) −5.29150 −0.271806 −0.135903 0.990722i \(-0.543394\pi\)
−0.135903 + 0.990722i \(0.543394\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −9.26013 + 16.0390i −0.473171 + 0.819555i −0.999528 0.0307077i \(-0.990224\pi\)
0.526358 + 0.850263i \(0.323557\pi\)
\(384\) 0 0
\(385\) −21.0000 −1.07026
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7.50000 12.9904i −0.380265 0.658638i 0.610835 0.791758i \(-0.290834\pi\)
−0.991100 + 0.133120i \(0.957501\pi\)
\(390\) 0 0
\(391\) −2.64575 −0.133801
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3.96863 + 6.87386i 0.199683 + 0.345862i
\(396\) 0 0
\(397\) −2.50000 + 4.33013i −0.125471 + 0.217323i −0.921917 0.387387i \(-0.873378\pi\)
0.796446 + 0.604710i \(0.206711\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −11.5000 + 19.9186i −0.574283 + 0.994687i 0.421837 + 0.906672i \(0.361386\pi\)
−0.996119 + 0.0880147i \(0.971948\pi\)
\(402\) 0 0
\(403\) −5.29150 9.16515i −0.263589 0.456549i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −13.2288 −0.655725
\(408\) 0 0
\(409\) 11.5000 + 19.9186i 0.568638 + 0.984911i 0.996701 + 0.0811615i \(0.0258630\pi\)
−0.428063 + 0.903749i \(0.640804\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −3.50000 6.06218i −0.172224 0.298300i
\(414\) 0 0
\(415\) −15.8745 + 27.4955i −0.779249 + 1.34970i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 31.7490 1.55104 0.775520 0.631322i \(-0.217488\pi\)
0.775520 + 0.631322i \(0.217488\pi\)
\(420\) 0 0
\(421\) −12.0000 −0.584844 −0.292422 0.956289i \(-0.594461\pi\)
−0.292422 + 0.956289i \(0.594461\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.00000 3.46410i 0.0970143 0.168034i
\(426\) 0 0
\(427\) −6.61438 + 11.4564i −0.320092 + 0.554416i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.32288 2.29129i −0.0637207 0.110367i 0.832405 0.554168i \(-0.186963\pi\)
−0.896126 + 0.443800i \(0.853630\pi\)
\(432\) 0 0
\(433\) −32.0000 −1.53782 −0.768911 0.639356i \(-0.779201\pi\)
−0.768911 + 0.639356i \(0.779201\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 10.5000 + 18.1865i 0.502283 + 0.869980i
\(438\) 0 0
\(439\) −11.9059 + 20.6216i −0.568237 + 0.984215i 0.428504 + 0.903540i \(0.359041\pi\)
−0.996740 + 0.0806748i \(0.974292\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3.96863 + 6.87386i −0.188555 + 0.326587i −0.944769 0.327738i \(-0.893714\pi\)
0.756214 + 0.654325i \(0.227047\pi\)
\(444\) 0 0
\(445\) −13.5000 23.3827i −0.639961 1.10845i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 10.5830 + 18.3303i 0.498334 + 0.863140i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −15.8745 + 27.4955i −0.744208 + 1.28901i
\(456\) 0 0
\(457\) −3.50000 + 6.06218i −0.163723 + 0.283577i −0.936201 0.351465i \(-0.885684\pi\)
0.772478 + 0.635042i \(0.219017\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 20.0000 0.931493 0.465746 0.884918i \(-0.345786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.96863 6.87386i 0.183646 0.318084i −0.759473 0.650538i \(-0.774543\pi\)
0.943119 + 0.332454i \(0.107877\pi\)
\(468\) 0 0
\(469\) 3.50000 + 6.06218i 0.161615 + 0.279925i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −14.0000 24.2487i −0.643721 1.11496i
\(474\) 0 0
\(475\) −31.7490 −1.45674
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −19.8431 34.3693i −0.906656 1.57037i −0.818679 0.574252i \(-0.805293\pi\)
−0.0879772 0.996122i \(-0.528040\pi\)
\(480\) 0 0
\(481\) −10.0000 + 17.3205i −0.455961 + 0.789747i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 12.0000 20.7846i 0.544892 0.943781i
\(486\) 0 0
\(487\) −11.9059 20.6216i −0.539507 0.934453i −0.998931 0.0462362i \(-0.985277\pi\)
0.459424 0.888217i \(-0.348056\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −37.0405 −1.67162 −0.835808 0.549022i \(-0.815000\pi\)
−0.835808 + 0.549022i \(0.815000\pi\)
\(492\) 0 0
\(493\) 2.00000 + 3.46410i 0.0900755 + 0.156015i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 6.61438 11.4564i 0.296100 0.512861i −0.679140 0.734009i \(-0.737647\pi\)
0.975240 + 0.221148i \(0.0709804\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −21.1660 −0.943746 −0.471873 0.881667i \(-0.656422\pi\)
−0.471873 + 0.881667i \(0.656422\pi\)
\(504\) 0 0
\(505\) 45.0000 2.00247
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −9.50000 + 16.4545i −0.421080 + 0.729332i −0.996045 0.0888457i \(-0.971682\pi\)
0.574965 + 0.818178i \(0.305016\pi\)
\(510\) 0 0
\(511\) −11.9059 20.6216i −0.526685 0.912245i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 3.96863 + 6.87386i 0.174879 + 0.302899i
\(516\) 0 0
\(517\) −7.00000 −0.307860
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 11.5000 + 19.9186i 0.503824 + 0.872649i 0.999990 + 0.00442139i \(0.00140738\pi\)
−0.496166 + 0.868228i \(0.665259\pi\)
\(522\) 0 0
\(523\) −17.1974 + 29.7867i −0.751989 + 1.30248i 0.194868 + 0.980829i \(0.437572\pi\)
−0.946857 + 0.321654i \(0.895761\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.32288 + 2.29129i −0.0576254 + 0.0998101i
\(528\) 0 0
\(529\) 8.00000 + 13.8564i 0.347826 + 0.602452i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 32.0000 1.38607
\(534\) 0 0
\(535\) 19.8431 + 34.3693i 0.857894 + 1.48592i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −9.26013 16.0390i −0.398862 0.690849i
\(540\) 0 0
\(541\) −10.5000 + 18.1865i −0.451430 + 0.781900i −0.998475 0.0552031i \(-0.982419\pi\)
0.547045 + 0.837103i \(0.315753\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3.00000 0.128506
\(546\) 0 0
\(547\) 26.4575 1.13124 0.565621 0.824665i \(-0.308637\pi\)
0.565621 + 0.824665i \(0.308637\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 15.8745 27.4955i 0.676277 1.17135i
\(552\) 0 0
\(553\) −3.50000 + 6.06218i −0.148835 + 0.257790i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −19.5000 33.7750i −0.826242 1.43109i −0.900967 0.433888i \(-0.857141\pi\)
0.0747252 0.997204i \(-0.476192\pi\)
\(558\) 0 0
\(559\) −42.3320 −1.79045
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.32288 + 2.29129i 0.0557526 + 0.0965663i 0.892555 0.450939i \(-0.148911\pi\)
−0.836802 + 0.547505i \(0.815578\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −16.5000 + 28.5788i −0.691716 + 1.19809i 0.279559 + 0.960128i \(0.409812\pi\)
−0.971275 + 0.237959i \(0.923522\pi\)
\(570\) 0 0
\(571\) 1.32288 + 2.29129i 0.0553606 + 0.0958874i 0.892378 0.451290i \(-0.149036\pi\)
−0.837017 + 0.547177i \(0.815702\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 10.5830 0.441342
\(576\) 0 0
\(577\) 20.5000 + 35.5070i 0.853426 + 1.47818i 0.878097 + 0.478482i \(0.158813\pi\)
−0.0246713 + 0.999696i \(0.507854\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −28.0000 −1.16164
\(582\) 0 0
\(583\) 9.26013 16.0390i 0.383515 0.664268i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −31.7490 −1.31042 −0.655211 0.755446i \(-0.727420\pi\)
−0.655211 + 0.755446i \(0.727420\pi\)
\(588\) 0 0
\(589\) 21.0000 0.865290
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 16.5000 28.5788i 0.677574 1.17359i −0.298136 0.954524i \(-0.596365\pi\)
0.975709 0.219069i \(-0.0703019\pi\)
\(594\) 0 0
\(595\) 7.93725 0.325396
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 11.9059 + 20.6216i 0.486461 + 0.842575i 0.999879 0.0155634i \(-0.00495420\pi\)
−0.513418 + 0.858139i \(0.671621\pi\)
\(600\) 0 0
\(601\) 8.00000 0.326327 0.163163 0.986599i \(-0.447830\pi\)
0.163163 + 0.986599i \(0.447830\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6.00000 + 10.3923i 0.243935 + 0.422507i
\(606\) 0 0
\(607\) 19.8431 34.3693i 0.805408 1.39501i −0.110607 0.993864i \(-0.535280\pi\)
0.916015 0.401143i \(-0.131387\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5.29150 + 9.16515i −0.214071 + 0.370782i
\(612\) 0 0
\(613\) −20.5000 35.5070i −0.827987 1.43412i −0.899615 0.436684i \(-0.856153\pi\)
0.0716275 0.997431i \(-0.477181\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 32.0000 1.28827 0.644136 0.764911i \(-0.277217\pi\)
0.644136 + 0.764911i \(0.277217\pi\)
\(618\) 0 0
\(619\) −22.4889 38.9519i −0.903905 1.56561i −0.822381 0.568937i \(-0.807355\pi\)
−0.0815238 0.996671i \(-0.525979\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 11.9059 20.6216i 0.476999 0.826187i
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5.00000 0.199363
\(630\) 0 0
\(631\) −42.3320 −1.68521 −0.842606 0.538531i \(-0.818979\pi\)
−0.842606 + 0.538531i \(0.818979\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −31.7490 + 54.9909i −1.25992 + 2.18225i
\(636\) 0 0
\(637\) −28.0000 −1.10940
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.500000 0.866025i −0.0197488 0.0342059i 0.855982 0.517005i \(-0.172953\pi\)
−0.875731 + 0.482800i \(0.839620\pi\)
\(642\) 0 0
\(643\) −10.5830 −0.417353 −0.208676 0.977985i \(-0.566916\pi\)
−0.208676 + 0.977985i \(0.566916\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −19.8431 34.3693i −0.780114 1.35120i −0.931875 0.362780i \(-0.881828\pi\)
0.151761 0.988417i \(-0.451506\pi\)
\(648\) 0 0
\(649\) 3.50000 6.06218i 0.137387 0.237961i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9.50000 16.4545i 0.371764 0.643914i −0.618073 0.786121i \(-0.712086\pi\)
0.989837 + 0.142207i \(0.0454198\pi\)
\(654\) 0 0
\(655\) 11.9059 + 20.6216i 0.465201 + 0.805752i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 31.7490 1.23677 0.618383 0.785877i \(-0.287788\pi\)
0.618383 + 0.785877i \(0.287788\pi\)
\(660\) 0 0
\(661\) 16.5000 + 28.5788i 0.641776 + 1.11159i 0.985036 + 0.172348i \(0.0551353\pi\)
−0.343261 + 0.939240i \(0.611531\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −31.5000 54.5596i −1.22152 2.11573i
\(666\) 0 0
\(667\) −5.29150 + 9.16515i −0.204888 + 0.354876i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −13.2288 −0.510690
\(672\) 0 0
\(673\) −24.0000 −0.925132 −0.462566 0.886585i \(-0.653071\pi\)
−0.462566 + 0.886585i \(0.653071\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.50000 + 2.59808i −0.0576497 + 0.0998522i −0.893410 0.449242i \(-0.851694\pi\)
0.835760 + 0.549095i \(0.185027\pi\)
\(678\) 0 0
\(679\) 21.1660 0.812277
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −11.9059 20.6216i −0.455566 0.789063i 0.543155 0.839633i \(-0.317230\pi\)
−0.998721 + 0.0505694i \(0.983896\pi\)
\(684\) 0 0
\(685\) −3.00000 −0.114624
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −14.0000 24.2487i −0.533358 0.923802i
\(690\) 0 0
\(691\) −14.5516 + 25.2042i −0.553570 + 0.958812i 0.444443 + 0.895807i \(0.353402\pi\)
−0.998013 + 0.0630046i \(0.979932\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 15.8745 27.4955i 0.602154 1.04296i
\(696\) 0 0
\(697\) −4.00000 6.92820i −0.151511 0.262424i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) −19.8431 34.3693i −0.748398 1.29626i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 19.8431 + 34.3693i 0.746278 + 1.29259i
\(708\) 0 0
\(709\) 18.5000 32.0429i 0.694782 1.20340i −0.275472 0.961309i \(-0.588834\pi\)
0.970254 0.242089i \(-0.0778325\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −7.00000 −0.262152
\(714\) 0 0
\(715\) −31.7490 −1.18735
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 19.8431 34.3693i 0.740024 1.28176i −0.212460 0.977170i \(-0.568147\pi\)
0.952484 0.304589i \(-0.0985192\pi\)
\(720\) 0 0
\(721\) −3.50000 + 6.06218i −0.130347 + 0.225767i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −8.00000 13.8564i −0.297113 0.514614i
\(726\) 0 0
\(727\) 42.3320 1.57001 0.785004 0.619491i \(-0.212661\pi\)
0.785004 + 0.619491i \(0.212661\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 5.29150 + 9.16515i 0.195713 + 0.338985i
\(732\) 0 0
\(733\) −5.50000 + 9.52628i −0.203147 + 0.351861i −0.949541 0.313644i \(-0.898450\pi\)
0.746394 + 0.665505i \(0.231784\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.50000 + 6.06218i −0.128924 + 0.223303i
\(738\) 0 0
\(739\) 22.4889 + 38.9519i 0.827267 + 1.43287i 0.900174 + 0.435530i \(0.143439\pi\)
−0.0729072 + 0.997339i \(0.523228\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 21.1660 0.776506 0.388253 0.921553i \(-0.373079\pi\)
0.388253 + 0.921553i \(0.373079\pi\)
\(744\) 0 0
\(745\) 31.5000 + 54.5596i 1.15407 + 1.99891i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −17.5000 + 30.3109i −0.639436 + 1.10754i
\(750\) 0 0
\(751\) 19.8431 34.3693i 0.724086 1.25415i −0.235263 0.971932i \(-0.575595\pi\)
0.959349 0.282222i \(-0.0910716\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −7.93725 −0.288866
\(756\) 0 0
\(757\) 4.00000 0.145382 0.0726912 0.997354i \(-0.476841\pi\)
0.0726912 + 0.997354i \(0.476841\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 4.50000 7.79423i 0.163125 0.282541i −0.772863 0.634573i \(-0.781176\pi\)
0.935988 + 0.352032i \(0.114509\pi\)
\(762\) 0 0
\(763\) 1.32288 + 2.29129i 0.0478913 + 0.0829502i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.29150 9.16515i −0.191065 0.330934i
\(768\) 0 0
\(769\) −24.0000 −0.865462 −0.432731 0.901523i \(-0.642450\pi\)
−0.432731 + 0.901523i \(0.642450\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 16.5000 + 28.5788i 0.593464 + 1.02791i 0.993762 + 0.111524i \(0.0355733\pi\)
−0.400298 + 0.916385i \(0.631093\pi\)
\(774\) 0 0
\(775\) 5.29150 9.16515i 0.190076 0.329222i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −31.7490 + 54.9909i −1.13753 + 1.97025i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −27.0000 −0.963671
\(786\) 0 0
\(787\) 9.26013 + 16.0390i 0.330088 + 0.571729i 0.982529 0.186111i \(-0.0595882\pi\)
−0.652441 + 0.757840i \(0.726255\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −10.0000 + 17.3205i −0.355110 + 0.615069i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 52.0000 1.84193 0.920967 0.389640i \(-0.127401\pi\)
0.920967 + 0.389640i \(0.127401\pi\)
\(798\) 0 0
\(799\) 2.64575 0.0936000
\(800\) 0 0
\(801\) 0 0