Properties

Label 363.2.f.c.161.1
Level $363$
Weight $2$
Character 363.161
Analytic conductor $2.899$
Analytic rank $0$
Dimension $8$
CM discriminant -11
Inner twists $16$

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Newspace parameters

Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 363.f (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.89856959337\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: 8.0.228765625.1
Defining polynomial: \( x^{8} - x^{7} - 2x^{6} + 5x^{5} + x^{4} + 15x^{3} - 18x^{2} - 27x + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{U}(1)[D_{10}]$

Embedding invariants

Embedding label 161.1
Root \(1.42264 + 0.987975i\) of defining polynomial
Character \(\chi\) \(=\) 363.161
Dual form 363.2.f.c.239.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.42264 - 0.987975i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(-1.94946 - 2.68321i) q^{5} +(1.04781 + 2.81107i) q^{9} +O(q^{10})\) \(q+(-1.42264 - 0.987975i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(-1.94946 - 2.68321i) q^{5} +(1.04781 + 2.81107i) q^{9} +(-1.00000 + 3.31662i) q^{12} +(0.122445 + 5.74326i) q^{15} +(-3.23607 + 2.35114i) q^{16} +(-3.89893 + 5.36641i) q^{20} +3.31662i q^{23} +(-1.85410 + 5.70634i) q^{25} +(1.28660 - 5.03435i) q^{27} +(-4.04508 - 2.93893i) q^{31} +(4.69938 - 3.73039i) q^{36} +(-2.16312 - 6.65740i) q^{37} +(5.50000 - 8.29156i) q^{45} +(-6.30860 - 2.04979i) q^{47} +(6.92663 - 0.147674i) q^{48} +(-5.66312 + 4.11450i) q^{49} +(7.79785 - 10.7328i) q^{53} +(-3.15430 + 1.02489i) q^{59} +(10.8487 - 3.78243i) q^{60} +(6.47214 + 4.70228i) q^{64} -13.0000 q^{67} +(3.27674 - 4.71836i) q^{69} +(9.74732 + 13.4160i) q^{71} +(8.27544 - 6.28626i) q^{75} +(12.6172 + 4.09957i) q^{80} +(-6.80418 + 5.89093i) q^{81} -16.5831i q^{89} +(6.30860 - 2.04979i) q^{92} +(2.85112 + 8.17748i) q^{93} +(-13.7533 - 9.99235i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{3} + 4 q^{4} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{3} + 4 q^{4} + 5 q^{9} - 8 q^{12} - 11 q^{15} - 8 q^{16} + 12 q^{25} + 8 q^{27} - 10 q^{31} - 10 q^{36} + 14 q^{37} + 44 q^{45} - 4 q^{48} - 14 q^{49} + 22 q^{60} + 16 q^{64} - 104 q^{67} - 11 q^{69} + 6 q^{75} - 7 q^{81} - 5 q^{93} - 34 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{10}\right)\)

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 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(3\) −1.42264 0.987975i −0.821362 0.570408i
\(4\) −0.618034 1.90211i −0.309017 0.951057i
\(5\) −1.94946 2.68321i −0.871826 1.19997i −0.978618 0.205685i \(-0.934058\pi\)
0.106792 0.994281i \(-0.465942\pi\)
\(6\) 0 0
\(7\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(8\) 0 0
\(9\) 1.04781 + 2.81107i 0.349270 + 0.937022i
\(10\) 0 0
\(11\) 0 0
\(12\) −1.00000 + 3.31662i −0.288675 + 0.957427i
\(13\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(14\) 0 0
\(15\) 0.122445 + 5.74326i 0.0316151 + 1.48290i
\(16\) −3.23607 + 2.35114i −0.809017 + 0.587785i
\(17\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(18\) 0 0
\(19\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(20\) −3.89893 + 5.36641i −0.871826 + 1.19997i
\(21\) 0 0
\(22\) 0 0
\(23\) 3.31662i 0.691564i 0.938315 + 0.345782i \(0.112386\pi\)
−0.938315 + 0.345782i \(0.887614\pi\)
\(24\) 0 0
\(25\) −1.85410 + 5.70634i −0.370820 + 1.14127i
\(26\) 0 0
\(27\) 1.28660 5.03435i 0.247607 0.968860i
\(28\) 0 0
\(29\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(30\) 0 0
\(31\) −4.04508 2.93893i −0.726519 0.527847i 0.161942 0.986800i \(-0.448224\pi\)
−0.888460 + 0.458954i \(0.848224\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 4.69938 3.73039i 0.783230 0.621732i
\(37\) −2.16312 6.65740i −0.355615 1.09447i −0.955652 0.294497i \(-0.904848\pi\)
0.600038 0.799972i \(-0.295152\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 5.50000 8.29156i 0.819892 1.23603i
\(46\) 0 0
\(47\) −6.30860 2.04979i −0.920203 0.298992i −0.189653 0.981851i \(-0.560736\pi\)
−0.730550 + 0.682859i \(0.760736\pi\)
\(48\) 6.92663 0.147674i 0.999773 0.0213149i
\(49\) −5.66312 + 4.11450i −0.809017 + 0.587785i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7.79785 10.7328i 1.07112 1.47427i 0.202178 0.979349i \(-0.435198\pi\)
0.868940 0.494918i \(-0.164802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.15430 + 1.02489i −0.410655 + 0.133430i −0.507057 0.861913i \(-0.669267\pi\)
0.0964021 + 0.995342i \(0.469267\pi\)
\(60\) 10.8487 3.78243i 1.40055 0.488310i
\(61\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 6.47214 + 4.70228i 0.809017 + 0.587785i
\(65\) 0 0
\(66\) 0 0
\(67\) −13.0000 −1.58820 −0.794101 0.607785i \(-0.792058\pi\)
−0.794101 + 0.607785i \(0.792058\pi\)
\(68\) 0 0
\(69\) 3.27674 4.71836i 0.394473 0.568024i
\(70\) 0 0
\(71\) 9.74732 + 13.4160i 1.15679 + 1.59219i 0.722416 + 0.691459i \(0.243032\pi\)
0.434378 + 0.900731i \(0.356968\pi\)
\(72\) 0 0
\(73\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(74\) 0 0
\(75\) 8.27544 6.28626i 0.955566 0.725875i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(80\) 12.6172 + 4.09957i 1.41064 + 0.458346i
\(81\) −6.80418 + 5.89093i −0.756021 + 0.654548i
\(82\) 0 0
\(83\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 16.5831i 1.75781i −0.476999 0.878904i \(-0.658275\pi\)
0.476999 0.878904i \(-0.341725\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 6.30860 2.04979i 0.657717 0.213705i
\(93\) 2.85112 + 8.17748i 0.295647 + 0.847965i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −13.7533 9.99235i −1.39643 1.01457i −0.995124 0.0986273i \(-0.968555\pi\)
−0.401310 0.915942i \(-0.631445\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 12.0000 1.20000
\(101\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(102\) 0 0
\(103\) −1.23607 3.80423i −0.121793 0.374842i 0.871510 0.490378i \(-0.163141\pi\)
−0.993303 + 0.115536i \(0.963141\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(108\) −10.3711 + 0.664130i −0.997956 + 0.0639059i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) −3.50000 + 11.6082i −0.332205 + 1.10180i
\(112\) 0 0
\(113\) 3.15430 + 1.02489i 0.296731 + 0.0964139i 0.453599 0.891206i \(-0.350140\pi\)
−0.156868 + 0.987620i \(0.550140\pi\)
\(114\) 0 0
\(115\) 8.89919 6.46564i 0.829853 0.602924i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) −3.09017 + 9.51057i −0.277505 + 0.854074i
\(125\) 3.15430 1.02489i 0.282129 0.0916693i
\(126\) 0 0
\(127\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −16.0164 + 6.36205i −1.37847 + 0.547558i
\(136\) 0 0
\(137\) −13.6462 18.7824i −1.16588 1.60469i −0.686617 0.727019i \(-0.740905\pi\)
−0.479260 0.877673i \(-0.659095\pi\)
\(138\) 0 0
\(139\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(140\) 0 0
\(141\) 6.94972 + 9.14884i 0.585272 + 0.770472i
\(142\) 0 0
\(143\) 0 0
\(144\) −10.0000 6.63325i −0.833333 0.552771i
\(145\) 0 0
\(146\) 0 0
\(147\) 12.1216 0.258429i 0.999773 0.0213149i
\(148\) −11.3262 + 8.22899i −0.931011 + 0.676419i
\(149\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(150\) 0 0
\(151\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 16.5831i 1.33199i
\(156\) 0 0
\(157\) 7.10739 21.8743i 0.567232 1.74576i −0.0939948 0.995573i \(-0.529964\pi\)
0.661226 0.750186i \(-0.270036\pi\)
\(158\) 0 0
\(159\) −21.6973 + 7.56486i −1.72071 + 0.599933i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 12.9443 + 9.40456i 1.01387 + 0.736622i 0.965018 0.262184i \(-0.0844426\pi\)
0.0488556 + 0.998806i \(0.484443\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(168\) 0 0
\(169\) 4.01722 + 12.3637i 0.309017 + 0.951057i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.50000 + 1.65831i 0.413405 + 0.124646i
\(178\) 0 0
\(179\) −15.7715 5.12447i −1.17882 0.383021i −0.346890 0.937906i \(-0.612762\pi\)
−0.831927 + 0.554885i \(0.812762\pi\)
\(180\) −19.1707 5.33715i −1.42890 0.397808i
\(181\) 20.2254 14.6946i 1.50334 1.09224i 0.534318 0.845283i \(-0.320568\pi\)
0.969026 0.246960i \(-0.0794316\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −13.6462 + 18.7824i −1.00329 + 1.38091i
\(186\) 0 0
\(187\) 0 0
\(188\) 13.2665i 0.967559i
\(189\) 0 0
\(190\) 0 0
\(191\) −22.0801 + 7.17425i −1.59766 + 0.519111i −0.966527 0.256565i \(-0.917409\pi\)
−0.631132 + 0.775676i \(0.717409\pi\)
\(192\) −4.56178 13.0840i −0.329218 0.944254i
\(193\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 11.3262 + 8.22899i 0.809017 + 0.587785i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) 0 0
\(201\) 18.4943 + 12.8437i 1.30449 + 0.905923i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −9.32325 + 3.47520i −0.648011 + 0.241543i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(212\) −25.2344 8.19915i −1.73310 0.563120i
\(213\) −0.612223 28.7163i −0.0419488 1.96761i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −0.309017 + 0.951057i −0.0206933 + 0.0636875i −0.960870 0.277000i \(-0.910660\pi\)
0.940177 + 0.340687i \(0.110660\pi\)
\(224\) 0 0
\(225\) −17.9836 + 0.767161i −1.19891 + 0.0511441i
\(226\) 0 0
\(227\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(228\) 0 0
\(229\) −4.04508 2.93893i −0.267307 0.194210i 0.446055 0.895005i \(-0.352828\pi\)
−0.713362 + 0.700796i \(0.752828\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(234\) 0 0
\(235\) 6.79837 + 20.9232i 0.443477 + 1.36488i
\(236\) 3.89893 + 5.36641i 0.253798 + 0.349324i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(240\) −13.8994 18.2977i −0.897205 1.18111i
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 15.5000 1.65831i 0.994325 0.106381i
\(244\) 0 0
\(245\) 22.0801 + 7.17425i 1.41064 + 0.458346i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −9.74732 + 13.4160i −0.615245 + 0.846812i −0.996996 0.0774530i \(-0.975321\pi\)
0.381751 + 0.924265i \(0.375321\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 4.94427 15.2169i 0.309017 0.951057i
\(257\) 25.2344 8.19915i 1.57408 0.511449i 0.613555 0.789652i \(-0.289739\pi\)
0.960522 + 0.278203i \(0.0897388\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −44.0000 −2.70290
\(266\) 0 0
\(267\) −16.3837 + 23.5918i −1.00267 + 1.44380i
\(268\) 8.03444 + 24.7275i 0.490782 + 1.51047i
\(269\) −7.79785 10.7328i −0.475443 0.654392i 0.502178 0.864764i \(-0.332532\pi\)
−0.977621 + 0.210373i \(0.932532\pi\)
\(270\) 0 0
\(271\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −11.0000 3.31662i −0.662122 0.199637i
\(277\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(278\) 0 0
\(279\) 4.02303 14.4504i 0.240853 0.865125i
\(280\) 0 0
\(281\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(282\) 0 0
\(283\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(284\) 19.4946 26.8321i 1.15679 1.59219i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −5.25329 + 16.1680i −0.309017 + 0.951057i
\(290\) 0 0
\(291\) 9.69379 + 27.8034i 0.568260 + 1.62987i
\(292\) 0 0
\(293\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(294\) 0 0
\(295\) 8.89919 + 6.46564i 0.518131 + 0.376444i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −17.0717 11.8557i −0.985634 0.684489i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −2.00000 + 6.63325i −0.113776 + 0.377352i
\(310\) 0 0
\(311\) 31.5430 + 10.2489i 1.78864 + 0.581164i 0.999456 0.0329949i \(-0.0105045\pi\)
0.789183 + 0.614159i \(0.210505\pi\)
\(312\) 0 0
\(313\) 15.3713 11.1679i 0.868839 0.631248i −0.0614365 0.998111i \(-0.519568\pi\)
0.930275 + 0.366863i \(0.119568\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 13.6462 18.7824i 0.766449 1.05493i −0.230201 0.973143i \(-0.573938\pi\)
0.996650 0.0817838i \(-0.0260617\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 26.5330i 1.48324i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 15.4104 + 9.30153i 0.856135 + 0.516752i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 35.0000 1.92377 0.961887 0.273447i \(-0.0881639\pi\)
0.961887 + 0.273447i \(0.0881639\pi\)
\(332\) 0 0
\(333\) 16.4478 13.0564i 0.901336 0.715484i
\(334\) 0 0
\(335\) 25.3430 + 34.8817i 1.38464 + 1.90579i
\(336\) 0 0
\(337\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(338\) 0 0
\(339\) −3.47486 4.57442i −0.188729 0.248448i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −19.0482 + 0.406103i −1.02552 + 0.0218639i
\(346\) 0 0
\(347\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(348\) 0 0
\(349\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 36.4829i 1.94179i −0.239511 0.970894i \(-0.576987\pi\)
0.239511 0.970894i \(-0.423013\pi\)
\(354\) 0 0
\(355\) 16.9959 52.3081i 0.902051 2.77623i
\(356\) −31.5430 + 10.2489i −1.67177 + 0.543192i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(360\) 0 0
\(361\) −15.3713 11.1679i −0.809017 0.587785i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −11.4336 35.1891i −0.596831 1.83686i −0.545395 0.838179i \(-0.683620\pi\)
−0.0514358 0.998676i \(-0.516380\pi\)
\(368\) −7.79785 10.7328i −0.406491 0.559487i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 13.7924 10.4771i 0.715103 0.543212i
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) −5.50000 1.65831i −0.284019 0.0856349i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 20.2254 14.6946i 1.03891 0.754813i 0.0688378 0.997628i \(-0.478071\pi\)
0.970073 + 0.242815i \(0.0780709\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.94946 2.68321i 0.0996129 0.137105i −0.756301 0.654224i \(-0.772995\pi\)
0.855914 + 0.517119i \(0.172995\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −10.5066 + 32.3359i −0.533391 + 1.64161i
\(389\) 34.6973 11.2738i 1.75922 0.571606i 0.762102 0.647456i \(-0.224167\pi\)
0.997119 + 0.0758507i \(0.0241672\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −7.41641 22.8254i −0.370820 1.14127i
\(401\) 15.5957 + 21.4656i 0.778812 + 1.07194i 0.995412 + 0.0956827i \(0.0305034\pi\)
−0.216600 + 0.976261i \(0.569497\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 29.0711 + 6.77287i 1.44455 + 0.336547i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(410\) 0 0
\(411\) 0.857113 + 40.2028i 0.0422782 + 1.98306i
\(412\) −6.47214 + 4.70228i −0.318859 + 0.231665i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 33.1662i 1.62028i 0.586238 + 0.810139i \(0.300608\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) 0 0
\(421\) −3.09017 + 9.51057i −0.150606 + 0.463517i −0.997689 0.0679432i \(-0.978356\pi\)
0.847084 + 0.531460i \(0.178356\pi\)
\(422\) 0 0
\(423\) −0.848129 19.8817i −0.0412374 0.966680i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(432\) 7.67292 + 19.3165i 0.369163 + 0.929364i
\(433\) 8.96149 + 27.5806i 0.430662 + 1.32544i 0.897467 + 0.441081i \(0.145405\pi\)
−0.466805 + 0.884360i \(0.654595\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −17.5000 11.6082i −0.833333 0.552771i
\(442\) 0 0
\(443\) −34.6973 11.2738i −1.64852 0.535636i −0.670099 0.742271i \(-0.733748\pi\)
−0.978418 + 0.206636i \(0.933748\pi\)
\(444\) 24.2432 0.516858i 1.15053 0.0245290i
\(445\) −44.4959 + 32.3282i −2.10931 + 1.53250i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −9.74732 + 13.4160i −0.460004 + 0.633142i −0.974510 0.224346i \(-0.927976\pi\)
0.514505 + 0.857487i \(0.327976\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 6.63325i 0.312002i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −17.7984 12.9313i −0.829853 0.602924i
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) −31.0000 −1.44069 −0.720346 0.693615i \(-0.756017\pi\)
−0.720346 + 0.693615i \(0.756017\pi\)
\(464\) 0 0
\(465\) 16.3837 23.5918i 0.759776 1.09404i
\(466\) 0 0
\(467\) −25.3430 34.8817i −1.17274 1.61413i −0.642523 0.766267i \(-0.722112\pi\)
−0.530212 0.847865i \(-0.677888\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −31.7225 + 24.0973i −1.46170 + 1.11035i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 38.3414 + 10.6743i 1.75553 + 0.488743i
\(478\) 0 0
\(479\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 56.3826i 2.56020i
\(486\) 0 0
\(487\) −13.2877 + 40.8954i −0.602125 + 1.85315i −0.0866600 + 0.996238i \(0.527619\pi\)
−0.515465 + 0.856911i \(0.672381\pi\)
\(488\) 0 0
\(489\) −9.12357 26.1679i −0.412582 1.18335i
\(490\) 0 0
\(491\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 20.0000 0.898027
\(497\) 0 0
\(498\) 0 0
\(499\) −12.3607 38.0423i −0.553340 1.70301i −0.700287 0.713861i \(-0.746945\pi\)
0.146947 0.989144i \(-0.453055\pi\)
\(500\) −3.89893 5.36641i −0.174365 0.239993i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 6.50000 21.5581i 0.288675 0.957427i
\(508\) 0 0
\(509\) 3.15430 + 1.02489i 0.139812 + 0.0454276i 0.378087 0.925770i \(-0.376582\pi\)
−0.238275 + 0.971198i \(0.576582\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −7.79785 + 10.7328i −0.343614 + 0.472945i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −41.0059 + 13.3236i −1.79650 + 0.583718i −0.999787 0.0206400i \(-0.993430\pi\)
−0.796713 + 0.604358i \(0.793430\pi\)
\(522\) 0 0
\(523\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 12.0000 0.521739
\(530\) 0 0
\(531\) −6.18615 7.79304i −0.268456 0.338189i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 17.3743 + 22.8721i 0.749757 + 0.987004i
\(538\) 0 0
\(539\) 0 0
\(540\) 22.0000 + 26.5330i 0.946729 + 1.14180i
\(541\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(542\) 0 0
\(543\) −43.2914 + 0.922961i −1.85781 + 0.0396081i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(548\) −27.2925 + 37.5649i −1.16588 + 1.60469i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 37.9703 13.2385i 1.61175 0.561944i
\(556\) 0 0
\(557\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(564\) 13.1070 18.8735i 0.551903 0.794716i
\(565\) −3.39919 10.4616i −0.143005 0.440124i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 38.5000 + 11.6082i 1.60836 + 0.484939i
\(574\) 0 0
\(575\) −18.9258 6.14936i −0.789260 0.256446i
\(576\) −6.43685 + 23.1207i −0.268202 + 0.963363i
\(577\) −38.0238 + 27.6259i −1.58295 + 1.15008i −0.669740 + 0.742596i \(0.733594\pi\)
−0.913212 + 0.407486i \(0.866406\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6.30860 2.04979i 0.260384 0.0846038i −0.175916 0.984405i \(-0.556289\pi\)
0.436300 + 0.899801i \(0.356289\pi\)
\(588\) −7.98312 22.8969i −0.329218 0.944254i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 22.6525 + 16.4580i 0.931011 + 0.676419i
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −28.4528 19.7595i −1.16450 0.808702i
\(598\) 0 0
\(599\) −19.4946 26.8321i −0.796529 1.09633i −0.993264 0.115872i \(-0.963034\pi\)
0.196735 0.980457i \(-0.436966\pi\)
\(600\) 0 0
\(601\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(602\) 0 0
\(603\) −13.6215 36.5439i −0.554712 1.48818i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 26.5330i 1.06818i −0.845428 0.534089i \(-0.820655\pi\)
0.845428 0.534089i \(-0.179345\pi\)
\(618\) 0 0
\(619\) −0.309017 + 0.951057i −0.0124204 + 0.0382262i −0.957075 0.289841i \(-0.906397\pi\)
0.944654 + 0.328068i \(0.106397\pi\)
\(620\) 31.5430 10.2489i 1.26680 0.411607i
\(621\) 16.6970 + 4.26719i 0.670029 + 0.171236i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 15.3713 + 11.1679i 0.614853 + 0.446717i
\(626\) 0 0
\(627\) 0 0
\(628\) −46.0000 −1.83560
\(629\) 0 0
\(630\) 0 0
\(631\) −2.16312 6.65740i −0.0861124 0.265027i 0.898723 0.438516i \(-0.144496\pi\)
−0.984836 + 0.173489i \(0.944496\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 27.7989 + 36.5954i 1.10230 + 1.45110i
\(637\) 0 0
\(638\) 0 0
\(639\) −27.5000 + 41.4578i −1.08788 + 1.64005i
\(640\) 0 0
\(641\) 22.0801 + 7.17425i 0.872111 + 0.283366i 0.710678 0.703518i \(-0.248388\pi\)
0.161433 + 0.986884i \(0.448388\pi\)
\(642\) 0 0
\(643\) −33.1697 + 24.0992i −1.30809 + 0.950379i −1.00000 0.000979141i \(-0.999688\pi\)
−0.308086 + 0.951359i \(0.599688\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 25.3430 34.8817i 0.996337 1.37134i 0.0687910 0.997631i \(-0.478086\pi\)
0.927546 0.373709i \(-0.121914\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 9.88854 30.4338i 0.387265 1.19188i
\(653\) −3.15430 + 1.02489i −0.123437 + 0.0401072i −0.370084 0.928998i \(-0.620671\pi\)
0.246647 + 0.969105i \(0.420671\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −13.0000 −0.505641 −0.252821 0.967513i \(-0.581358\pi\)
−0.252821 + 0.967513i \(0.581358\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 1.37924 1.04771i 0.0533245 0.0405068i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(674\) 0 0
\(675\) 26.3422 + 16.6760i 1.01391 + 0.641859i
\(676\) 21.0344 15.2824i 0.809017 0.587785i
\(677\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 46.4327i 1.77670i −0.459167 0.888350i \(-0.651852\pi\)
0.459167 0.888350i \(-0.348148\pi\)
\(684\) 0 0
\(685\) −23.7943 + 73.2314i −0.909134 + 2.79803i
\(686\) 0 0
\(687\) 2.85112 + 8.17748i 0.108777 + 0.311990i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −13.7533 9.99235i −0.523200 0.380127i 0.294608 0.955618i \(-0.404811\pi\)
−0.817808 + 0.575491i \(0.804811\pi\)
\(692\) 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 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 11.0000 36.4829i 0.414284 1.37402i
\(706\) 0 0
\(707\) 0 0
\(708\) −0.244889 11.4865i −0.00920350 0.431690i
\(709\) 15.3713 11.1679i 0.577282 0.419420i −0.260461 0.965484i \(-0.583875\pi\)
0.837743 + 0.546064i \(0.183875\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 9.74732 13.4160i 0.365040 0.502434i
\(714\) 0 0
\(715\) 0 0
\(716\) 33.1662i 1.23948i
\(717\) 0 0
\(718\) 0 0
\(719\) 15.7715 5.12447i 0.588177 0.191110i 0.000216702 1.00000i \(-0.499931\pi\)
0.587961 + 0.808890i \(0.299931\pi\)
\(720\) 1.69626 + 39.7633i 0.0632158 + 1.48189i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) −40.4508 29.3893i −1.50334 1.09224i
\(725\) 0 0
\(726\) 0 0
\(727\) 53.0000 1.96566 0.982831 0.184510i \(-0.0590699\pi\)
0.982831 + 0.184510i \(0.0590699\pi\)
\(728\) 0 0
\(729\) −23.6893 12.9544i −0.877381 0.479794i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(734\) 0 0
\(735\) −24.3240 32.0210i −0.897205 1.18111i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(740\) 44.1602 + 14.3485i 1.62336 + 0.527462i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 7.10739 21.8743i 0.259352 0.798205i −0.733588 0.679594i \(-0.762156\pi\)
0.992941 0.118611i \(-0.0378440\pi\)
\(752\) 25.2344 8.19915i 0.920203 0.298992i
\(753\) 27.1216 9.45608i 0.988367 0.344599i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −30.7426 22.3358i −1.11736 0.811810i −0.133554 0.991042i \(-0.542639\pi\)
−0.983807 + 0.179232i \(0.942639\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 27.2925 + 37.5649i 0.987407 + 1.35905i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −22.0678 + 16.7634i −0.796305 + 0.604896i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) −44.0000 13.2665i −1.58462 0.477781i
\(772\) 0 0
\(773\) 12.6172 + 4.09957i 0.453809 + 0.147451i 0.526998 0.849867i \(-0.323318\pi\)
−0.0731890 + 0.997318i \(0.523318\pi\)
\(774\) 0 0
\(775\) 24.2705 17.6336i 0.871822 0.633416i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 8.65248 26.6296i 0.309017 0.951057i
\(785\) −72.5488 + 23.5725i −2.58938 + 0.841340i
\(786\) 0 0
\(787\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 62.5962 + 43.4709i 2.22006 + 1.54175i
\(796\) −12.3607 38.0423i −0.438113 1.34837i
\(797\) 33.1409 + 45.6145i 1.17391 + 1.61575i 0.629940 + 0.776644i \(0.283079\pi\)
0.543970 + 0.839105i \(0.316921\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 46.6163 17.3760i 1.64710 0.613950i
\(802\) 0 0
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