Properties

Label 980.2.e.c.589.4
Level $980$
Weight $2$
Character 980.589
Analytic conductor $7.825$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-19})\)
Defining polynomial: \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 589.4
Root \(2.13746 + 0.656712i\) of defining polynomial
Character \(\chi\) \(=\) 980.589
Dual form 980.2.e.c.589.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.73205i q^{3} +(1.63746 + 1.52274i) q^{5} +O(q^{10})\) \(q+1.73205i q^{3} +(1.63746 + 1.52274i) q^{5} -5.27492 q^{11} +2.62685i q^{13} +(-2.63746 + 2.83616i) q^{15} -0.418627i q^{17} +3.27492 q^{19} +7.82300i q^{23} +(0.362541 + 4.98684i) q^{25} +5.19615i q^{27} -4.27492 q^{29} -3.27492 q^{31} -9.13642i q^{33} -9.97368i q^{37} -4.54983 q^{39} +3.72508 q^{41} +2.15068i q^{43} -6.50958i q^{47} +0.725083 q^{51} +5.67232i q^{53} +(-8.63746 - 8.03231i) q^{55} +5.67232i q^{57} -3.27492 q^{59} +13.5498 q^{61} +(-4.00000 + 4.30136i) q^{65} +3.52165i q^{67} -13.5498 q^{69} -4.54983 q^{71} +6.50958i q^{73} +(-8.63746 + 0.627940i) q^{75} -7.27492 q^{79} -9.00000 q^{81} -7.40437i q^{83} +(0.637459 - 0.685484i) q^{85} -7.40437i q^{87} -7.00000 q^{89} -5.67232i q^{93} +(5.36254 + 4.98684i) q^{95} +6.92820i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{5} - 6 q^{11} - 3 q^{15} - 2 q^{19} + 9 q^{25} - 2 q^{29} + 2 q^{31} + 12 q^{39} + 30 q^{41} + 18 q^{51} - 27 q^{55} + 2 q^{59} + 24 q^{61} - 16 q^{65} - 24 q^{69} + 12 q^{71} - 27 q^{75} - 14 q^{79} - 36 q^{81} - 5 q^{85} - 28 q^{89} + 29 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) 1.73205i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) 0 0
\(5\) 1.63746 + 1.52274i 0.732294 + 0.680989i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −5.27492 −1.59045 −0.795224 0.606316i \(-0.792647\pi\)
−0.795224 + 0.606316i \(0.792647\pi\)
\(12\) 0 0
\(13\) 2.62685i 0.728557i 0.931290 + 0.364278i \(0.118684\pi\)
−0.931290 + 0.364278i \(0.881316\pi\)
\(14\) 0 0
\(15\) −2.63746 + 2.83616i −0.680989 + 0.732294i
\(16\) 0 0
\(17\) 0.418627i 0.101532i −0.998711 0.0507659i \(-0.983834\pi\)
0.998711 0.0507659i \(-0.0161663\pi\)
\(18\) 0 0
\(19\) 3.27492 0.751318 0.375659 0.926758i \(-0.377416\pi\)
0.375659 + 0.926758i \(0.377416\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.82300i 1.63121i 0.578610 + 0.815604i \(0.303595\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) 0 0
\(25\) 0.362541 + 4.98684i 0.0725083 + 0.997368i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −4.27492 −0.793832 −0.396916 0.917855i \(-0.629920\pi\)
−0.396916 + 0.917855i \(0.629920\pi\)
\(30\) 0 0
\(31\) −3.27492 −0.588192 −0.294096 0.955776i \(-0.595019\pi\)
−0.294096 + 0.955776i \(0.595019\pi\)
\(32\) 0 0
\(33\) 9.13642i 1.59045i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 9.97368i 1.63966i −0.572605 0.819831i \(-0.694067\pi\)
0.572605 0.819831i \(-0.305933\pi\)
\(38\) 0 0
\(39\) −4.54983 −0.728557
\(40\) 0 0
\(41\) 3.72508 0.581760 0.290880 0.956760i \(-0.406052\pi\)
0.290880 + 0.956760i \(0.406052\pi\)
\(42\) 0 0
\(43\) 2.15068i 0.327975i 0.986462 + 0.163988i \(0.0524357\pi\)
−0.986462 + 0.163988i \(0.947564\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.50958i 0.949519i −0.880115 0.474760i \(-0.842535\pi\)
0.880115 0.474760i \(-0.157465\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0.725083 0.101532
\(52\) 0 0
\(53\) 5.67232i 0.779153i 0.920994 + 0.389577i \(0.127379\pi\)
−0.920994 + 0.389577i \(0.872621\pi\)
\(54\) 0 0
\(55\) −8.63746 8.03231i −1.16467 1.08308i
\(56\) 0 0
\(57\) 5.67232i 0.751318i
\(58\) 0 0
\(59\) −3.27492 −0.426358 −0.213179 0.977013i \(-0.568382\pi\)
−0.213179 + 0.977013i \(0.568382\pi\)
\(60\) 0 0
\(61\) 13.5498 1.73488 0.867439 0.497543i \(-0.165764\pi\)
0.867439 + 0.497543i \(0.165764\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.00000 + 4.30136i −0.496139 + 0.533517i
\(66\) 0 0
\(67\) 3.52165i 0.430237i 0.976588 + 0.215119i \(0.0690139\pi\)
−0.976588 + 0.215119i \(0.930986\pi\)
\(68\) 0 0
\(69\) −13.5498 −1.63121
\(70\) 0 0
\(71\) −4.54983 −0.539966 −0.269983 0.962865i \(-0.587018\pi\)
−0.269983 + 0.962865i \(0.587018\pi\)
\(72\) 0 0
\(73\) 6.50958i 0.761888i 0.924598 + 0.380944i \(0.124401\pi\)
−0.924598 + 0.380944i \(0.875599\pi\)
\(74\) 0 0
\(75\) −8.63746 + 0.627940i −0.997368 + 0.0725083i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −7.27492 −0.818492 −0.409246 0.912424i \(-0.634208\pi\)
−0.409246 + 0.912424i \(0.634208\pi\)
\(80\) 0 0
\(81\) −9.00000 −1.00000
\(82\) 0 0
\(83\) 7.40437i 0.812736i −0.913710 0.406368i \(-0.866795\pi\)
0.913710 0.406368i \(-0.133205\pi\)
\(84\) 0 0
\(85\) 0.637459 0.685484i 0.0691421 0.0743512i
\(86\) 0 0
\(87\) 7.40437i 0.793832i
\(88\) 0 0
\(89\) −7.00000 −0.741999 −0.370999 0.928633i \(-0.620985\pi\)
−0.370999 + 0.928633i \(0.620985\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 5.67232i 0.588192i
\(94\) 0 0
\(95\) 5.36254 + 4.98684i 0.550185 + 0.511639i
\(96\) 0 0
\(97\) 6.92820i 0.703452i 0.936103 + 0.351726i \(0.114405\pi\)
−0.936103 + 0.351726i \(0.885595\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 13.5498 1.34826 0.674129 0.738613i \(-0.264519\pi\)
0.674129 + 0.738613i \(0.264519\pi\)
\(102\) 0 0
\(103\) 11.2871i 1.11215i 0.831132 + 0.556076i \(0.187694\pi\)
−0.831132 + 0.556076i \(0.812306\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.52165i 0.340450i 0.985405 + 0.170225i \(0.0544495\pi\)
−0.985405 + 0.170225i \(0.945550\pi\)
\(108\) 0 0
\(109\) 11.5498 1.10627 0.553137 0.833090i \(-0.313431\pi\)
0.553137 + 0.833090i \(0.313431\pi\)
\(110\) 0 0
\(111\) 17.2749 1.63966
\(112\) 0 0
\(113\) 4.30136i 0.404637i −0.979320 0.202319i \(-0.935152\pi\)
0.979320 0.202319i \(-0.0648477\pi\)
\(114\) 0 0
\(115\) −11.9124 + 12.8098i −1.11083 + 1.19452i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 16.8248 1.52952
\(122\) 0 0
\(123\) 6.45203i 0.581760i
\(124\) 0 0
\(125\) −7.00000 + 8.71780i −0.626099 + 0.779744i
\(126\) 0 0
\(127\) 15.6460i 1.38836i −0.719802 0.694179i \(-0.755768\pi\)
0.719802 0.694179i \(-0.244232\pi\)
\(128\) 0 0
\(129\) −3.72508 −0.327975
\(130\) 0 0
\(131\) 10.7251 0.937055 0.468527 0.883449i \(-0.344785\pi\)
0.468527 + 0.883449i \(0.344785\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −7.91238 + 8.50848i −0.680989 + 0.732294i
\(136\) 0 0
\(137\) 21.3183i 1.82135i −0.413126 0.910674i \(-0.635563\pi\)
0.413126 0.910674i \(-0.364437\pi\)
\(138\) 0 0
\(139\) 13.0997 1.11110 0.555550 0.831483i \(-0.312508\pi\)
0.555550 + 0.831483i \(0.312508\pi\)
\(140\) 0 0
\(141\) 11.2749 0.949519
\(142\) 0 0
\(143\) 13.8564i 1.15873i
\(144\) 0 0
\(145\) −7.00000 6.50958i −0.581318 0.540591i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7.54983 0.618507 0.309253 0.950980i \(-0.399921\pi\)
0.309253 + 0.950980i \(0.399921\pi\)
\(150\) 0 0
\(151\) −12.7251 −1.03555 −0.517776 0.855516i \(-0.673240\pi\)
−0.517776 + 0.855516i \(0.673240\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −5.36254 4.98684i −0.430730 0.400553i
\(156\) 0 0
\(157\) 2.20822i 0.176235i 0.996110 + 0.0881176i \(0.0280851\pi\)
−0.996110 + 0.0881176i \(0.971915\pi\)
\(158\) 0 0
\(159\) −9.82475 −0.779153
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 5.67232i 0.444291i −0.975014 0.222145i \(-0.928694\pi\)
0.975014 0.222145i \(-0.0713059\pi\)
\(164\) 0 0
\(165\) 13.9124 14.9605i 1.08308 1.16467i
\(166\) 0 0
\(167\) 0.476171i 0.0368472i 0.999830 + 0.0184236i \(0.00586474\pi\)
−0.999830 + 0.0184236i \(0.994135\pi\)
\(168\) 0 0
\(169\) 6.09967 0.469205
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 20.4811i 1.55715i 0.627553 + 0.778573i \(0.284056\pi\)
−0.627553 + 0.778573i \(0.715944\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.67232i 0.426358i
\(178\) 0 0
\(179\) 7.27492 0.543753 0.271876 0.962332i \(-0.412356\pi\)
0.271876 + 0.962332i \(0.412356\pi\)
\(180\) 0 0
\(181\) 24.2749 1.80434 0.902170 0.431380i \(-0.141973\pi\)
0.902170 + 0.431380i \(0.141973\pi\)
\(182\) 0 0
\(183\) 23.4690i 1.73488i
\(184\) 0 0
\(185\) 15.1873 16.3315i 1.11659 1.20071i
\(186\) 0 0
\(187\) 2.20822i 0.161481i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0.175248 0.0126805 0.00634026 0.999980i \(-0.497982\pi\)
0.00634026 + 0.999980i \(0.497982\pi\)
\(192\) 0 0
\(193\) 21.3183i 1.53453i −0.641332 0.767263i \(-0.721618\pi\)
0.641332 0.767263i \(-0.278382\pi\)
\(194\) 0 0
\(195\) −7.45017 6.92820i −0.533517 0.496139i
\(196\) 0 0
\(197\) 8.60271i 0.612918i 0.951884 + 0.306459i \(0.0991442\pi\)
−0.951884 + 0.306459i \(0.900856\pi\)
\(198\) 0 0
\(199\) 17.2749 1.22459 0.612293 0.790631i \(-0.290247\pi\)
0.612293 + 0.790631i \(0.290247\pi\)
\(200\) 0 0
\(201\) −6.09967 −0.430237
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 6.09967 + 5.67232i 0.426019 + 0.396172i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −17.2749 −1.19493
\(210\) 0 0
\(211\) 25.6495 1.76578 0.882892 0.469576i \(-0.155593\pi\)
0.882892 + 0.469576i \(0.155593\pi\)
\(212\) 0 0
\(213\) 7.88054i 0.539966i
\(214\) 0 0
\(215\) −3.27492 + 3.52165i −0.223348 + 0.240174i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −11.2749 −0.761888
\(220\) 0 0
\(221\) 1.09967 0.0739717
\(222\) 0 0
\(223\) 8.71780i 0.583787i −0.956451 0.291893i \(-0.905715\pi\)
0.956451 0.291893i \(-0.0942853\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 19.5287i 1.29617i 0.761569 + 0.648084i \(0.224429\pi\)
−0.761569 + 0.648084i \(0.775571\pi\)
\(228\) 0 0
\(229\) 3.27492 0.216413 0.108206 0.994128i \(-0.465489\pi\)
0.108206 + 0.994128i \(0.465489\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.2750i 0.935189i −0.883943 0.467594i \(-0.845121\pi\)
0.883943 0.467594i \(-0.154879\pi\)
\(234\) 0 0
\(235\) 9.91238 10.6592i 0.646612 0.695327i
\(236\) 0 0
\(237\) 12.6005i 0.818492i
\(238\) 0 0
\(239\) −0.549834 −0.0355658 −0.0177829 0.999842i \(-0.505661\pi\)
−0.0177829 + 0.999842i \(0.505661\pi\)
\(240\) 0 0
\(241\) −9.82475 −0.632868 −0.316434 0.948615i \(-0.602486\pi\)
−0.316434 + 0.948615i \(0.602486\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 8.60271i 0.547377i
\(248\) 0 0
\(249\) 12.8248 0.812736
\(250\) 0 0
\(251\) 20.5498 1.29709 0.648547 0.761175i \(-0.275377\pi\)
0.648547 + 0.761175i \(0.275377\pi\)
\(252\) 0 0
\(253\) 41.2657i 2.59435i
\(254\) 0 0
\(255\) 1.18729 + 1.10411i 0.0743512 + 0.0691421i
\(256\) 0 0
\(257\) 11.6482i 0.726594i 0.931673 + 0.363297i \(0.118349\pi\)
−0.931673 + 0.363297i \(0.881651\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0.779710i 0.0480790i −0.999711 0.0240395i \(-0.992347\pi\)
0.999711 0.0240395i \(-0.00765274\pi\)
\(264\) 0 0
\(265\) −8.63746 + 9.28819i −0.530595 + 0.570569i
\(266\) 0 0
\(267\) 12.1244i 0.741999i
\(268\) 0 0
\(269\) −14.4502 −0.881042 −0.440521 0.897742i \(-0.645206\pi\)
−0.440521 + 0.897742i \(0.645206\pi\)
\(270\) 0 0
\(271\) −9.82475 −0.596811 −0.298406 0.954439i \(-0.596455\pi\)
−0.298406 + 0.954439i \(0.596455\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.91238 26.3052i −0.115321 1.58626i
\(276\) 0 0
\(277\) 14.2750i 0.857704i 0.903375 + 0.428852i \(0.141082\pi\)
−0.903375 + 0.428852i \(0.858918\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 10.9260i 0.649484i 0.945803 + 0.324742i \(0.105278\pi\)
−0.945803 + 0.324742i \(0.894722\pi\)
\(284\) 0 0
\(285\) −8.63746 + 9.28819i −0.511639 + 0.550185i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 16.8248 0.989691
\(290\) 0 0
\(291\) −12.0000 −0.703452
\(292\) 0 0
\(293\) 6.92820i 0.404750i 0.979308 + 0.202375i \(0.0648660\pi\)
−0.979308 + 0.202375i \(0.935134\pi\)
\(294\) 0 0
\(295\) −5.36254 4.98684i −0.312219 0.290345i
\(296\) 0 0
\(297\) 27.4093i 1.59045i
\(298\) 0 0
\(299\) −20.5498 −1.18843
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 23.4690i 1.34826i
\(304\) 0 0
\(305\) 22.1873 + 20.6328i 1.27044 + 1.18143i
\(306\) 0 0
\(307\) 26.5145i 1.51326i −0.653843 0.756631i \(-0.726844\pi\)
0.653843 0.756631i \(-0.273156\pi\)
\(308\) 0 0
\(309\) −19.5498 −1.11215
\(310\) 0 0
\(311\) 9.82475 0.557111 0.278555 0.960420i \(-0.410144\pi\)
0.278555 + 0.960420i \(0.410144\pi\)
\(312\) 0 0
\(313\) 33.5002i 1.89354i −0.321904 0.946772i \(-0.604323\pi\)
0.321904 0.946772i \(-0.395677\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 25.6197i 1.43894i 0.694521 + 0.719472i \(0.255616\pi\)
−0.694521 + 0.719472i \(0.744384\pi\)
\(318\) 0 0
\(319\) 22.5498 1.26255
\(320\) 0 0
\(321\) −6.09967 −0.340450
\(322\) 0 0
\(323\) 1.37097i 0.0762827i
\(324\) 0 0
\(325\) −13.0997 + 0.952341i −0.726639 + 0.0528264i
\(326\) 0 0
\(327\) 20.0049i 1.10627i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 17.8248 0.979737 0.489868 0.871796i \(-0.337045\pi\)
0.489868 + 0.871796i \(0.337045\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −5.36254 + 5.76655i −0.292987 + 0.315060i
\(336\) 0 0
\(337\) 4.30136i 0.234310i −0.993114 0.117155i \(-0.962623\pi\)
0.993114 0.117155i \(-0.0373774\pi\)
\(338\) 0 0
\(339\) 7.45017 0.404637
\(340\) 0 0
\(341\) 17.2749 0.935489
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −22.1873 20.6328i −1.19452 1.11083i
\(346\) 0 0
\(347\) 12.1244i 0.650870i 0.945564 + 0.325435i \(0.105511\pi\)
−0.945564 + 0.325435i \(0.894489\pi\)
\(348\) 0 0
\(349\) −3.72508 −0.199399 −0.0996996 0.995018i \(-0.531788\pi\)
−0.0996996 + 0.995018i \(0.531788\pi\)
\(350\) 0 0
\(351\) −13.6495 −0.728557
\(352\) 0 0
\(353\) 8.18408i 0.435595i 0.975994 + 0.217797i \(0.0698872\pi\)
−0.975994 + 0.217797i \(0.930113\pi\)
\(354\) 0 0
\(355\) −7.45017 6.92820i −0.395414 0.367711i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −36.3746 −1.91978 −0.959889 0.280382i \(-0.909539\pi\)
−0.959889 + 0.280382i \(0.909539\pi\)
\(360\) 0 0
\(361\) −8.27492 −0.435522
\(362\) 0 0
\(363\) 29.1413i 1.52952i
\(364\) 0 0
\(365\) −9.91238 + 10.6592i −0.518837 + 0.557926i
\(366\) 0 0
\(367\) 6.03341i 0.314941i 0.987524 + 0.157471i \(0.0503340\pi\)
−0.987524 + 0.157471i \(0.949666\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 9.97368i 0.516417i −0.966089 0.258209i \(-0.916868\pi\)
0.966089 0.258209i \(-0.0831322\pi\)
\(374\) 0 0
\(375\) −15.0997 12.1244i −0.779744 0.626099i
\(376\) 0 0
\(377\) 11.2296i 0.578352i
\(378\) 0 0
\(379\) 21.6495 1.11206 0.556030 0.831162i \(-0.312324\pi\)
0.556030 + 0.831162i \(0.312324\pi\)
\(380\) 0 0
\(381\) 27.0997 1.38836
\(382\) 0 0
\(383\) 6.14849i 0.314173i −0.987585 0.157087i \(-0.949790\pi\)
0.987585 0.157087i \(-0.0502102\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −32.3746 −1.64146 −0.820728 0.571319i \(-0.806432\pi\)
−0.820728 + 0.571319i \(0.806432\pi\)
\(390\) 0 0
\(391\) 3.27492 0.165620
\(392\) 0 0
\(393\) 18.5764i 0.937055i
\(394\) 0 0
\(395\) −11.9124 11.0778i −0.599377 0.557384i
\(396\) 0 0
\(397\) 10.8109i 0.542585i −0.962497 0.271293i \(-0.912549\pi\)
0.962497 0.271293i \(-0.0874511\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.00000 0.149813 0.0749064 0.997191i \(-0.476134\pi\)
0.0749064 + 0.997191i \(0.476134\pi\)
\(402\) 0 0
\(403\) 8.60271i 0.428532i
\(404\) 0 0
\(405\) −14.7371 13.7046i −0.732294 0.680989i
\(406\) 0 0
\(407\) 52.6103i 2.60780i
\(408\) 0 0
\(409\) −20.0997 −0.993865 −0.496932 0.867789i \(-0.665540\pi\)
−0.496932 + 0.867789i \(0.665540\pi\)
\(410\) 0 0
\(411\) 36.9244 1.82135
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 11.2749 12.1244i 0.553464 0.595161i
\(416\) 0 0
\(417\) 22.6893i 1.11110i
\(418\) 0 0
\(419\) −13.0997 −0.639961 −0.319980 0.947424i \(-0.603676\pi\)
−0.319980 + 0.947424i \(0.603676\pi\)
\(420\) 0 0
\(421\) −4.27492 −0.208347 −0.104173 0.994559i \(-0.533220\pi\)
−0.104173 + 0.994559i \(0.533220\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.08762 0.151770i 0.101265 0.00736190i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 24.0000 1.15873
\(430\) 0 0
\(431\) −18.3746 −0.885073 −0.442536 0.896751i \(-0.645921\pi\)
−0.442536 + 0.896751i \(0.645921\pi\)
\(432\) 0 0
\(433\) 18.1578i 0.872606i −0.899800 0.436303i \(-0.856288\pi\)
0.899800 0.436303i \(-0.143712\pi\)
\(434\) 0 0
\(435\) 11.2749 12.1244i 0.540591 0.581318i
\(436\) 0 0
\(437\) 25.6197i 1.22556i
\(438\) 0 0
\(439\) 23.8248 1.13709 0.568547 0.822651i \(-0.307506\pi\)
0.568547 + 0.822651i \(0.307506\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12.1244i 0.576046i 0.957624 + 0.288023i \(0.0929979\pi\)
−0.957624 + 0.288023i \(0.907002\pi\)
\(444\) 0 0
\(445\) −11.4622 10.6592i −0.543361 0.505293i
\(446\) 0 0
\(447\) 13.0767i 0.618507i
\(448\) 0 0
\(449\) 3.17525 0.149849 0.0749246 0.997189i \(-0.476128\pi\)
0.0749246 + 0.997189i \(0.476128\pi\)
\(450\) 0 0
\(451\) −19.6495 −0.925259
\(452\) 0 0
\(453\) 22.0405i 1.03555i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.37097i 0.0641312i −0.999486 0.0320656i \(-0.989791\pi\)
0.999486 0.0320656i \(-0.0102085\pi\)
\(458\) 0 0
\(459\) 2.17525 0.101532
\(460\) 0 0
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 0 0
\(463\) 2.15068i 0.0999505i −0.998750 0.0499752i \(-0.984086\pi\)
0.998750 0.0499752i \(-0.0159142\pi\)
\(464\) 0 0
\(465\) 8.63746 9.28819i 0.400553 0.430730i
\(466\) 0 0
\(467\) 15.7035i 0.726673i −0.931658 0.363337i \(-0.881637\pi\)
0.931658 0.363337i \(-0.118363\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −3.82475 −0.176235
\(472\) 0 0
\(473\) 11.3446i 0.521627i
\(474\) 0 0
\(475\) 1.18729 + 16.3315i 0.0544767 + 0.749340i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 9.82475 0.448904 0.224452 0.974485i \(-0.427941\pi\)
0.224452 + 0.974485i \(0.427941\pi\)
\(480\) 0 0
\(481\) 26.1993 1.19459
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −10.5498 + 11.3446i −0.479043 + 0.515134i
\(486\) 0 0
\(487\) 2.93039i 0.132789i 0.997793 + 0.0663943i \(0.0211495\pi\)
−0.997793 + 0.0663943i \(0.978850\pi\)
\(488\) 0 0
\(489\) 9.82475 0.444291
\(490\) 0 0
\(491\) −28.5498 −1.28844 −0.644218 0.764842i \(-0.722817\pi\)
−0.644218 + 0.764842i \(0.722817\pi\)
\(492\) 0 0
\(493\) 1.78959i 0.0805993i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −1.62541 −0.0727635 −0.0363818 0.999338i \(-0.511583\pi\)
−0.0363818 + 0.999338i \(0.511583\pi\)
\(500\) 0 0
\(501\) −0.824752 −0.0368472
\(502\) 0 0
\(503\) 31.7682i 1.41647i 0.705975 + 0.708236i \(0.250509\pi\)
−0.705975 + 0.708236i \(0.749491\pi\)
\(504\) 0 0
\(505\) 22.1873 + 20.6328i 0.987322 + 0.918149i
\(506\) 0 0
\(507\) 10.5649i 0.469205i
\(508\) 0 0
\(509\) −14.4502 −0.640492 −0.320246 0.947334i \(-0.603766\pi\)
−0.320246 + 0.947334i \(0.603766\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 17.0170i 0.751318i
\(514\) 0 0
\(515\) −17.1873 + 18.4822i −0.757363 + 0.814421i
\(516\) 0 0
\(517\) 34.3375i 1.51016i
\(518\) 0 0
\(519\) −35.4743 −1.55715
\(520\) 0 0
\(521\) −9.82475 −0.430430 −0.215215 0.976567i \(-0.569045\pi\)
−0.215215 + 0.976567i \(0.569045\pi\)
\(522\) 0 0
\(523\) 7.34683i 0.321254i 0.987015 + 0.160627i \(0.0513517\pi\)
−0.987015 + 0.160627i \(0.948648\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.37097i 0.0597203i
\(528\) 0 0
\(529\) −38.1993 −1.66084
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 9.78523i 0.423845i
\(534\) 0 0
\(535\) −5.36254 + 5.76655i −0.231843 + 0.249310i
\(536\) 0 0
\(537\) 12.6005i 0.543753i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −17.5498 −0.754526 −0.377263 0.926106i \(-0.623135\pi\)
−0.377263 + 0.926106i \(0.623135\pi\)
\(542\) 0 0
\(543\) 42.0454i 1.80434i
\(544\) 0 0
\(545\) 18.9124 + 17.5874i 0.810117 + 0.753360i
\(546\) 0 0
\(547\) 20.5386i 0.878168i −0.898446 0.439084i \(-0.855303\pi\)
0.898446 0.439084i \(-0.144697\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −14.0000 −0.596420
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 28.2870 + 26.3052i 1.20071 + 1.11659i
\(556\) 0 0
\(557\) 9.97368i 0.422598i 0.977421 + 0.211299i \(0.0677694\pi\)
−0.977421 + 0.211299i \(0.932231\pi\)
\(558\) 0 0
\(559\) −5.64950 −0.238949
\(560\) 0 0
\(561\) −3.82475 −0.161481
\(562\) 0 0
\(563\) 22.6317i 0.953814i −0.878954 0.476907i \(-0.841758\pi\)
0.878954 0.476907i \(-0.158242\pi\)
\(564\) 0 0
\(565\) 6.54983 7.04329i 0.275554 0.296313i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −8.37459 −0.351081 −0.175540 0.984472i \(-0.556167\pi\)
−0.175540 + 0.984472i \(0.556167\pi\)
\(570\) 0 0
\(571\) 7.27492 0.304446 0.152223 0.988346i \(-0.451357\pi\)
0.152223 + 0.988346i \(0.451357\pi\)
\(572\) 0 0
\(573\) 0.303539i 0.0126805i
\(574\) 0 0
\(575\) −39.0120 + 2.83616i −1.62691 + 0.118276i
\(576\) 0 0
\(577\) 3.88273i 0.161640i 0.996729 + 0.0808200i \(0.0257539\pi\)
−0.996729 + 0.0808200i \(0.974246\pi\)
\(578\) 0 0
\(579\) 36.9244 1.53453
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 29.9210i 1.23920i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 20.8997i 0.862623i −0.902203 0.431311i \(-0.858051\pi\)
0.902203 0.431311i \(-0.141949\pi\)
\(588\) 0 0
\(589\) −10.7251 −0.441919
\(590\) 0 0
\(591\) −14.9003 −0.612918
\(592\) 0 0
\(593\) 33.3851i 1.37096i 0.728090 + 0.685482i \(0.240408\pi\)
−0.728090 + 0.685482i \(0.759592\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 29.9210i 1.22459i
\(598\) 0 0
\(599\) −5.27492 −0.215527 −0.107764 0.994177i \(-0.534369\pi\)
−0.107764 + 0.994177i \(0.534369\pi\)
\(600\) 0 0
\(601\) −14.0000 −0.571072 −0.285536 0.958368i \(-0.592172\pi\)
−0.285536 + 0.958368i \(0.592172\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 27.5498 + 25.6197i 1.12006 + 1.04159i
\(606\) 0 0
\(607\) 11.4022i 0.462801i −0.972859 0.231400i \(-0.925669\pi\)
0.972859 0.231400i \(-0.0743307\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 17.0997 0.691779
\(612\) 0 0
\(613\) 28.3616i 1.14551i 0.819725 + 0.572757i \(0.194126\pi\)
−0.819725 + 0.572757i \(0.805874\pi\)
\(614\) 0 0
\(615\) −9.82475 + 10.5649i −0.396172 + 0.426019i
\(616\) 0 0
\(617\) 31.2920i 1.25977i −0.776689 0.629884i \(-0.783102\pi\)
0.776689 0.629884i \(-0.216898\pi\)
\(618\) 0 0
\(619\) −8.92442 −0.358703 −0.179351 0.983785i \(-0.557400\pi\)
−0.179351 + 0.983785i \(0.557400\pi\)
\(620\) 0 0
\(621\) −40.6495 −1.63121
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −24.7371 + 3.61587i −0.989485 + 0.144635i
\(626\) 0 0
\(627\) 29.9210i 1.19493i
\(628\) 0 0
\(629\) −4.17525 −0.166478
\(630\) 0 0
\(631\) 33.0997 1.31768 0.658839 0.752284i \(-0.271048\pi\)
0.658839 + 0.752284i \(0.271048\pi\)
\(632\) 0 0
\(633\) 44.4262i 1.76578i
\(634\) 0 0
\(635\) 23.8248 25.6197i 0.945456 1.01669i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −2.09967 −0.0829319 −0.0414660 0.999140i \(-0.513203\pi\)
−0.0414660 + 0.999140i \(0.513203\pi\)
\(642\) 0 0
\(643\) 31.4071i 1.23857i −0.785164 0.619287i \(-0.787422\pi\)
0.785164 0.619287i \(-0.212578\pi\)
\(644\) 0 0
\(645\) −6.09967 5.67232i −0.240174 0.223348i
\(646\) 0 0
\(647\) 26.9331i 1.05885i −0.848357 0.529425i \(-0.822408\pi\)
0.848357 0.529425i \(-0.177592\pi\)
\(648\) 0 0
\(649\) 17.2749 0.678100
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 28.3616i 1.10988i −0.831892 0.554938i \(-0.812742\pi\)
0.831892 0.554938i \(-0.187258\pi\)
\(654\) 0 0
\(655\) 17.5619 + 16.3315i 0.686199 + 0.638124i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 40.5498 1.57960 0.789799 0.613366i \(-0.210185\pi\)
0.789799 + 0.613366i \(0.210185\pi\)
\(660\) 0 0
\(661\) 0.450166 0.0175094 0.00875471 0.999962i \(-0.497213\pi\)
0.00875471 + 0.999962i \(0.497213\pi\)
\(662\) 0 0
\(663\) 1.90468i 0.0739717i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 33.4427i 1.29491i
\(668\) 0 0
\(669\) 15.0997 0.583787
\(670\) 0 0
\(671\) −71.4743 −2.75923
\(672\) 0 0
\(673\) 31.2920i 1.20622i 0.797659 + 0.603109i \(0.206072\pi\)
−0.797659 + 0.603109i \(0.793928\pi\)
\(674\) 0 0
\(675\) −25.9124 + 1.88382i −0.997368 + 0.0725083i
\(676\) 0 0
\(677\) 46.4043i 1.78346i −0.452566 0.891731i \(-0.649491\pi\)
0.452566 0.891731i \(-0.350509\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −33.8248 −1.29617
\(682\) 0 0
\(683\) 19.1676i 0.733430i −0.930333 0.366715i \(-0.880482\pi\)
0.930333 0.366715i \(-0.119518\pi\)
\(684\) 0 0
\(685\) 32.4622 34.9079i 1.24032 1.33376i
\(686\) 0 0
\(687\) 5.67232i 0.216413i
\(688\) 0 0
\(689\) −14.9003 −0.567657
\(690\) 0 0
\(691\) −30.3746 −1.15550 −0.577752 0.816212i \(-0.696070\pi\)
−0.577752 + 0.816212i \(0.696070\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 21.4502 + 19.9474i 0.813651 + 0.756646i
\(696\) 0 0
\(697\) 1.55942i 0.0590672i
\(698\) 0 0
\(699\) 24.7251 0.935189
\(700\) 0 0
\(701\) 8.82475 0.333306 0.166653 0.986016i \(-0.446704\pi\)
0.166653 + 0.986016i \(0.446704\pi\)
\(702\) 0 0
\(703\) 32.6630i 1.23191i
\(704\) 0 0
\(705\) 18.4622 + 17.1687i 0.695327 + 0.646612i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 10.4502 0.392464 0.196232 0.980557i \(-0.437129\pi\)
0.196232 + 0.980557i \(0.437129\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 25.6197i 0.959465i
\(714\) 0 0
\(715\) 21.0997 22.6893i 0.789083 0.848531i
\(716\) 0 0
\(717\) 0.952341i 0.0355658i
\(718\) 0 0
\(719\) −30.3746 −1.13278 −0.566390 0.824137i \(-0.691661\pi\)
−0.566390 + 0.824137i \(0.691661\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 17.0170i 0.632868i
\(724\) 0 0
\(725\) −1.54983 21.3183i −0.0575594 0.791743i
\(726\) 0 0
\(727\) 3.10302i 0.115085i −0.998343 0.0575423i \(-0.981674\pi\)
0.998343 0.0575423i \(-0.0183264\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 0.900331 0.0332999
\(732\) 0 0
\(733\) 37.6865i 1.39198i 0.718050 + 0.695991i \(0.245035\pi\)
−0.718050 + 0.695991i \(0.754965\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 18.5764i 0.684270i
\(738\) 0 0
\(739\) 20.9244 0.769717 0.384859 0.922976i \(-0.374250\pi\)
0.384859 + 0.922976i \(0.374250\pi\)
\(740\) 0 0
\(741\) −14.9003 −0.547377
\(742\) 0 0
\(743\) 6.45203i 0.236702i 0.992972 + 0.118351i \(0.0377608\pi\)
−0.992972 + 0.118351i \(0.962239\pi\)
\(744\) 0 0
\(745\) 12.3625 + 11.4964i 0.452928 + 0.421196i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −14.7251 −0.537326 −0.268663 0.963234i \(-0.586582\pi\)
−0.268663 + 0.963234i \(0.586582\pi\)
\(752\) 0 0
\(753\) 35.5934i 1.29709i
\(754\) 0 0
\(755\) −20.8368 19.3770i −0.758329 0.705200i
\(756\) 0 0
\(757\) 35.5934i 1.29366i 0.762633 + 0.646831i \(0.223906\pi\)
−0.762633 + 0.646831i \(0.776094\pi\)
\(758\) 0 0
\(759\) 71.4743 2.59435
\(760\) 0 0
\(761\) −22.9244 −0.831010 −0.415505 0.909591i \(-0.636395\pi\)
−0.415505 + 0.909591i \(0.636395\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8.60271i 0.310626i
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) −20.1752 −0.726594
\(772\) 0 0
\(773\) 40.3133i 1.44997i −0.688765 0.724985i \(-0.741847\pi\)
0.688765 0.724985i \(-0.258153\pi\)
\(774\) 0 0
\(775\) −1.18729 16.3315i −0.0426488 0.586644i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 12.1993 0.437087
\(780\) 0 0
\(781\) 24.0000 0.858788
\(782\) 0 0
\(783\) 22.2131i 0.793832i
\(784\) 0 0
\(785\) −3.36254 + 3.61587i −0.120014 + 0.129056i
\(786\) 0 0
\(787\) 1.73205i 0.0617409i 0.999523 + 0.0308705i \(0.00982794\pi\)
−0.999523 + 0.0308705i \(0.990172\pi\)
\(788\) 0 0
\(789\) 1.35050 0.0480790
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 35.5934i 1.26396i
\(794\) 0 0
\(795\) −16.0876 14.9605i −0.570569 0.530595i
\(796\) 0 0
\(797\) 46.8229i 1.65855i 0.558839 + 0.829276i \(0.311247\pi\)
−0.558839 + 0.829276i \(0.688753\pi\)
\(798\) 0 0
\(799\) −2.72508 −0.0964065
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 34.3375i 1.21174i
\(804\) 0 0