Properties

Label 1148.2.d.a.1065.12
Level $1148$
Weight $2$
Character 1148.1065
Analytic conductor $9.167$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 39 x^{18} + 531 x^{16} + 3488 x^{14} + 12661 x^{12} + 27027 x^{10} + 34540 x^{8} + 25909 x^{6} + 10677 x^{4} + 2092 x^{2} + 144\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1065.12
Root \(0.911088i\) of defining polynomial
Character \(\chi\) \(=\) 1148.1065
Dual form 1148.2.d.a.1065.9

$q$-expansion

\(f(q)\) \(=\) \(q+0.162086i q^{3} -1.05958 q^{5} -1.00000i q^{7} +2.97373 q^{9} +O(q^{10})\) \(q+0.162086i q^{3} -1.05958 q^{5} -1.00000i q^{7} +2.97373 q^{9} +6.18973i q^{11} -5.55048i q^{13} -0.171744i q^{15} -3.90747i q^{17} +2.97153i q^{19} +0.162086 q^{21} +7.17619 q^{23} -3.87728 q^{25} +0.968259i q^{27} +2.56302i q^{29} +0.343450 q^{31} -1.00327 q^{33} +1.05958i q^{35} +8.19624 q^{37} +0.899657 q^{39} +(0.710016 + 6.36364i) q^{41} +10.0205 q^{43} -3.15091 q^{45} -7.52873i q^{47} -1.00000 q^{49} +0.633347 q^{51} +1.52927i q^{53} -6.55854i q^{55} -0.481644 q^{57} +11.7505 q^{59} +11.1776 q^{61} -2.97373i q^{63} +5.88120i q^{65} -4.12911i q^{67} +1.16316i q^{69} +7.66832i q^{71} -12.2487 q^{73} -0.628454i q^{75} +6.18973 q^{77} -11.8357i q^{79} +8.76424 q^{81} +14.0549 q^{83} +4.14029i q^{85} -0.415430 q^{87} +1.32263i q^{89} -5.55048 q^{91} +0.0556685i q^{93} -3.14858i q^{95} -1.93000i q^{97} +18.4066i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 4q^{5} - 20q^{9} + O(q^{10}) \) \( 20q + 4q^{5} - 20q^{9} + 4q^{21} + 8q^{31} + 20q^{37} + 4q^{39} - 16q^{41} + 20q^{43} - 4q^{45} - 20q^{49} + 52q^{51} - 36q^{57} + 20q^{59} - 4q^{61} - 12q^{73} + 8q^{77} + 20q^{81} - 48q^{83} + 44q^{87} - 4q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(3\) 0.162086i 0.0935806i 0.998905 + 0.0467903i \(0.0148992\pi\)
−0.998905 + 0.0467903i \(0.985101\pi\)
\(4\) 0 0
\(5\) −1.05958 −0.473860 −0.236930 0.971527i \(-0.576141\pi\)
−0.236930 + 0.971527i \(0.576141\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 2.97373 0.991243
\(10\) 0 0
\(11\) 6.18973i 1.86627i 0.359520 + 0.933137i \(0.382941\pi\)
−0.359520 + 0.933137i \(0.617059\pi\)
\(12\) 0 0
\(13\) 5.55048i 1.53943i −0.638390 0.769713i \(-0.720399\pi\)
0.638390 0.769713i \(-0.279601\pi\)
\(14\) 0 0
\(15\) 0.171744i 0.0443441i
\(16\) 0 0
\(17\) 3.90747i 0.947701i −0.880605 0.473850i \(-0.842864\pi\)
0.880605 0.473850i \(-0.157136\pi\)
\(18\) 0 0
\(19\) 2.97153i 0.681716i 0.940115 + 0.340858i \(0.110718\pi\)
−0.940115 + 0.340858i \(0.889282\pi\)
\(20\) 0 0
\(21\) 0.162086 0.0353701
\(22\) 0 0
\(23\) 7.17619 1.49634 0.748170 0.663507i \(-0.230933\pi\)
0.748170 + 0.663507i \(0.230933\pi\)
\(24\) 0 0
\(25\) −3.87728 −0.775457
\(26\) 0 0
\(27\) 0.968259i 0.186342i
\(28\) 0 0
\(29\) 2.56302i 0.475940i 0.971272 + 0.237970i \(0.0764821\pi\)
−0.971272 + 0.237970i \(0.923518\pi\)
\(30\) 0 0
\(31\) 0.343450 0.0616854 0.0308427 0.999524i \(-0.490181\pi\)
0.0308427 + 0.999524i \(0.490181\pi\)
\(32\) 0 0
\(33\) −1.00327 −0.174647
\(34\) 0 0
\(35\) 1.05958i 0.179102i
\(36\) 0 0
\(37\) 8.19624 1.34745 0.673727 0.738981i \(-0.264692\pi\)
0.673727 + 0.738981i \(0.264692\pi\)
\(38\) 0 0
\(39\) 0.899657 0.144060
\(40\) 0 0
\(41\) 0.710016 + 6.36364i 0.110886 + 0.993833i
\(42\) 0 0
\(43\) 10.0205 1.52812 0.764059 0.645146i \(-0.223204\pi\)
0.764059 + 0.645146i \(0.223204\pi\)
\(44\) 0 0
\(45\) −3.15091 −0.469710
\(46\) 0 0
\(47\) 7.52873i 1.09818i −0.835764 0.549089i \(-0.814975\pi\)
0.835764 0.549089i \(-0.185025\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0.633347 0.0886864
\(52\) 0 0
\(53\) 1.52927i 0.210061i 0.994469 + 0.105031i \(0.0334940\pi\)
−0.994469 + 0.105031i \(0.966506\pi\)
\(54\) 0 0
\(55\) 6.55854i 0.884353i
\(56\) 0 0
\(57\) −0.481644 −0.0637953
\(58\) 0 0
\(59\) 11.7505 1.52978 0.764891 0.644160i \(-0.222793\pi\)
0.764891 + 0.644160i \(0.222793\pi\)
\(60\) 0 0
\(61\) 11.1776 1.43115 0.715574 0.698537i \(-0.246165\pi\)
0.715574 + 0.698537i \(0.246165\pi\)
\(62\) 0 0
\(63\) 2.97373i 0.374655i
\(64\) 0 0
\(65\) 5.88120i 0.729473i
\(66\) 0 0
\(67\) 4.12911i 0.504451i −0.967668 0.252226i \(-0.918837\pi\)
0.967668 0.252226i \(-0.0811625\pi\)
\(68\) 0 0
\(69\) 1.16316i 0.140028i
\(70\) 0 0
\(71\) 7.66832i 0.910062i 0.890476 + 0.455031i \(0.150372\pi\)
−0.890476 + 0.455031i \(0.849628\pi\)
\(72\) 0 0
\(73\) −12.2487 −1.43360 −0.716802 0.697277i \(-0.754395\pi\)
−0.716802 + 0.697277i \(0.754395\pi\)
\(74\) 0 0
\(75\) 0.628454i 0.0725677i
\(76\) 0 0
\(77\) 6.18973 0.705386
\(78\) 0 0
\(79\) 11.8357i 1.33162i −0.746120 0.665811i \(-0.768086\pi\)
0.746120 0.665811i \(-0.231914\pi\)
\(80\) 0 0
\(81\) 8.76424 0.973805
\(82\) 0 0
\(83\) 14.0549 1.54272 0.771362 0.636396i \(-0.219576\pi\)
0.771362 + 0.636396i \(0.219576\pi\)
\(84\) 0 0
\(85\) 4.14029i 0.449078i
\(86\) 0 0
\(87\) −0.415430 −0.0445388
\(88\) 0 0
\(89\) 1.32263i 0.140199i 0.997540 + 0.0700993i \(0.0223316\pi\)
−0.997540 + 0.0700993i \(0.977668\pi\)
\(90\) 0 0
\(91\) −5.55048 −0.581848
\(92\) 0 0
\(93\) 0.0556685i 0.00577255i
\(94\) 0 0
\(95\) 3.14858i 0.323038i
\(96\) 0 0
\(97\) 1.93000i 0.195962i −0.995188 0.0979810i \(-0.968762\pi\)
0.995188 0.0979810i \(-0.0312384\pi\)
\(98\) 0 0
\(99\) 18.4066i 1.84993i
\(100\) 0 0
\(101\) 7.16465i 0.712909i 0.934313 + 0.356455i \(0.116015\pi\)
−0.934313 + 0.356455i \(0.883985\pi\)
\(102\) 0 0
\(103\) −0.161576 −0.0159206 −0.00796029 0.999968i \(-0.502534\pi\)
−0.00796029 + 0.999968i \(0.502534\pi\)
\(104\) 0 0
\(105\) −0.171744 −0.0167605
\(106\) 0 0
\(107\) −11.8496 −1.14554 −0.572772 0.819715i \(-0.694132\pi\)
−0.572772 + 0.819715i \(0.694132\pi\)
\(108\) 0 0
\(109\) 15.2534i 1.46101i 0.682907 + 0.730505i \(0.260715\pi\)
−0.682907 + 0.730505i \(0.739285\pi\)
\(110\) 0 0
\(111\) 1.32850i 0.126095i
\(112\) 0 0
\(113\) −7.38582 −0.694799 −0.347400 0.937717i \(-0.612935\pi\)
−0.347400 + 0.937717i \(0.612935\pi\)
\(114\) 0 0
\(115\) −7.60378 −0.709056
\(116\) 0 0
\(117\) 16.5056i 1.52594i
\(118\) 0 0
\(119\) −3.90747 −0.358197
\(120\) 0 0
\(121\) −27.3128 −2.48298
\(122\) 0 0
\(123\) −1.03146 + 0.115084i −0.0930035 + 0.0103768i
\(124\) 0 0
\(125\) 9.40622 0.841318
\(126\) 0 0
\(127\) −3.01362 −0.267416 −0.133708 0.991021i \(-0.542688\pi\)
−0.133708 + 0.991021i \(0.542688\pi\)
\(128\) 0 0
\(129\) 1.62419i 0.143002i
\(130\) 0 0
\(131\) 4.02732 0.351869 0.175934 0.984402i \(-0.443705\pi\)
0.175934 + 0.984402i \(0.443705\pi\)
\(132\) 0 0
\(133\) 2.97153 0.257664
\(134\) 0 0
\(135\) 1.02595i 0.0882999i
\(136\) 0 0
\(137\) 3.77667i 0.322663i 0.986900 + 0.161331i \(0.0515788\pi\)
−0.986900 + 0.161331i \(0.948421\pi\)
\(138\) 0 0
\(139\) −11.5981 −0.983742 −0.491871 0.870668i \(-0.663687\pi\)
−0.491871 + 0.870668i \(0.663687\pi\)
\(140\) 0 0
\(141\) 1.22030 0.102768
\(142\) 0 0
\(143\) 34.3560 2.87299
\(144\) 0 0
\(145\) 2.71573i 0.225529i
\(146\) 0 0
\(147\) 0.162086i 0.0133687i
\(148\) 0 0
\(149\) 18.2620i 1.49609i −0.663651 0.748043i \(-0.730994\pi\)
0.663651 0.748043i \(-0.269006\pi\)
\(150\) 0 0
\(151\) 7.77175i 0.632456i 0.948683 + 0.316228i \(0.102416\pi\)
−0.948683 + 0.316228i \(0.897584\pi\)
\(152\) 0 0
\(153\) 11.6198i 0.939401i
\(154\) 0 0
\(155\) −0.363913 −0.0292302
\(156\) 0 0
\(157\) 9.50772i 0.758799i −0.925233 0.379400i \(-0.876131\pi\)
0.925233 0.379400i \(-0.123869\pi\)
\(158\) 0 0
\(159\) −0.247873 −0.0196576
\(160\) 0 0
\(161\) 7.17619i 0.565563i
\(162\) 0 0
\(163\) −8.47898 −0.664125 −0.332063 0.943257i \(-0.607745\pi\)
−0.332063 + 0.943257i \(0.607745\pi\)
\(164\) 0 0
\(165\) 1.06305 0.0827583
\(166\) 0 0
\(167\) 1.73491i 0.134251i −0.997745 0.0671255i \(-0.978617\pi\)
0.997745 0.0671255i \(-0.0213828\pi\)
\(168\) 0 0
\(169\) −17.8078 −1.36983
\(170\) 0 0
\(171\) 8.83652i 0.675746i
\(172\) 0 0
\(173\) −14.7405 −1.12070 −0.560351 0.828255i \(-0.689334\pi\)
−0.560351 + 0.828255i \(0.689334\pi\)
\(174\) 0 0
\(175\) 3.87728i 0.293095i
\(176\) 0 0
\(177\) 1.90459i 0.143158i
\(178\) 0 0
\(179\) 23.3480i 1.74511i −0.488517 0.872555i \(-0.662462\pi\)
0.488517 0.872555i \(-0.337538\pi\)
\(180\) 0 0
\(181\) 6.31988i 0.469753i −0.972025 0.234877i \(-0.924531\pi\)
0.972025 0.234877i \(-0.0754686\pi\)
\(182\) 0 0
\(183\) 1.81174i 0.133928i
\(184\) 0 0
\(185\) −8.68460 −0.638505
\(186\) 0 0
\(187\) 24.1862 1.76867
\(188\) 0 0
\(189\) 0.968259 0.0704305
\(190\) 0 0
\(191\) 4.69246i 0.339535i −0.985484 0.169767i \(-0.945698\pi\)
0.985484 0.169767i \(-0.0543016\pi\)
\(192\) 0 0
\(193\) 6.65756i 0.479222i −0.970869 0.239611i \(-0.922980\pi\)
0.970869 0.239611i \(-0.0770198\pi\)
\(194\) 0 0
\(195\) −0.953261 −0.0682645
\(196\) 0 0
\(197\) 1.88925 0.134603 0.0673017 0.997733i \(-0.478561\pi\)
0.0673017 + 0.997733i \(0.478561\pi\)
\(198\) 0 0
\(199\) 23.9076i 1.69476i 0.530984 + 0.847382i \(0.321822\pi\)
−0.530984 + 0.847382i \(0.678178\pi\)
\(200\) 0 0
\(201\) 0.669273 0.0472068
\(202\) 0 0
\(203\) 2.56302 0.179889
\(204\) 0 0
\(205\) −0.752321 6.74281i −0.0525444 0.470938i
\(206\) 0 0
\(207\) 21.3400 1.48324
\(208\) 0 0
\(209\) −18.3930 −1.27227
\(210\) 0 0
\(211\) 17.8111i 1.22616i 0.790019 + 0.613082i \(0.210071\pi\)
−0.790019 + 0.613082i \(0.789929\pi\)
\(212\) 0 0
\(213\) −1.24293 −0.0851641
\(214\) 0 0
\(215\) −10.6176 −0.724114
\(216\) 0 0
\(217\) 0.343450i 0.0233149i
\(218\) 0 0
\(219\) 1.98535i 0.134157i
\(220\) 0 0
\(221\) −21.6883 −1.45892
\(222\) 0 0
\(223\) −7.07864 −0.474021 −0.237010 0.971507i \(-0.576168\pi\)
−0.237010 + 0.971507i \(0.576168\pi\)
\(224\) 0 0
\(225\) −11.5300 −0.768666
\(226\) 0 0
\(227\) 16.1206i 1.06996i 0.844864 + 0.534982i \(0.179682\pi\)
−0.844864 + 0.534982i \(0.820318\pi\)
\(228\) 0 0
\(229\) 9.51140i 0.628531i −0.949335 0.314266i \(-0.898242\pi\)
0.949335 0.314266i \(-0.101758\pi\)
\(230\) 0 0
\(231\) 1.00327i 0.0660104i
\(232\) 0 0
\(233\) 11.4323i 0.748955i 0.927236 + 0.374477i \(0.122178\pi\)
−0.927236 + 0.374477i \(0.877822\pi\)
\(234\) 0 0
\(235\) 7.97732i 0.520383i
\(236\) 0 0
\(237\) 1.91841 0.124614
\(238\) 0 0
\(239\) 4.60112i 0.297621i −0.988866 0.148811i \(-0.952455\pi\)
0.988866 0.148811i \(-0.0475445\pi\)
\(240\) 0 0
\(241\) −13.2766 −0.855218 −0.427609 0.903964i \(-0.640644\pi\)
−0.427609 + 0.903964i \(0.640644\pi\)
\(242\) 0 0
\(243\) 4.32534i 0.277471i
\(244\) 0 0
\(245\) 1.05958 0.0676943
\(246\) 0 0
\(247\) 16.4934 1.04945
\(248\) 0 0
\(249\) 2.27810i 0.144369i
\(250\) 0 0
\(251\) −8.38211 −0.529074 −0.264537 0.964375i \(-0.585219\pi\)
−0.264537 + 0.964375i \(0.585219\pi\)
\(252\) 0 0
\(253\) 44.4187i 2.79258i
\(254\) 0 0
\(255\) −0.671084 −0.0420249
\(256\) 0 0
\(257\) 8.60975i 0.537062i −0.963271 0.268531i \(-0.913462\pi\)
0.963271 0.268531i \(-0.0865381\pi\)
\(258\) 0 0
\(259\) 8.19624i 0.509290i
\(260\) 0 0
\(261\) 7.62172i 0.471772i
\(262\) 0 0
\(263\) 0.535071i 0.0329939i −0.999864 0.0164970i \(-0.994749\pi\)
0.999864 0.0164970i \(-0.00525138\pi\)
\(264\) 0 0
\(265\) 1.62039i 0.0995396i
\(266\) 0 0
\(267\) −0.214380 −0.0131199
\(268\) 0 0
\(269\) 8.12937 0.495656 0.247828 0.968804i \(-0.420283\pi\)
0.247828 + 0.968804i \(0.420283\pi\)
\(270\) 0 0
\(271\) −23.8952 −1.45153 −0.725766 0.687941i \(-0.758515\pi\)
−0.725766 + 0.687941i \(0.758515\pi\)
\(272\) 0 0
\(273\) 0.899657i 0.0544497i
\(274\) 0 0
\(275\) 23.9993i 1.44722i
\(276\) 0 0
\(277\) −23.8739 −1.43444 −0.717221 0.696846i \(-0.754586\pi\)
−0.717221 + 0.696846i \(0.754586\pi\)
\(278\) 0 0
\(279\) 1.02133 0.0611452
\(280\) 0 0
\(281\) 3.98234i 0.237566i 0.992920 + 0.118783i \(0.0378993\pi\)
−0.992920 + 0.118783i \(0.962101\pi\)
\(282\) 0 0
\(283\) −18.0961 −1.07570 −0.537852 0.843040i \(-0.680764\pi\)
−0.537852 + 0.843040i \(0.680764\pi\)
\(284\) 0 0
\(285\) 0.510342 0.0302301
\(286\) 0 0
\(287\) 6.36364 0.710016i 0.375634 0.0419109i
\(288\) 0 0
\(289\) 1.73168 0.101864
\(290\) 0 0
\(291\) 0.312827 0.0183382
\(292\) 0 0
\(293\) 23.3041i 1.36144i −0.732544 0.680720i \(-0.761667\pi\)
0.732544 0.680720i \(-0.238333\pi\)
\(294\) 0 0
\(295\) −12.4506 −0.724902
\(296\) 0 0
\(297\) −5.99327 −0.347765
\(298\) 0 0
\(299\) 39.8313i 2.30350i
\(300\) 0 0
\(301\) 10.0205i 0.577574i
\(302\) 0 0
\(303\) −1.16129 −0.0667144
\(304\) 0 0
\(305\) −11.8436 −0.678164
\(306\) 0 0
\(307\) 3.83573 0.218917 0.109458 0.993991i \(-0.465088\pi\)
0.109458 + 0.993991i \(0.465088\pi\)
\(308\) 0 0
\(309\) 0.0261893i 0.00148986i
\(310\) 0 0
\(311\) 2.98814i 0.169442i −0.996405 0.0847210i \(-0.973000\pi\)
0.996405 0.0847210i \(-0.0269999\pi\)
\(312\) 0 0
\(313\) 28.5943i 1.61625i −0.589014 0.808123i \(-0.700484\pi\)
0.589014 0.808123i \(-0.299516\pi\)
\(314\) 0 0
\(315\) 3.15091i 0.177534i
\(316\) 0 0
\(317\) 24.8997i 1.39850i 0.714875 + 0.699252i \(0.246484\pi\)
−0.714875 + 0.699252i \(0.753516\pi\)
\(318\) 0 0
\(319\) −15.8644 −0.888236
\(320\) 0 0
\(321\) 1.92066i 0.107201i
\(322\) 0 0
\(323\) 11.6112 0.646062
\(324\) 0 0
\(325\) 21.5208i 1.19376i
\(326\) 0 0
\(327\) −2.47237 −0.136722
\(328\) 0 0
\(329\) −7.52873 −0.415072
\(330\) 0 0
\(331\) 12.4659i 0.685189i −0.939483 0.342594i \(-0.888694\pi\)
0.939483 0.342594i \(-0.111306\pi\)
\(332\) 0 0
\(333\) 24.3734 1.33565
\(334\) 0 0
\(335\) 4.37514i 0.239039i
\(336\) 0 0
\(337\) −15.8361 −0.862649 −0.431325 0.902197i \(-0.641954\pi\)
−0.431325 + 0.902197i \(0.641954\pi\)
\(338\) 0 0
\(339\) 1.19714i 0.0650197i
\(340\) 0 0
\(341\) 2.12586i 0.115122i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 1.23247i 0.0663538i
\(346\) 0 0
\(347\) 5.19452i 0.278857i −0.990232 0.139428i \(-0.955474\pi\)
0.990232 0.139428i \(-0.0445265\pi\)
\(348\) 0 0
\(349\) −16.4617 −0.881173 −0.440586 0.897710i \(-0.645229\pi\)
−0.440586 + 0.897710i \(0.645229\pi\)
\(350\) 0 0
\(351\) 5.37430 0.286859
\(352\) 0 0
\(353\) −18.7888 −1.00002 −0.500012 0.866018i \(-0.666671\pi\)
−0.500012 + 0.866018i \(0.666671\pi\)
\(354\) 0 0
\(355\) 8.12522i 0.431242i
\(356\) 0 0
\(357\) 0.633347i 0.0335203i
\(358\) 0 0
\(359\) 26.8931 1.41937 0.709683 0.704521i \(-0.248838\pi\)
0.709683 + 0.704521i \(0.248838\pi\)
\(360\) 0 0
\(361\) 10.1700 0.535264
\(362\) 0 0
\(363\) 4.42703i 0.232359i
\(364\) 0 0
\(365\) 12.9785 0.679328
\(366\) 0 0
\(367\) −27.7107 −1.44648 −0.723242 0.690594i \(-0.757349\pi\)
−0.723242 + 0.690594i \(0.757349\pi\)
\(368\) 0 0
\(369\) 2.11139 + 18.9237i 0.109915 + 0.985130i
\(370\) 0 0
\(371\) 1.52927 0.0793957
\(372\) 0 0
\(373\) −0.426013 −0.0220581 −0.0110290 0.999939i \(-0.503511\pi\)
−0.0110290 + 0.999939i \(0.503511\pi\)
\(374\) 0 0
\(375\) 1.52462i 0.0787310i
\(376\) 0 0
\(377\) 14.2260 0.732675
\(378\) 0 0
\(379\) 28.0114 1.43885 0.719425 0.694570i \(-0.244405\pi\)
0.719425 + 0.694570i \(0.244405\pi\)
\(380\) 0 0
\(381\) 0.488467i 0.0250249i
\(382\) 0 0
\(383\) 14.8248i 0.757511i 0.925497 + 0.378755i \(0.123648\pi\)
−0.925497 + 0.378755i \(0.876352\pi\)
\(384\) 0 0
\(385\) −6.55854 −0.334254
\(386\) 0 0
\(387\) 29.7984 1.51474
\(388\) 0 0
\(389\) −32.7871 −1.66237 −0.831185 0.555996i \(-0.812337\pi\)
−0.831185 + 0.555996i \(0.812337\pi\)
\(390\) 0 0
\(391\) 28.0408i 1.41808i
\(392\) 0 0
\(393\) 0.652774i 0.0329281i
\(394\) 0 0
\(395\) 12.5409i 0.631003i
\(396\) 0 0
\(397\) 16.2173i 0.813923i 0.913445 + 0.406961i \(0.133412\pi\)
−0.913445 + 0.406961i \(0.866588\pi\)
\(398\) 0 0
\(399\) 0.481644i 0.0241124i
\(400\) 0 0
\(401\) 15.8298 0.790501 0.395251 0.918573i \(-0.370658\pi\)
0.395251 + 0.918573i \(0.370658\pi\)
\(402\) 0 0
\(403\) 1.90631i 0.0949601i
\(404\) 0 0
\(405\) −9.28645 −0.461447
\(406\) 0 0
\(407\) 50.7325i 2.51472i
\(408\) 0 0
\(409\) 33.1844 1.64086 0.820430 0.571747i \(-0.193734\pi\)
0.820430 + 0.571747i \(0.193734\pi\)
\(410\) 0 0
\(411\) −0.612147 −0.0301950
\(412\) 0 0
\(413\) 11.7505i 0.578203i
\(414\) 0 0
\(415\) −14.8923 −0.731036
\(416\) 0 0
\(417\) 1.87990i 0.0920591i
\(418\) 0 0
\(419\) 15.7444 0.769166 0.384583 0.923090i \(-0.374345\pi\)
0.384583 + 0.923090i \(0.374345\pi\)
\(420\) 0 0
\(421\) 4.43254i 0.216029i −0.994149 0.108014i \(-0.965551\pi\)
0.994149 0.108014i \(-0.0344493\pi\)
\(422\) 0 0
\(423\) 22.3884i 1.08856i
\(424\) 0 0
\(425\) 15.1504i 0.734901i
\(426\) 0 0
\(427\) 11.1776i 0.540923i
\(428\) 0 0
\(429\) 5.56864i 0.268856i
\(430\) 0 0
\(431\) 3.53857 0.170447 0.0852236 0.996362i \(-0.472840\pi\)
0.0852236 + 0.996362i \(0.472840\pi\)
\(432\) 0 0
\(433\) −23.3178 −1.12058 −0.560291 0.828296i \(-0.689311\pi\)
−0.560291 + 0.828296i \(0.689311\pi\)
\(434\) 0 0
\(435\) 0.440183 0.0211051
\(436\) 0 0
\(437\) 21.3243i 1.02008i
\(438\) 0 0
\(439\) 28.3096i 1.35114i 0.737295 + 0.675571i \(0.236103\pi\)
−0.737295 + 0.675571i \(0.763897\pi\)
\(440\) 0 0
\(441\) −2.97373 −0.141606
\(442\) 0 0
\(443\) −5.43738 −0.258338 −0.129169 0.991623i \(-0.541231\pi\)
−0.129169 + 0.991623i \(0.541231\pi\)
\(444\) 0 0
\(445\) 1.40144i 0.0664345i
\(446\) 0 0
\(447\) 2.96003 0.140004
\(448\) 0 0
\(449\) 22.3814 1.05625 0.528123 0.849168i \(-0.322896\pi\)
0.528123 + 0.849168i \(0.322896\pi\)
\(450\) 0 0
\(451\) −39.3892 + 4.39481i −1.85477 + 0.206943i
\(452\) 0 0
\(453\) −1.25969 −0.0591856
\(454\) 0 0
\(455\) 5.88120 0.275715
\(456\) 0 0
\(457\) 19.4445i 0.909576i −0.890600 0.454788i \(-0.849715\pi\)
0.890600 0.454788i \(-0.150285\pi\)
\(458\) 0 0
\(459\) 3.78344 0.176596
\(460\) 0 0
\(461\) 29.2163 1.36074 0.680368 0.732870i \(-0.261820\pi\)
0.680368 + 0.732870i \(0.261820\pi\)
\(462\) 0 0
\(463\) 16.4977i 0.766714i −0.923600 0.383357i \(-0.874768\pi\)
0.923600 0.383357i \(-0.125232\pi\)
\(464\) 0 0
\(465\) 0.0589854i 0.00273538i
\(466\) 0 0
\(467\) 18.8138 0.870601 0.435300 0.900285i \(-0.356642\pi\)
0.435300 + 0.900285i \(0.356642\pi\)
\(468\) 0 0
\(469\) −4.12911 −0.190665
\(470\) 0 0
\(471\) 1.54107 0.0710088
\(472\) 0 0
\(473\) 62.0245i 2.85189i
\(474\) 0 0
\(475\) 11.5215i 0.528641i
\(476\) 0 0
\(477\) 4.54763i 0.208222i
\(478\) 0 0
\(479\) 18.8829i 0.862781i 0.902165 + 0.431391i \(0.141977\pi\)
−0.902165 + 0.431391i \(0.858023\pi\)
\(480\) 0 0
\(481\) 45.4931i 2.07431i
\(482\) 0 0
\(483\) 1.16316 0.0529257
\(484\) 0 0
\(485\) 2.04500i 0.0928585i
\(486\) 0 0
\(487\) −4.05043 −0.183543 −0.0917713 0.995780i \(-0.529253\pi\)
−0.0917713 + 0.995780i \(0.529253\pi\)
\(488\) 0 0
\(489\) 1.37433i 0.0621492i
\(490\) 0 0
\(491\) −30.6318 −1.38239 −0.691197 0.722666i \(-0.742916\pi\)
−0.691197 + 0.722666i \(0.742916\pi\)
\(492\) 0 0
\(493\) 10.0149 0.451049
\(494\) 0 0
\(495\) 19.5033i 0.876609i
\(496\) 0 0
\(497\) 7.66832 0.343971
\(498\) 0 0
\(499\) 7.27069i 0.325481i −0.986669 0.162741i \(-0.947967\pi\)
0.986669 0.162741i \(-0.0520333\pi\)
\(500\) 0 0
\(501\) 0.281204 0.0125633
\(502\) 0 0
\(503\) 11.5631i 0.515573i 0.966202 + 0.257786i \(0.0829931\pi\)
−0.966202 + 0.257786i \(0.917007\pi\)
\(504\) 0 0
\(505\) 7.59154i 0.337819i
\(506\) 0 0
\(507\) 2.88641i 0.128190i
\(508\) 0 0
\(509\) 28.0892i 1.24503i −0.782607 0.622516i \(-0.786111\pi\)
0.782607 0.622516i \(-0.213889\pi\)
\(510\) 0 0
\(511\) 12.2487i 0.541851i
\(512\) 0 0
\(513\) −2.87721 −0.127032
\(514\) 0 0
\(515\) 0.171203 0.00754412
\(516\) 0 0
\(517\) 46.6008 2.04950
\(518\) 0 0
\(519\) 2.38924i 0.104876i
\(520\) 0 0
\(521\) 33.3339i 1.46038i −0.683243 0.730191i \(-0.739431\pi\)
0.683243 0.730191i \(-0.260569\pi\)
\(522\) 0 0
\(523\) −12.0223 −0.525698 −0.262849 0.964837i \(-0.584662\pi\)
−0.262849 + 0.964837i \(0.584662\pi\)
\(524\) 0 0
\(525\) −0.628454 −0.0274280
\(526\) 0 0
\(527\) 1.34202i 0.0584593i
\(528\) 0 0
\(529\) 28.4978 1.23903
\(530\) 0 0
\(531\) 34.9427 1.51638
\(532\) 0 0
\(533\) 35.3212 3.94093i 1.52993 0.170701i
\(534\) 0 0
\(535\) 12.5556 0.542828
\(536\) 0 0
\(537\) 3.78439 0.163308
\(538\) 0 0
\(539\) 6.18973i 0.266611i
\(540\) 0 0
\(541\) −13.9705 −0.600640 −0.300320 0.953838i \(-0.597094\pi\)
−0.300320 + 0.953838i \(0.597094\pi\)
\(542\) 0 0
\(543\) 1.02437 0.0439598
\(544\) 0 0
\(545\) 16.1622i 0.692315i
\(546\) 0 0
\(547\) 41.6867i 1.78239i 0.453618 + 0.891196i \(0.350133\pi\)
−0.453618 + 0.891196i \(0.649867\pi\)
\(548\) 0 0
\(549\) 33.2392 1.41861
\(550\) 0 0
\(551\) −7.61608 −0.324456
\(552\) 0 0
\(553\) −11.8357 −0.503306
\(554\) 0 0
\(555\) 1.40765i 0.0597516i
\(556\) 0 0
\(557\) 33.5882i 1.42318i 0.702595 + 0.711590i \(0.252024\pi\)
−0.702595 + 0.711590i \(0.747976\pi\)
\(558\) 0 0
\(559\) 55.6188i 2.35243i
\(560\) 0 0
\(561\) 3.92025i 0.165513i
\(562\) 0 0
\(563\) 23.8748i 1.00620i 0.864227 + 0.503101i \(0.167808\pi\)
−0.864227 + 0.503101i \(0.832192\pi\)
\(564\) 0 0
\(565\) 7.82589 0.329238
\(566\) 0 0
\(567\) 8.76424i 0.368064i
\(568\) 0 0
\(569\) 6.26387 0.262595 0.131297 0.991343i \(-0.458086\pi\)
0.131297 + 0.991343i \(0.458086\pi\)
\(570\) 0 0
\(571\) 6.98816i 0.292445i −0.989252 0.146223i \(-0.953288\pi\)
0.989252 0.146223i \(-0.0467116\pi\)
\(572\) 0 0
\(573\) 0.760584 0.0317738
\(574\) 0 0
\(575\) −27.8241 −1.16035
\(576\) 0 0
\(577\) 0.784626i 0.0326644i 0.999867 + 0.0163322i \(0.00519893\pi\)
−0.999867 + 0.0163322i \(0.994801\pi\)
\(578\) 0 0
\(579\) 1.07910 0.0448458
\(580\) 0 0
\(581\) 14.0549i 0.583095i
\(582\) 0 0
\(583\) −9.46576 −0.392032
\(584\) 0 0
\(585\) 17.4891i 0.723085i
\(586\) 0 0
\(587\) 18.5371i 0.765109i 0.923933 + 0.382554i \(0.124956\pi\)
−0.923933 + 0.382554i \(0.875044\pi\)
\(588\) 0 0
\(589\) 1.02057i 0.0420519i
\(590\) 0 0
\(591\) 0.306221i 0.0125963i
\(592\) 0 0
\(593\) 0.684309i 0.0281012i −0.999901 0.0140506i \(-0.995527\pi\)
0.999901 0.0140506i \(-0.00447259\pi\)
\(594\) 0 0
\(595\) 4.14029 0.169735
\(596\) 0 0
\(597\) −3.87509 −0.158597
\(598\) 0 0
\(599\) 32.0764 1.31061 0.655304 0.755366i \(-0.272541\pi\)
0.655304 + 0.755366i \(0.272541\pi\)
\(600\) 0 0
\(601\) 34.7609i 1.41793i −0.705246 0.708963i \(-0.749163\pi\)
0.705246 0.708963i \(-0.250837\pi\)
\(602\) 0 0
\(603\) 12.2789i 0.500034i
\(604\) 0 0
\(605\) 28.9402 1.17659
\(606\) 0 0
\(607\) 32.8192 1.33209 0.666046 0.745911i \(-0.267986\pi\)
0.666046 + 0.745911i \(0.267986\pi\)
\(608\) 0 0
\(609\) 0.415430i 0.0168341i
\(610\) 0 0
\(611\) −41.7881 −1.69056
\(612\) 0 0
\(613\) 33.4712 1.35189 0.675944 0.736953i \(-0.263736\pi\)
0.675944 + 0.736953i \(0.263736\pi\)
\(614\) 0 0
\(615\) 1.09292 0.121941i 0.0440706 0.00491713i
\(616\) 0 0
\(617\) −40.8434 −1.64429 −0.822146 0.569277i \(-0.807223\pi\)
−0.822146 + 0.569277i \(0.807223\pi\)
\(618\) 0 0
\(619\) 23.4192 0.941297 0.470649 0.882321i \(-0.344020\pi\)
0.470649 + 0.882321i \(0.344020\pi\)
\(620\) 0 0
\(621\) 6.94842i 0.278830i
\(622\) 0 0
\(623\) 1.32263 0.0529901
\(624\) 0 0
\(625\) 9.41973 0.376789
\(626\) 0 0
\(627\) 2.98125i 0.119060i
\(628\) 0 0
\(629\) 32.0266i 1.27698i
\(630\) 0 0
\(631\) −12.0864 −0.481154 −0.240577 0.970630i \(-0.577337\pi\)
−0.240577 + 0.970630i \(0.577337\pi\)
\(632\) 0 0
\(633\) −2.88693 −0.114745
\(634\) 0 0
\(635\) 3.19318 0.126718
\(636\) 0 0
\(637\) 5.55048i 0.219918i
\(638\) 0 0
\(639\) 22.8035i 0.902092i
\(640\) 0 0
\(641\) 2.65389i 0.104822i −0.998626 0.0524112i \(-0.983309\pi\)
0.998626 0.0524112i \(-0.0166907\pi\)
\(642\) 0 0
\(643\) 48.6653i 1.91917i 0.281414 + 0.959586i \(0.409196\pi\)
−0.281414 + 0.959586i \(0.590804\pi\)
\(644\) 0 0
\(645\) 1.72097i 0.0677630i
\(646\) 0 0
\(647\) 24.9782 0.981992 0.490996 0.871162i \(-0.336633\pi\)
0.490996 + 0.871162i \(0.336633\pi\)
\(648\) 0 0
\(649\) 72.7323i 2.85499i
\(650\) 0 0
\(651\) 0.0556685 0.00218182
\(652\) 0 0
\(653\) 45.6996i 1.78836i −0.447704 0.894182i \(-0.647758\pi\)
0.447704 0.894182i \(-0.352242\pi\)
\(654\) 0 0
\(655\) −4.26728 −0.166737
\(656\) 0 0
\(657\) −36.4244 −1.42105
\(658\) 0 0
\(659\) 36.5674i 1.42446i 0.701944 + 0.712232i \(0.252316\pi\)
−0.701944 + 0.712232i \(0.747684\pi\)
\(660\) 0 0
\(661\) 15.4438 0.600695 0.300348 0.953830i \(-0.402897\pi\)
0.300348 + 0.953830i \(0.402897\pi\)
\(662\) 0 0
\(663\) 3.51538i 0.136526i
\(664\) 0 0
\(665\) −3.14858 −0.122097
\(666\) 0 0
\(667\) 18.3927i 0.712169i
\(668\) 0 0
\(669\) 1.14735i 0.0443591i
\(670\) 0 0
\(671\) 69.1865i 2.67092i
\(672\) 0 0
\(673\) 4.03761i 0.155639i 0.996967 + 0.0778193i \(0.0247957\pi\)
−0.996967 + 0.0778193i \(0.975204\pi\)
\(674\) 0 0
\(675\) 3.75422i 0.144500i
\(676\) 0 0
\(677\) 17.9382 0.689420 0.344710 0.938709i \(-0.387977\pi\)
0.344710 + 0.938709i \(0.387977\pi\)
\(678\) 0 0
\(679\) −1.93000 −0.0740666
\(680\) 0 0
\(681\) −2.61293 −0.100128
\(682\) 0 0
\(683\) 1.97784i 0.0756798i 0.999284 + 0.0378399i \(0.0120477\pi\)
−0.999284 + 0.0378399i \(0.987952\pi\)
\(684\) 0 0
\(685\) 4.00170i 0.152897i
\(686\) 0 0
\(687\) 1.54167 0.0588183
\(688\) 0 0
\(689\) 8.48817 0.323374
\(690\) 0 0
\(691\) 48.5157i 1.84563i −0.385248 0.922813i \(-0.625884\pi\)
0.385248 0.922813i \(-0.374116\pi\)
\(692\) 0 0
\(693\) 18.4066 0.699208
\(694\) 0 0
\(695\) 12.2892 0.466156
\(696\) 0 0
\(697\) 24.8657 2.77436i 0.941856 0.105087i
\(698\) 0 0
\(699\) −1.85302 −0.0700876
\(700\) 0 0
\(701\) −5.74537 −0.217000 −0.108500 0.994096i \(-0.534605\pi\)
−0.108500 + 0.994096i \(0.534605\pi\)
\(702\) 0 0
\(703\) 24.3554i 0.918580i
\(704\) 0 0
\(705\) −1.29301 −0.0486977
\(706\) 0 0
\(707\) 7.16465 0.269454
\(708\) 0 0
\(709\) 10.8010i 0.405639i 0.979216 + 0.202820i \(0.0650105\pi\)
−0.979216 + 0.202820i \(0.934990\pi\)
\(710\) 0 0
\(711\) 35.1962i 1.31996i
\(712\) 0 0
\(713\) 2.46466 0.0923023
\(714\) 0 0
\(715\) −36.4030 −1.36140
\(716\) 0 0
\(717\) 0.745778 0.0278516
\(718\) 0 0
\(719\) 18.8952i 0.704674i −0.935873 0.352337i \(-0.885387\pi\)
0.935873 0.352337i \(-0.114613\pi\)
\(720\) 0 0
\(721\) 0.161576i 0.00601741i
\(722\) 0 0
\(723\) 2.15195i 0.0800318i
\(724\) 0 0
\(725\) 9.93754i 0.369071i
\(726\) 0 0
\(727\) 28.0884i 1.04174i 0.853636 + 0.520870i \(0.174392\pi\)
−0.853636 + 0.520870i \(0.825608\pi\)
\(728\) 0 0
\(729\) 25.5916 0.947839
\(730\) 0 0
\(731\) 39.1550i 1.44820i
\(732\) 0 0
\(733\) −38.5190 −1.42273 −0.711365 0.702823i \(-0.751923\pi\)
−0.711365 + 0.702823i \(0.751923\pi\)
\(734\) 0 0
\(735\) 0.171744i 0.00633487i
\(736\) 0 0
\(737\) 25.5581 0.941445
\(738\) 0 0
\(739\) −18.3384 −0.674590 −0.337295 0.941399i \(-0.609512\pi\)
−0.337295 + 0.941399i \(0.609512\pi\)
\(740\) 0 0
\(741\) 2.67336i 0.0982082i
\(742\) 0 0
\(743\) 39.4951 1.44894 0.724468 0.689308i \(-0.242085\pi\)
0.724468 + 0.689308i \(0.242085\pi\)
\(744\) 0 0
\(745\) 19.3502i 0.708935i
\(746\) 0 0
\(747\) 41.7954 1.52921
\(748\) 0 0
\(749\) 11.8496i 0.432975i
\(750\) 0 0
\(751\) 7.77300i 0.283641i −0.989892 0.141820i \(-0.954704\pi\)
0.989892 0.141820i \(-0.0452956\pi\)
\(752\) 0 0
\(753\) 1.35863i 0.0495111i
\(754\) 0 0
\(755\) 8.23482i 0.299696i
\(756\) 0 0
\(757\) 21.1823i 0.769883i −0.922941 0.384941i \(-0.874222\pi\)
0.922941 0.384941i \(-0.125778\pi\)
\(758\) 0 0
\(759\) −7.19967 −0.261331
\(760\) 0 0
\(761\) −31.5478 −1.14361 −0.571804 0.820390i \(-0.693756\pi\)
−0.571804 + 0.820390i \(0.693756\pi\)
\(762\) 0 0
\(763\) 15.2534 0.552210
\(764\) 0 0
\(765\) 12.3121i 0.445145i
\(766\) 0 0
\(767\) 65.2208i 2.35499i
\(768\) 0 0
\(769\) −24.4006 −0.879907 −0.439953 0.898021i \(-0.645005\pi\)
−0.439953 + 0.898021i \(0.645005\pi\)
\(770\) 0 0
\(771\) 1.39552 0.0502585
\(772\) 0 0
\(773\) 24.3531i 0.875922i −0.898994 0.437961i \(-0.855701\pi\)
0.898994 0.437961i \(-0.144299\pi\)
\(774\) 0 0
\(775\) −1.33165 −0.0478343
\(776\) 0 0
\(777\) 1.32850 0.0476596
\(778\) 0 0
\(779\) −18.9097 + 2.10983i −0.677512 + 0.0755926i
\(780\) 0 0
\(781\) −47.4648 −1.69843
\(782\) 0 0
\(783\) −2.48167 −0.0886875
\(784\) 0 0
\(785\) 10.0742i 0.359565i
\(786\) 0 0
\(787\) −31.7856 −1.13303 −0.566517 0.824050i \(-0.691710\pi\)
−0.566517 + 0.824050i \(0.691710\pi\)
\(788\) 0 0
\(789\) 0.0867277 0.00308759
\(790\) 0 0
\(791\) 7.38582i 0.262609i
\(792\) 0 0
\(793\) 62.0412i 2.20315i
\(794\) 0 0
\(795\) 0.262643 0.00931497
\(796\) 0 0
\(797\) −8.18095 −0.289784 −0.144892 0.989447i \(-0.546284\pi\)
−0.144892 + 0.989447i \(0.546284\pi\)
\(798\) 0 0
\(799\) −29.4183 −1.04074
\(800\) 0 0
\(801\) 3.93314i 0.138971i
\(802\) 0 0
\(803\) 75.8163i 2.67550i
\(804\) 0 0
\(805\) 7.60378i 0.267998i