Properties

Label 1440.2.bj.a.17.1
Level $1440$
Weight $2$
Character 1440.17
Analytic conductor $11.498$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.bj (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.4984578911\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 360)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 17.1
Character \(\chi\) \(=\) 1440.17
Dual form 1440.2.bj.a.593.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.23604 - 0.0113158i) q^{5} +(-0.471963 - 0.471963i) q^{7} +O(q^{10})\) \(q+(-2.23604 - 0.0113158i) q^{5} +(-0.471963 - 0.471963i) q^{7} -0.335652 q^{11} +(3.50404 + 3.50404i) q^{13} +(2.53299 - 2.53299i) q^{17} -4.07474 q^{19} +(-6.20627 - 6.20627i) q^{23} +(4.99974 + 0.0506050i) q^{25} +2.42367i q^{29} +6.41004 q^{31} +(1.04999 + 1.06067i) q^{35} +(2.24893 - 2.24893i) q^{37} -5.80736i q^{41} +(-4.87603 - 4.87603i) q^{43} +(1.68276 - 1.68276i) q^{47} -6.55450i q^{49} +(-3.05444 + 3.05444i) q^{53} +(0.750530 + 0.00379815i) q^{55} -12.2950i q^{59} -7.49787i q^{61} +(-7.79553 - 7.87483i) q^{65} +(5.55519 - 5.55519i) q^{67} -13.4793i q^{71} +(5.05035 - 5.05035i) q^{73} +(0.158415 + 0.158415i) q^{77} +8.85503i q^{79} +(-4.78510 + 4.78510i) q^{83} +(-5.69252 + 5.63520i) q^{85} -8.33405 q^{89} -3.30755i q^{91} +(9.11128 + 0.0461088i) q^{95} +(10.1367 + 10.1367i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + O(q^{10}) \) \( 48 q - 32 q^{31} - 32 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(991\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(-1\) \(1\)

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 0
\(4\) 0 0
\(5\) −2.23604 0.0113158i −0.999987 0.00506057i
\(6\) 0 0
\(7\) −0.471963 0.471963i −0.178385 0.178385i 0.612266 0.790652i \(-0.290258\pi\)
−0.790652 + 0.612266i \(0.790258\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.335652 −0.101203 −0.0506014 0.998719i \(-0.516114\pi\)
−0.0506014 + 0.998719i \(0.516114\pi\)
\(12\) 0 0
\(13\) 3.50404 + 3.50404i 0.971846 + 0.971846i 0.999614 0.0277680i \(-0.00883995\pi\)
−0.0277680 + 0.999614i \(0.508840\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.53299 2.53299i 0.614340 0.614340i −0.329734 0.944074i \(-0.606959\pi\)
0.944074 + 0.329734i \(0.106959\pi\)
\(18\) 0 0
\(19\) −4.07474 −0.934809 −0.467405 0.884044i \(-0.654811\pi\)
−0.467405 + 0.884044i \(0.654811\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.20627 6.20627i −1.29410 1.29410i −0.932229 0.361868i \(-0.882139\pi\)
−0.361868 0.932229i \(-0.617861\pi\)
\(24\) 0 0
\(25\) 4.99974 + 0.0506050i 0.999949 + 0.0101210i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.42367i 0.450065i 0.974351 + 0.225032i \(0.0722488\pi\)
−0.974351 + 0.225032i \(0.927751\pi\)
\(30\) 0 0
\(31\) 6.41004 1.15128 0.575639 0.817704i \(-0.304753\pi\)
0.575639 + 0.817704i \(0.304753\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.04999 + 1.06067i 0.177480 + 0.179286i
\(36\) 0 0
\(37\) 2.24893 2.24893i 0.369721 0.369721i −0.497654 0.867375i \(-0.665805\pi\)
0.867375 + 0.497654i \(0.165805\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.80736i 0.906957i −0.891267 0.453479i \(-0.850183\pi\)
0.891267 0.453479i \(-0.149817\pi\)
\(42\) 0 0
\(43\) −4.87603 4.87603i −0.743588 0.743588i 0.229678 0.973267i \(-0.426233\pi\)
−0.973267 + 0.229678i \(0.926233\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.68276 1.68276i 0.245455 0.245455i −0.573647 0.819102i \(-0.694472\pi\)
0.819102 + 0.573647i \(0.194472\pi\)
\(48\) 0 0
\(49\) 6.55450i 0.936358i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3.05444 + 3.05444i −0.419560 + 0.419560i −0.885052 0.465492i \(-0.845877\pi\)
0.465492 + 0.885052i \(0.345877\pi\)
\(54\) 0 0
\(55\) 0.750530 + 0.00379815i 0.101201 + 0.000512143i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.2950i 1.60067i −0.599553 0.800335i \(-0.704655\pi\)
0.599553 0.800335i \(-0.295345\pi\)
\(60\) 0 0
\(61\) 7.49787i 0.960004i −0.877267 0.480002i \(-0.840636\pi\)
0.877267 0.480002i \(-0.159364\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −7.79553 7.87483i −0.966916 0.976752i
\(66\) 0 0
\(67\) 5.55519 5.55519i 0.678674 0.678674i −0.281026 0.959700i \(-0.590675\pi\)
0.959700 + 0.281026i \(0.0906748\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 13.4793i 1.59970i −0.600199 0.799851i \(-0.704912\pi\)
0.600199 0.799851i \(-0.295088\pi\)
\(72\) 0 0
\(73\) 5.05035 5.05035i 0.591099 0.591099i −0.346830 0.937928i \(-0.612742\pi\)
0.937928 + 0.346830i \(0.112742\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.158415 + 0.158415i 0.0180531 + 0.0180531i
\(78\) 0 0
\(79\) 8.85503i 0.996268i 0.867100 + 0.498134i \(0.165981\pi\)
−0.867100 + 0.498134i \(0.834019\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.78510 + 4.78510i −0.525233 + 0.525233i −0.919147 0.393914i \(-0.871121\pi\)
0.393914 + 0.919147i \(0.371121\pi\)
\(84\) 0 0
\(85\) −5.69252 + 5.63520i −0.617441 + 0.611223i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −8.33405 −0.883408 −0.441704 0.897161i \(-0.645626\pi\)
−0.441704 + 0.897161i \(0.645626\pi\)
\(90\) 0 0
\(91\) 3.30755i 0.346726i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 9.11128 + 0.0461088i 0.934797 + 0.00473066i
\(96\) 0 0
\(97\) 10.1367 + 10.1367i 1.02922 + 1.02922i 0.999560 + 0.0296647i \(0.00944397\pi\)
0.0296647 + 0.999560i \(0.490556\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.88830 0.983922 0.491961 0.870617i \(-0.336280\pi\)
0.491961 + 0.870617i \(0.336280\pi\)
\(102\) 0 0
\(103\) 10.0033 10.0033i 0.985653 0.985653i −0.0142455 0.999899i \(-0.504535\pi\)
0.999899 + 0.0142455i \(0.00453463\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 10.2013 + 10.2013i 0.986198 + 0.986198i 0.999906 0.0137076i \(-0.00436339\pi\)
−0.0137076 + 0.999906i \(0.504363\pi\)
\(108\) 0 0
\(109\) −11.0144 −1.05498 −0.527492 0.849560i \(-0.676867\pi\)
−0.527492 + 0.849560i \(0.676867\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.45369 + 2.45369i 0.230823 + 0.230823i 0.813036 0.582213i \(-0.197813\pi\)
−0.582213 + 0.813036i \(0.697813\pi\)
\(114\) 0 0
\(115\) 13.8072 + 13.9477i 1.28753 + 1.30063i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.39095 −0.219178
\(120\) 0 0
\(121\) −10.8873 −0.989758
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −11.1791 0.169731i −0.999885 0.0151812i
\(126\) 0 0
\(127\) −6.00329 6.00329i −0.532705 0.532705i 0.388671 0.921377i \(-0.372934\pi\)
−0.921377 + 0.388671i \(0.872934\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −11.3345 −0.990301 −0.495151 0.868807i \(-0.664887\pi\)
−0.495151 + 0.868807i \(0.664887\pi\)
\(132\) 0 0
\(133\) 1.92312 + 1.92312i 0.166756 + 0.166756i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10.8670 10.8670i 0.928434 0.928434i −0.0691711 0.997605i \(-0.522035\pi\)
0.997605 + 0.0691711i \(0.0220354\pi\)
\(138\) 0 0
\(139\) −13.3432 −1.13176 −0.565878 0.824489i \(-0.691463\pi\)
−0.565878 + 0.824489i \(0.691463\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.17614 1.17614i −0.0983535 0.0983535i
\(144\) 0 0
\(145\) 0.0274257 5.41943i 0.00227758 0.450059i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 13.5961i 1.11384i −0.830566 0.556919i \(-0.811983\pi\)
0.830566 0.556919i \(-0.188017\pi\)
\(150\) 0 0
\(151\) 9.64289 0.784727 0.392364 0.919810i \(-0.371657\pi\)
0.392364 + 0.919810i \(0.371657\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −14.3331 0.0725345i −1.15126 0.00582611i
\(156\) 0 0
\(157\) 7.62403 7.62403i 0.608464 0.608464i −0.334080 0.942545i \(-0.608426\pi\)
0.942545 + 0.334080i \(0.108426\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.85826i 0.461695i
\(162\) 0 0
\(163\) 16.2490 + 16.2490i 1.27272 + 1.27272i 0.944655 + 0.328065i \(0.106397\pi\)
0.328065 + 0.944655i \(0.393603\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −13.7067 + 13.7067i −1.06066 + 1.06066i −0.0626204 + 0.998037i \(0.519946\pi\)
−0.998037 + 0.0626204i \(0.980054\pi\)
\(168\) 0 0
\(169\) 11.5566i 0.888971i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3.35678 3.35678i 0.255211 0.255211i −0.567892 0.823103i \(-0.692241\pi\)
0.823103 + 0.567892i \(0.192241\pi\)
\(174\) 0 0
\(175\) −2.33581 2.38358i −0.176571 0.180181i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 10.7537i 0.803772i 0.915690 + 0.401886i \(0.131645\pi\)
−0.915690 + 0.401886i \(0.868355\pi\)
\(180\) 0 0
\(181\) 10.1290i 0.752883i −0.926440 0.376441i \(-0.877148\pi\)
0.926440 0.376441i \(-0.122852\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5.05414 + 5.00324i −0.371587 + 0.367845i
\(186\) 0 0
\(187\) −0.850201 + 0.850201i −0.0621728 + 0.0621728i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4.32194i 0.312725i 0.987700 + 0.156362i \(0.0499768\pi\)
−0.987700 + 0.156362i \(0.950023\pi\)
\(192\) 0 0
\(193\) −7.97419 + 7.97419i −0.573995 + 0.573995i −0.933242 0.359248i \(-0.883033\pi\)
0.359248 + 0.933242i \(0.383033\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4.30206 4.30206i −0.306509 0.306509i 0.537045 0.843554i \(-0.319541\pi\)
−0.843554 + 0.537045i \(0.819541\pi\)
\(198\) 0 0
\(199\) 3.02113i 0.214162i −0.994250 0.107081i \(-0.965850\pi\)
0.994250 0.107081i \(-0.0341505\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.14388 1.14388i 0.0802849 0.0802849i
\(204\) 0 0
\(205\) −0.0657147 + 12.9855i −0.00458972 + 0.906946i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.36769 0.0946052
\(210\) 0 0
\(211\) 8.87754i 0.611155i −0.952167 0.305577i \(-0.901151\pi\)
0.952167 0.305577i \(-0.0988495\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 10.8478 + 10.9582i 0.739816 + 0.747342i
\(216\) 0 0
\(217\) −3.02530 3.02530i −0.205371 0.205371i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 17.7514 1.19409
\(222\) 0 0
\(223\) −9.93808 + 9.93808i −0.665503 + 0.665503i −0.956672 0.291169i \(-0.905956\pi\)
0.291169 + 0.956672i \(0.405956\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 7.21442 + 7.21442i 0.478838 + 0.478838i 0.904760 0.425922i \(-0.140050\pi\)
−0.425922 + 0.904760i \(0.640050\pi\)
\(228\) 0 0
\(229\) −21.8687 −1.44512 −0.722562 0.691306i \(-0.757035\pi\)
−0.722562 + 0.691306i \(0.757035\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.78300 + 6.78300i 0.444369 + 0.444369i 0.893477 0.449108i \(-0.148258\pi\)
−0.449108 + 0.893477i \(0.648258\pi\)
\(234\) 0 0
\(235\) −3.78175 + 3.74367i −0.246694 + 0.244210i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 4.63287 0.299676 0.149838 0.988711i \(-0.452125\pi\)
0.149838 + 0.988711i \(0.452125\pi\)
\(240\) 0 0
\(241\) −9.72150 −0.626217 −0.313109 0.949717i \(-0.601370\pi\)
−0.313109 + 0.949717i \(0.601370\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.0741692 + 14.6561i −0.00473850 + 0.936346i
\(246\) 0 0
\(247\) −14.2781 14.2781i −0.908491 0.908491i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 30.6190 1.93265 0.966327 0.257316i \(-0.0828382\pi\)
0.966327 + 0.257316i \(0.0828382\pi\)
\(252\) 0 0
\(253\) 2.08314 + 2.08314i 0.130966 + 0.130966i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.63773 1.63773i 0.102158 0.102158i −0.654180 0.756339i \(-0.726986\pi\)
0.756339 + 0.654180i \(0.226986\pi\)
\(258\) 0 0
\(259\) −2.12282 −0.131905
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 7.77099 + 7.77099i 0.479180 + 0.479180i 0.904869 0.425689i \(-0.139968\pi\)
−0.425689 + 0.904869i \(0.639968\pi\)
\(264\) 0 0
\(265\) 6.86441 6.79529i 0.421678 0.417431i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 16.1341i 0.983714i −0.870676 0.491857i \(-0.836318\pi\)
0.870676 0.491857i \(-0.163682\pi\)
\(270\) 0 0
\(271\) −16.8474 −1.02341 −0.511704 0.859162i \(-0.670986\pi\)
−0.511704 + 0.859162i \(0.670986\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.67817 0.0169856i −0.101198 0.00102427i
\(276\) 0 0
\(277\) 16.3206 16.3206i 0.980611 0.980611i −0.0192042 0.999816i \(-0.506113\pi\)
0.999816 + 0.0192042i \(0.00611328\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 31.2898i 1.86659i 0.359106 + 0.933297i \(0.383082\pi\)
−0.359106 + 0.933297i \(0.616918\pi\)
\(282\) 0 0
\(283\) −9.97554 9.97554i −0.592984 0.592984i 0.345452 0.938436i \(-0.387726\pi\)
−0.938436 + 0.345452i \(0.887726\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.74086 + 2.74086i −0.161788 + 0.161788i
\(288\) 0 0
\(289\) 4.16795i 0.245174i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −5.26253 + 5.26253i −0.307440 + 0.307440i −0.843916 0.536476i \(-0.819755\pi\)
0.536476 + 0.843916i \(0.319755\pi\)
\(294\) 0 0
\(295\) −0.139127 + 27.4921i −0.00810030 + 1.60065i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 43.4941i 2.51533i
\(300\) 0 0
\(301\) 4.60261i 0.265290i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.0848442 + 16.7655i −0.00485816 + 0.959992i
\(306\) 0 0
\(307\) 9.54586 9.54586i 0.544811 0.544811i −0.380124 0.924935i \(-0.624119\pi\)
0.924935 + 0.380124i \(0.124119\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4.08587i 0.231688i 0.993267 + 0.115844i \(0.0369573\pi\)
−0.993267 + 0.115844i \(0.963043\pi\)
\(312\) 0 0
\(313\) −14.4004 + 14.4004i −0.813958 + 0.813958i −0.985225 0.171266i \(-0.945214\pi\)
0.171266 + 0.985225i \(0.445214\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 12.0841 + 12.0841i 0.678710 + 0.678710i 0.959708 0.280998i \(-0.0906656\pi\)
−0.280998 + 0.959708i \(0.590666\pi\)
\(318\) 0 0
\(319\) 0.813510i 0.0455478i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −10.3213 + 10.3213i −0.574290 + 0.574290i
\(324\) 0 0
\(325\) 17.3420 + 17.6966i 0.961961 + 0.981633i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.58840 −0.0875711
\(330\) 0 0
\(331\) 33.6119i 1.84747i −0.383027 0.923737i \(-0.625118\pi\)
0.383027 0.923737i \(-0.374882\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −12.4845 + 12.3588i −0.682100 + 0.675231i
\(336\) 0 0
\(337\) −20.2142 20.2142i −1.10114 1.10114i −0.994274 0.106864i \(-0.965919\pi\)
−0.106864 0.994274i \(-0.534081\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.15154 −0.116512
\(342\) 0 0
\(343\) −6.39722 + 6.39722i −0.345417 + 0.345417i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.443163 0.443163i −0.0237903 0.0237903i 0.695112 0.718902i \(-0.255355\pi\)
−0.718902 + 0.695112i \(0.755355\pi\)
\(348\) 0 0
\(349\) −10.8766 −0.582212 −0.291106 0.956691i \(-0.594023\pi\)
−0.291106 + 0.956691i \(0.594023\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.0437 + 10.0437i 0.534572 + 0.534572i 0.921930 0.387357i \(-0.126612\pi\)
−0.387357 + 0.921930i \(0.626612\pi\)
\(354\) 0 0
\(355\) −0.152529 + 30.1403i −0.00809540 + 1.59968i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 19.6724 1.03827 0.519136 0.854692i \(-0.326254\pi\)
0.519136 + 0.854692i \(0.326254\pi\)
\(360\) 0 0
\(361\) −2.39651 −0.126132
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −11.3499 + 11.2356i −0.594082 + 0.588100i
\(366\) 0 0
\(367\) 9.86005 + 9.86005i 0.514690 + 0.514690i 0.915960 0.401270i \(-0.131431\pi\)
−0.401270 + 0.915960i \(0.631431\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2.88316 0.149686
\(372\) 0 0
\(373\) 12.6526 + 12.6526i 0.655127 + 0.655127i 0.954223 0.299096i \(-0.0966852\pi\)
−0.299096 + 0.954223i \(0.596685\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8.49265 + 8.49265i −0.437394 + 0.437394i
\(378\) 0 0
\(379\) −37.9577 −1.94975 −0.974877 0.222743i \(-0.928499\pi\)
−0.974877 + 0.222743i \(0.928499\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9.18320 + 9.18320i 0.469240 + 0.469240i 0.901668 0.432428i \(-0.142343\pi\)
−0.432428 + 0.901668i \(0.642343\pi\)
\(384\) 0 0
\(385\) −0.352429 0.356015i −0.0179615 0.0181442i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 4.22258i 0.214093i 0.994254 + 0.107047i \(0.0341394\pi\)
−0.994254 + 0.107047i \(0.965861\pi\)
\(390\) 0 0
\(391\) −31.4408 −1.59003
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.100201 19.8002i 0.00504168 0.996256i
\(396\) 0 0
\(397\) −1.27679 + 1.27679i −0.0640801 + 0.0640801i −0.738421 0.674340i \(-0.764428\pi\)
0.674340 + 0.738421i \(0.264428\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0.899990i 0.0449434i 0.999747 + 0.0224717i \(0.00715356\pi\)
−0.999747 + 0.0224717i \(0.992846\pi\)
\(402\) 0 0
\(403\) 22.4611 + 22.4611i 1.11886 + 1.11886i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.754855 + 0.754855i −0.0374168 + 0.0374168i
\(408\) 0 0
\(409\) 24.1722i 1.19524i −0.801781 0.597618i \(-0.796114\pi\)
0.801781 0.597618i \(-0.203886\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −5.80277 + 5.80277i −0.285536 + 0.285536i
\(414\) 0 0
\(415\) 10.7538 10.6455i 0.527884 0.522568i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 8.45513i 0.413060i 0.978440 + 0.206530i \(0.0662171\pi\)
−0.978440 + 0.206530i \(0.933783\pi\)
\(420\) 0 0
\(421\) 13.8561i 0.675307i 0.941270 + 0.337654i \(0.109633\pi\)
−0.941270 + 0.337654i \(0.890367\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 12.7925 12.5361i 0.620526 0.608090i
\(426\) 0 0
\(427\) −3.53872 + 3.53872i −0.171250 + 0.171250i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5.84351i 0.281472i 0.990047 + 0.140736i \(0.0449469\pi\)
−0.990047 + 0.140736i \(0.955053\pi\)
\(432\) 0 0
\(433\) 10.0632 10.0632i 0.483605 0.483605i −0.422676 0.906281i \(-0.638909\pi\)
0.906281 + 0.422676i \(0.138909\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 25.2889 + 25.2889i 1.20973 + 1.20973i
\(438\) 0 0
\(439\) 34.0222i 1.62379i 0.583802 + 0.811896i \(0.301564\pi\)
−0.583802 + 0.811896i \(0.698436\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.45259 6.45259i 0.306572 0.306572i −0.537006 0.843578i \(-0.680445\pi\)
0.843578 + 0.537006i \(0.180445\pi\)
\(444\) 0 0
\(445\) 18.6353 + 0.0943062i 0.883396 + 0.00447054i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −5.72541 −0.270199 −0.135099 0.990832i \(-0.543135\pi\)
−0.135099 + 0.990832i \(0.543135\pi\)
\(450\) 0 0
\(451\) 1.94925i 0.0917866i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −0.0374275 + 7.39582i −0.00175463 + 0.346721i
\(456\) 0 0
\(457\) 14.9718 + 14.9718i 0.700352 + 0.700352i 0.964486 0.264134i \(-0.0850862\pi\)
−0.264134 + 0.964486i \(0.585086\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −25.8187 −1.20250 −0.601249 0.799062i \(-0.705330\pi\)
−0.601249 + 0.799062i \(0.705330\pi\)
\(462\) 0 0
\(463\) 20.5140 20.5140i 0.953368 0.953368i −0.0455925 0.998960i \(-0.514518\pi\)
0.998960 + 0.0455925i \(0.0145176\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.07112 + 3.07112i 0.142114 + 0.142114i 0.774585 0.632470i \(-0.217959\pi\)
−0.632470 + 0.774585i \(0.717959\pi\)
\(468\) 0 0
\(469\) −5.24368 −0.242131
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.63665 + 1.63665i 0.0752532 + 0.0752532i
\(474\) 0 0
\(475\) −20.3726 0.206202i −0.934761 0.00946120i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −33.2621 −1.51979 −0.759893 0.650049i \(-0.774748\pi\)
−0.759893 + 0.650049i \(0.774748\pi\)
\(480\) 0 0
\(481\) 15.7607 0.718624
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −22.5513 22.7807i −1.02400 1.03442i
\(486\) 0 0
\(487\) −1.39322 1.39322i −0.0631329 0.0631329i 0.674835 0.737968i \(-0.264215\pi\)
−0.737968 + 0.674835i \(0.764215\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 14.4709 0.653061 0.326530 0.945187i \(-0.394120\pi\)
0.326530 + 0.945187i \(0.394120\pi\)
\(492\) 0 0
\(493\) 6.13913 + 6.13913i 0.276493 + 0.276493i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −6.36174 + 6.36174i −0.285363 + 0.285363i
\(498\) 0 0
\(499\) 20.4107 0.913710 0.456855 0.889541i \(-0.348976\pi\)
0.456855 + 0.889541i \(0.348976\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2.54697 2.54697i −0.113564 0.113564i 0.648041 0.761605i \(-0.275588\pi\)
−0.761605 + 0.648041i \(0.775588\pi\)
\(504\) 0 0
\(505\) −22.1106 0.111894i −0.983910 0.00497920i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 13.5045i 0.598575i −0.954163 0.299288i \(-0.903251\pi\)
0.954163 0.299288i \(-0.0967490\pi\)
\(510\) 0 0
\(511\) −4.76715 −0.210886
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −22.4809 + 22.2545i −0.990628 + 0.980652i
\(516\) 0 0
\(517\) −0.564820 + 0.564820i −0.0248407 + 0.0248407i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 13.5151i 0.592108i −0.955171 0.296054i \(-0.904329\pi\)
0.955171 0.296054i \(-0.0956708\pi\)
\(522\) 0 0
\(523\) −12.6641 12.6641i −0.553760 0.553760i 0.373764 0.927524i \(-0.378067\pi\)
−0.927524 + 0.373764i \(0.878067\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 16.2365 16.2365i 0.707275 0.707275i
\(528\) 0 0
\(529\) 54.0356i 2.34938i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 20.3492 20.3492i 0.881423 0.881423i
\(534\) 0 0
\(535\) −22.6951 22.9260i −0.981195 0.991177i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.20003i 0.0947619i
\(540\) 0 0
\(541\) 17.1804i 0.738644i −0.929301 0.369322i \(-0.879590\pi\)
0.929301 0.369322i \(-0.120410\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 24.6285 + 0.124636i 1.05497 + 0.00533881i
\(546\) 0 0
\(547\) 17.4105 17.4105i 0.744417 0.744417i −0.229007 0.973425i \(-0.573548\pi\)
0.973425 + 0.229007i \(0.0735480\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 9.87584i 0.420725i
\(552\) 0 0
\(553\) 4.17924 4.17924i 0.177719 0.177719i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9.22732 9.22732i −0.390974 0.390974i 0.484060 0.875035i \(-0.339162\pi\)
−0.875035 + 0.484060i \(0.839162\pi\)
\(558\) 0 0
\(559\) 34.1717i 1.44531i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −19.8727 + 19.8727i −0.837535 + 0.837535i −0.988534 0.150999i \(-0.951751\pi\)
0.150999 + 0.988534i \(0.451751\pi\)
\(564\) 0 0
\(565\) −5.45877 5.51430i −0.229652 0.231988i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.73031 0.198305 0.0991524 0.995072i \(-0.468387\pi\)
0.0991524 + 0.995072i \(0.468387\pi\)
\(570\) 0 0
\(571\) 5.54039i 0.231858i −0.993257 0.115929i \(-0.963015\pi\)
0.993257 0.115929i \(-0.0369845\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −30.7157 31.3438i −1.28093 1.30713i
\(576\) 0 0
\(577\) −12.9105 12.9105i −0.537472 0.537472i 0.385314 0.922786i \(-0.374093\pi\)
−0.922786 + 0.385314i \(0.874093\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4.51677 0.187387
\(582\) 0 0
\(583\) 1.02523 1.02523i 0.0424606 0.0424606i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.90309 1.90309i −0.0785487 0.0785487i 0.666741 0.745290i \(-0.267689\pi\)
−0.745290 + 0.666741i \(0.767689\pi\)
\(588\) 0 0
\(589\) −26.1192 −1.07622
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −11.7312 11.7312i −0.481745 0.481745i 0.423944 0.905688i \(-0.360645\pi\)
−0.905688 + 0.423944i \(0.860645\pi\)
\(594\) 0 0
\(595\) 5.34626 + 0.0270554i 0.219175 + 0.00110916i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 2.61594 0.106884 0.0534422 0.998571i \(-0.482981\pi\)
0.0534422 + 0.998571i \(0.482981\pi\)
\(600\) 0 0
\(601\) 20.1722 0.822840 0.411420 0.911446i \(-0.365033\pi\)
0.411420 + 0.911446i \(0.365033\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 24.3445 + 0.123199i 0.989745 + 0.00500873i
\(606\) 0 0
\(607\) 17.3218 + 17.3218i 0.703069 + 0.703069i 0.965068 0.261999i \(-0.0843819\pi\)
−0.261999 + 0.965068i \(0.584382\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 11.7929 0.477090
\(612\) 0 0
\(613\) −16.8299 16.8299i −0.679754 0.679754i 0.280191 0.959944i \(-0.409602\pi\)
−0.959944 + 0.280191i \(0.909602\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2.56139 2.56139i 0.103118 0.103118i −0.653666 0.756783i \(-0.726770\pi\)
0.756783 + 0.653666i \(0.226770\pi\)
\(618\) 0 0
\(619\) −16.9662 −0.681931 −0.340965 0.940076i \(-0.610754\pi\)
−0.340965 + 0.940076i \(0.610754\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 3.93336 + 3.93336i 0.157587 + 0.157587i
\(624\) 0 0
\(625\) 24.9949 + 0.506024i 0.999795 + 0.0202410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 11.3930i 0.454269i
\(630\) 0 0
\(631\) 39.5630 1.57498 0.787488 0.616330i \(-0.211381\pi\)
0.787488 + 0.616330i \(0.211381\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 13.3557 + 13.4915i 0.530003 + 0.535394i
\(636\) 0 0
\(637\) 22.9673 22.9673i 0.909996 0.909996i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 47.3441i 1.86998i −0.354676 0.934989i \(-0.615409\pi\)
0.354676 0.934989i \(-0.384591\pi\)
\(642\) 0 0
\(643\) 14.8250 + 14.8250i 0.584639 + 0.584639i 0.936175 0.351535i \(-0.114340\pi\)
−0.351535 + 0.936175i \(0.614340\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4.86574 4.86574i 0.191292 0.191292i −0.604962 0.796254i \(-0.706812\pi\)
0.796254 + 0.604962i \(0.206812\pi\)
\(648\) 0 0
\(649\) 4.12683i 0.161992i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −11.8214 + 11.8214i −0.462609 + 0.462609i −0.899510 0.436901i \(-0.856076\pi\)
0.436901 + 0.899510i \(0.356076\pi\)
\(654\) 0 0
\(655\) 25.3444 + 0.128259i 0.990289 + 0.00501149i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6.02230i 0.234595i −0.993097 0.117298i \(-0.962577\pi\)
0.993097 0.117298i \(-0.0374232\pi\)
\(660\) 0 0
\(661\) 37.9790i 1.47721i −0.674137 0.738606i \(-0.735484\pi\)
0.674137 0.738606i \(-0.264516\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.27842 4.32194i −0.165910 0.167598i
\(666\) 0 0
\(667\) 15.0420 15.0420i 0.582428 0.582428i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2.51667i 0.0971551i
\(672\) 0 0
\(673\) 7.99686 7.99686i 0.308256 0.308256i −0.535977 0.844233i \(-0.680057\pi\)
0.844233 + 0.535977i \(0.180057\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7.11103 7.11103i −0.273299 0.273299i 0.557128 0.830427i \(-0.311903\pi\)
−0.830427 + 0.557128i \(0.811903\pi\)
\(678\) 0 0
\(679\) 9.56827i 0.367197i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 7.99061 7.99061i 0.305752 0.305752i −0.537507 0.843259i \(-0.680634\pi\)
0.843259 + 0.537507i \(0.180634\pi\)
\(684\) 0 0
\(685\) −24.4221 + 24.1762i −0.933120 + 0.923723i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −21.4058 −0.815495
\(690\) 0 0
\(691\) 32.5931i 1.23990i 0.784641 + 0.619951i \(0.212848\pi\)
−0.784641 + 0.619951i \(0.787152\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 29.8359 + 0.150989i 1.13174 + 0.00572732i
\(696\) 0 0
\(697\) −14.7100 14.7100i −0.557180 0.557180i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 42.9064 1.62055 0.810277 0.586047i \(-0.199317\pi\)
0.810277 + 0.586047i \(0.199317\pi\)
\(702\) 0 0
\(703\) −9.16379 + 9.16379i −0.345619 + 0.345619i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.66691 4.66691i −0.175517 0.175517i
\(708\) 0 0
\(709\) −10.3299 −0.387949 −0.193975 0.981007i \(-0.562138\pi\)
−0.193975 + 0.981007i \(0.562138\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −39.7825 39.7825i −1.48986 1.48986i
\(714\) 0 0
\(715\) 2.61658 + 2.64320i 0.0978545 + 0.0988500i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −6.49219 −0.242118 −0.121059 0.992645i \(-0.538629\pi\)
−0.121059 + 0.992645i \(0.538629\pi\)
\(720\) 0 0
\(721\) −9.44235 −0.351652
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.122650 + 12.1177i −0.00455511 + 0.450042i
\(726\) 0 0
\(727\) 11.0479 + 11.0479i 0.409744 + 0.409744i 0.881649 0.471905i \(-0.156434\pi\)
−0.471905 + 0.881649i \(0.656434\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −24.7019 −0.913631
\(732\) 0 0
\(733\) −19.5376 19.5376i −0.721636 0.721636i 0.247302 0.968938i \(-0.420456\pi\)
−0.968938 + 0.247302i \(0.920456\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.86461 + 1.86461i −0.0686837 + 0.0686837i
\(738\) 0 0
\(739\) 24.8980 0.915890 0.457945 0.888981i \(-0.348586\pi\)
0.457945 + 0.888981i \(0.348586\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −15.8961 15.8961i −0.583171 0.583171i 0.352602 0.935773i \(-0.385297\pi\)
−0.935773 + 0.352602i \(0.885297\pi\)
\(744\) 0 0
\(745\) −0.153851 + 30.4015i −0.00563665 + 1.11382i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 9.62928i 0.351846i
\(750\) 0 0
\(751\) −11.5535 −0.421594 −0.210797 0.977530i \(-0.567606\pi\)
−0.210797 + 0.977530i \(0.567606\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −21.5619 0.109117i −0.784717 0.00397116i
\(756\) 0 0
\(757\) −18.8612 + 18.8612i −0.685524 + 0.685524i −0.961239 0.275716i \(-0.911085\pi\)
0.275716 + 0.961239i \(0.411085\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 33.0567i 1.19830i −0.800636 0.599151i \(-0.795505\pi\)
0.800636 0.599151i \(-0.204495\pi\)
\(762\) 0 0
\(763\) 5.19836 + 5.19836i 0.188193 + 0.188193i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 43.0821 43.0821i 1.55561 1.55561i
\(768\) 0 0
\(769\) 44.9240i 1.62000i −0.586429 0.810001i \(-0.699467\pi\)
0.586429 0.810001i \(-0.300533\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −28.3672 + 28.3672i −1.02030 + 1.02030i −0.0205060 + 0.999790i \(0.506528\pi\)
−0.999790 + 0.0205060i \(0.993472\pi\)
\(774\) 0 0
\(775\) 32.0486 + 0.324380i 1.15122 + 0.0116521i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 23.6635i 0.847832i
\(780\) 0 0
\(781\) 4.52436i 0.161894i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −17.1339 + 16.9614i −0.611536 + 0.605377i
\(786\) 0 0
\(787\) −4.79302 + 4.79302i −0.170853 + 0.170853i −0.787354 0.616501i \(-0.788550\pi\)
0.616501 + 0.787354i \(0.288550\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.31610i 0.0823509i
\(792\) 0 0
\(793\) 26.2729 26.2729i 0.932977 0.932977i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 7.30136 + 7.30136i 0.258627 + 0.258627i 0.824496 0.565868i \(-0.191459\pi\)
−0.565868 + 0.824496i \(0.691459\pi\)
\(798\) 0 0
\(799\) 8.52480i 0.301586i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.69516 + 1.69516i −0.0598208 + 0.0598208i
\(804\) 0 0
\(805\) 0.0662907 13.0993i 0.00233644 0.461689i
\(806\) 0 0