Properties

Label 1440.2.bj.a.17.21
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 17.21
Character \(\chi\) \(=\) 1440.17
Dual form 1440.2.bj.a.593.21

$q$-expansion

\(f(q)\) \(=\) \(q+(2.03368 - 0.929591i) q^{5} +(2.49469 + 2.49469i) q^{7} +O(q^{10})\) \(q+(2.03368 - 0.929591i) q^{5} +(2.49469 + 2.49469i) q^{7} +3.92878 q^{11} +(4.55591 + 4.55591i) q^{13} +(-1.88566 + 1.88566i) q^{17} -4.61555 q^{19} +(-0.741221 - 0.741221i) q^{23} +(3.27172 - 3.78098i) q^{25} +4.35885i q^{29} -9.67119 q^{31} +(7.39245 + 2.75436i) q^{35} +(-5.39704 + 5.39704i) q^{37} -6.33584i q^{41} +(-0.206110 - 0.206110i) q^{43} +(3.48081 - 3.48081i) q^{47} +5.44695i q^{49} +(1.01974 - 1.01974i) q^{53} +(7.98989 - 3.65216i) q^{55} -0.531064i q^{59} +3.00356i q^{61} +(13.5004 + 5.03014i) q^{65} +(1.28660 - 1.28660i) q^{67} -7.61692i q^{71} +(-0.509262 + 0.509262i) q^{73} +(9.80109 + 9.80109i) q^{77} +1.31920i q^{79} +(9.85533 - 9.85533i) q^{83} +(-2.08194 + 5.58774i) q^{85} -2.91798 q^{89} +22.7312i q^{91} +(-9.38656 + 4.29057i) q^{95} +(-8.11369 - 8.11369i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + O(q^{10}) \) \( 48 q - 32 q^{31} - 32 q^{97} + O(q^{100}) \)

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
\(5\) 2.03368 0.929591i 0.909490 0.415726i
\(6\) 0 0
\(7\) 2.49469 + 2.49469i 0.942904 + 0.942904i 0.998456 0.0555517i \(-0.0176918\pi\)
−0.0555517 + 0.998456i \(0.517692\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.92878 1.18457 0.592286 0.805728i \(-0.298226\pi\)
0.592286 + 0.805728i \(0.298226\pi\)
\(12\) 0 0
\(13\) 4.55591 + 4.55591i 1.26358 + 1.26358i 0.949345 + 0.314237i \(0.101749\pi\)
0.314237 + 0.949345i \(0.398251\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.88566 + 1.88566i −0.457341 + 0.457341i −0.897782 0.440441i \(-0.854822\pi\)
0.440441 + 0.897782i \(0.354822\pi\)
\(18\) 0 0
\(19\) −4.61555 −1.05888 −0.529440 0.848347i \(-0.677598\pi\)
−0.529440 + 0.848347i \(0.677598\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.741221 0.741221i −0.154555 0.154555i 0.625594 0.780149i \(-0.284857\pi\)
−0.780149 + 0.625594i \(0.784857\pi\)
\(24\) 0 0
\(25\) 3.27172 3.78098i 0.654344 0.756197i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.35885i 0.809418i 0.914446 + 0.404709i \(0.132627\pi\)
−0.914446 + 0.404709i \(0.867373\pi\)
\(30\) 0 0
\(31\) −9.67119 −1.73700 −0.868499 0.495691i \(-0.834915\pi\)
−0.868499 + 0.495691i \(0.834915\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 7.39245 + 2.75436i 1.24955 + 0.465572i
\(36\) 0 0
\(37\) −5.39704 + 5.39704i −0.887267 + 0.887267i −0.994260 0.106992i \(-0.965878\pi\)
0.106992 + 0.994260i \(0.465878\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.33584i 0.989492i −0.869038 0.494746i \(-0.835261\pi\)
0.869038 0.494746i \(-0.164739\pi\)
\(42\) 0 0
\(43\) −0.206110 0.206110i −0.0314315 0.0314315i 0.691216 0.722648i \(-0.257075\pi\)
−0.722648 + 0.691216i \(0.757075\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.48081 3.48081i 0.507729 0.507729i −0.406100 0.913829i \(-0.633112\pi\)
0.913829 + 0.406100i \(0.133112\pi\)
\(48\) 0 0
\(49\) 5.44695i 0.778136i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.01974 1.01974i 0.140073 0.140073i −0.633593 0.773666i \(-0.718421\pi\)
0.773666 + 0.633593i \(0.218421\pi\)
\(54\) 0 0
\(55\) 7.98989 3.65216i 1.07736 0.492457i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.531064i 0.0691386i −0.999402 0.0345693i \(-0.988994\pi\)
0.999402 0.0345693i \(-0.0110059\pi\)
\(60\) 0 0
\(61\) 3.00356i 0.384566i 0.981340 + 0.192283i \(0.0615892\pi\)
−0.981340 + 0.192283i \(0.938411\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 13.5004 + 5.03014i 1.67452 + 0.623912i
\(66\) 0 0
\(67\) 1.28660 1.28660i 0.157183 0.157183i −0.624134 0.781317i \(-0.714548\pi\)
0.781317 + 0.624134i \(0.214548\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.61692i 0.903962i −0.892028 0.451981i \(-0.850718\pi\)
0.892028 0.451981i \(-0.149282\pi\)
\(72\) 0 0
\(73\) −0.509262 + 0.509262i −0.0596047 + 0.0596047i −0.736281 0.676676i \(-0.763420\pi\)
0.676676 + 0.736281i \(0.263420\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 9.80109 + 9.80109i 1.11694 + 1.11694i
\(78\) 0 0
\(79\) 1.31920i 0.148422i 0.997243 + 0.0742111i \(0.0236439\pi\)
−0.997243 + 0.0742111i \(0.976356\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 9.85533 9.85533i 1.08176 1.08176i 0.0854172 0.996345i \(-0.472778\pi\)
0.996345 0.0854172i \(-0.0272223\pi\)
\(84\) 0 0
\(85\) −2.08194 + 5.58774i −0.225819 + 0.606075i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.91798 −0.309306 −0.154653 0.987969i \(-0.549426\pi\)
−0.154653 + 0.987969i \(0.549426\pi\)
\(90\) 0 0
\(91\) 22.7312i 2.38287i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −9.38656 + 4.29057i −0.963041 + 0.440204i
\(96\) 0 0
\(97\) −8.11369 8.11369i −0.823820 0.823820i 0.162834 0.986654i \(-0.447937\pi\)
−0.986654 + 0.162834i \(0.947937\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 11.0269 1.09721 0.548607 0.836080i \(-0.315158\pi\)
0.548607 + 0.836080i \(0.315158\pi\)
\(102\) 0 0
\(103\) 2.89128 2.89128i 0.284887 0.284887i −0.550168 0.835054i \(-0.685436\pi\)
0.835054 + 0.550168i \(0.185436\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 5.23891 + 5.23891i 0.506465 + 0.506465i 0.913439 0.406975i \(-0.133416\pi\)
−0.406975 + 0.913439i \(0.633416\pi\)
\(108\) 0 0
\(109\) 5.31464 0.509050 0.254525 0.967066i \(-0.418081\pi\)
0.254525 + 0.967066i \(0.418081\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −10.3559 10.3559i −0.974204 0.974204i 0.0254720 0.999676i \(-0.491891\pi\)
−0.999676 + 0.0254720i \(0.991891\pi\)
\(114\) 0 0
\(115\) −2.19644 0.818375i −0.204819 0.0763138i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −9.40829 −0.862457
\(120\) 0 0
\(121\) 4.43532 0.403211
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 3.13887 10.7307i 0.280749 0.959781i
\(126\) 0 0
\(127\) 1.10872 + 1.10872i 0.0983826 + 0.0983826i 0.754585 0.656202i \(-0.227838\pi\)
−0.656202 + 0.754585i \(0.727838\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0.996979 0.0871065 0.0435532 0.999051i \(-0.486132\pi\)
0.0435532 + 0.999051i \(0.486132\pi\)
\(132\) 0 0
\(133\) −11.5144 11.5144i −0.998422 0.998422i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.03232 1.03232i 0.0881970 0.0881970i −0.661632 0.749829i \(-0.730136\pi\)
0.749829 + 0.661632i \(0.230136\pi\)
\(138\) 0 0
\(139\) 16.9830 1.44048 0.720239 0.693726i \(-0.244032\pi\)
0.720239 + 0.693726i \(0.244032\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 17.8992 + 17.8992i 1.49680 + 1.49680i
\(144\) 0 0
\(145\) 4.05194 + 8.86451i 0.336496 + 0.736157i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 6.48772i 0.531495i −0.964043 0.265747i \(-0.914381\pi\)
0.964043 0.265747i \(-0.0856187\pi\)
\(150\) 0 0
\(151\) −4.21210 −0.342776 −0.171388 0.985204i \(-0.554825\pi\)
−0.171388 + 0.985204i \(0.554825\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −19.6681 + 8.99025i −1.57978 + 0.722114i
\(156\) 0 0
\(157\) −0.0368875 + 0.0368875i −0.00294395 + 0.00294395i −0.708577 0.705633i \(-0.750663\pi\)
0.705633 + 0.708577i \(0.250663\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.69823i 0.291461i
\(162\) 0 0
\(163\) −1.33256 1.33256i −0.104374 0.104374i 0.652991 0.757365i \(-0.273514\pi\)
−0.757365 + 0.652991i \(0.773514\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 15.0291 15.0291i 1.16299 1.16299i 0.179169 0.983818i \(-0.442659\pi\)
0.983818 0.179169i \(-0.0573410\pi\)
\(168\) 0 0
\(169\) 28.5126i 2.19328i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2.16963 + 2.16963i −0.164954 + 0.164954i −0.784757 0.619804i \(-0.787212\pi\)
0.619804 + 0.784757i \(0.287212\pi\)
\(174\) 0 0
\(175\) 17.5943 1.27045i 1.33000 0.0960371i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 14.2973i 1.06863i 0.845285 + 0.534316i \(0.179431\pi\)
−0.845285 + 0.534316i \(0.820569\pi\)
\(180\) 0 0
\(181\) 11.0562i 0.821800i −0.911680 0.410900i \(-0.865215\pi\)
0.911680 0.410900i \(-0.134785\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5.95882 + 15.9929i −0.438101 + 1.17582i
\(186\) 0 0
\(187\) −7.40836 + 7.40836i −0.541753 + 0.541753i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.7129i 0.919873i 0.887952 + 0.459937i \(0.152128\pi\)
−0.887952 + 0.459937i \(0.847872\pi\)
\(192\) 0 0
\(193\) 16.5832 16.5832i 1.19368 1.19368i 0.217659 0.976025i \(-0.430158\pi\)
0.976025 0.217659i \(-0.0698420\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −9.96244 9.96244i −0.709794 0.709794i 0.256698 0.966492i \(-0.417366\pi\)
−0.966492 + 0.256698i \(0.917366\pi\)
\(198\) 0 0
\(199\) 15.6722i 1.11097i 0.831525 + 0.555487i \(0.187468\pi\)
−0.831525 + 0.555487i \(0.812532\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −10.8740 + 10.8740i −0.763203 + 0.763203i
\(204\) 0 0
\(205\) −5.88974 12.8851i −0.411357 0.899933i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −18.1335 −1.25432
\(210\) 0 0
\(211\) 22.1294i 1.52345i −0.647901 0.761725i \(-0.724353\pi\)
0.647901 0.761725i \(-0.275647\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.610761 0.227564i −0.0416535 0.0155198i
\(216\) 0 0
\(217\) −24.1266 24.1266i −1.63782 1.63782i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −17.1818 −1.15577
\(222\) 0 0
\(223\) 3.17650 3.17650i 0.212714 0.212714i −0.592705 0.805420i \(-0.701940\pi\)
0.805420 + 0.592705i \(0.201940\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −18.4920 18.4920i −1.22735 1.22735i −0.964961 0.262393i \(-0.915488\pi\)
−0.262393 0.964961i \(-0.584512\pi\)
\(228\) 0 0
\(229\) 19.2316 1.27086 0.635428 0.772160i \(-0.280824\pi\)
0.635428 + 0.772160i \(0.280824\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 13.7302 + 13.7302i 0.899495 + 0.899495i 0.995391 0.0958959i \(-0.0305716\pi\)
−0.0958959 + 0.995391i \(0.530572\pi\)
\(234\) 0 0
\(235\) 3.84313 10.3146i 0.250698 0.672850i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −26.7732 −1.73182 −0.865908 0.500203i \(-0.833259\pi\)
−0.865908 + 0.500203i \(0.833259\pi\)
\(240\) 0 0
\(241\) −17.6357 −1.13601 −0.568007 0.823023i \(-0.692286\pi\)
−0.568007 + 0.823023i \(0.692286\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 5.06344 + 11.0774i 0.323491 + 0.707707i
\(246\) 0 0
\(247\) −21.0280 21.0280i −1.33798 1.33798i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −13.0522 −0.823846 −0.411923 0.911219i \(-0.635143\pi\)
−0.411923 + 0.911219i \(0.635143\pi\)
\(252\) 0 0
\(253\) −2.91209 2.91209i −0.183082 0.183082i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 9.03127 9.03127i 0.563355 0.563355i −0.366904 0.930259i \(-0.619582\pi\)
0.930259 + 0.366904i \(0.119582\pi\)
\(258\) 0 0
\(259\) −26.9279 −1.67322
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2.83442 + 2.83442i 0.174778 + 0.174778i 0.789075 0.614297i \(-0.210560\pi\)
−0.614297 + 0.789075i \(0.710560\pi\)
\(264\) 0 0
\(265\) 1.12589 3.02178i 0.0691629 0.185627i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 9.89975i 0.603599i −0.953371 0.301799i \(-0.902413\pi\)
0.953371 0.301799i \(-0.0975873\pi\)
\(270\) 0 0
\(271\) −16.6235 −1.00981 −0.504904 0.863176i \(-0.668472\pi\)
−0.504904 + 0.863176i \(0.668472\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 12.8539 14.8547i 0.775118 0.895769i
\(276\) 0 0
\(277\) −6.42695 + 6.42695i −0.386158 + 0.386158i −0.873315 0.487156i \(-0.838034\pi\)
0.487156 + 0.873315i \(0.338034\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 27.0270i 1.61230i −0.591714 0.806148i \(-0.701549\pi\)
0.591714 0.806148i \(-0.298451\pi\)
\(282\) 0 0
\(283\) 18.1481 + 18.1481i 1.07879 + 1.07879i 0.996618 + 0.0821722i \(0.0261857\pi\)
0.0821722 + 0.996618i \(0.473814\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 15.8060 15.8060i 0.932996 0.932996i
\(288\) 0 0
\(289\) 9.88854i 0.581679i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −11.4905 + 11.4905i −0.671281 + 0.671281i −0.958011 0.286730i \(-0.907432\pi\)
0.286730 + 0.958011i \(0.407432\pi\)
\(294\) 0 0
\(295\) −0.493672 1.08001i −0.0287427 0.0628809i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 6.75387i 0.390586i
\(300\) 0 0
\(301\) 1.02836i 0.0592738i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2.79208 + 6.10828i 0.159874 + 0.349759i
\(306\) 0 0
\(307\) 17.8635 17.8635i 1.01953 1.01953i 0.0197205 0.999806i \(-0.493722\pi\)
0.999806 0.0197205i \(-0.00627765\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 9.93768i 0.563514i 0.959486 + 0.281757i \(0.0909173\pi\)
−0.959486 + 0.281757i \(0.909083\pi\)
\(312\) 0 0
\(313\) 5.20616 5.20616i 0.294269 0.294269i −0.544495 0.838764i \(-0.683279\pi\)
0.838764 + 0.544495i \(0.183279\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −13.2883 13.2883i −0.746346 0.746346i 0.227445 0.973791i \(-0.426963\pi\)
−0.973791 + 0.227445i \(0.926963\pi\)
\(318\) 0 0
\(319\) 17.1250i 0.958813i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.70338 8.70338i 0.484269 0.484269i
\(324\) 0 0
\(325\) 32.1315 2.32015i 1.78233 0.128699i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 17.3671 0.957479
\(330\) 0 0
\(331\) 8.60834i 0.473157i −0.971612 0.236579i \(-0.923974\pi\)
0.971612 0.236579i \(-0.0760261\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.42052 3.81255i 0.0776114 0.208302i
\(336\) 0 0
\(337\) 1.29928 + 1.29928i 0.0707764 + 0.0707764i 0.741609 0.670832i \(-0.234063\pi\)
−0.670832 + 0.741609i \(0.734063\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −37.9960 −2.05760
\(342\) 0 0
\(343\) 3.87437 3.87437i 0.209196 0.209196i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −18.3626 18.3626i −0.985756 0.985756i 0.0141438 0.999900i \(-0.495498\pi\)
−0.999900 + 0.0141438i \(0.995498\pi\)
\(348\) 0 0
\(349\) −31.1787 −1.66896 −0.834478 0.551041i \(-0.814231\pi\)
−0.834478 + 0.551041i \(0.814231\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 9.04629 + 9.04629i 0.481485 + 0.481485i 0.905606 0.424120i \(-0.139417\pi\)
−0.424120 + 0.905606i \(0.639417\pi\)
\(354\) 0 0
\(355\) −7.08062 15.4904i −0.375800 0.822144i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −13.1073 −0.691776 −0.345888 0.938276i \(-0.612422\pi\)
−0.345888 + 0.938276i \(0.612422\pi\)
\(360\) 0 0
\(361\) 2.30330 0.121226
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −0.562272 + 1.50908i −0.0294307 + 0.0789890i
\(366\) 0 0
\(367\) −3.44746 3.44746i −0.179956 0.179956i 0.611381 0.791337i \(-0.290614\pi\)
−0.791337 + 0.611381i \(0.790614\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 5.08789 0.264150
\(372\) 0 0
\(373\) 7.24984 + 7.24984i 0.375382 + 0.375382i 0.869433 0.494051i \(-0.164484\pi\)
−0.494051 + 0.869433i \(0.664484\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −19.8585 + 19.8585i −1.02277 + 1.02277i
\(378\) 0 0
\(379\) 29.1664 1.49818 0.749088 0.662470i \(-0.230492\pi\)
0.749088 + 0.662470i \(0.230492\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −12.2895 12.2895i −0.627965 0.627965i 0.319591 0.947556i \(-0.396455\pi\)
−0.947556 + 0.319591i \(0.896455\pi\)
\(384\) 0 0
\(385\) 29.0433 + 10.8213i 1.48018 + 0.551504i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 31.4290i 1.59351i 0.604301 + 0.796756i \(0.293452\pi\)
−0.604301 + 0.796756i \(0.706548\pi\)
\(390\) 0 0
\(391\) 2.79539 0.141369
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.22632 + 2.68284i 0.0617029 + 0.134988i
\(396\) 0 0
\(397\) 14.9362 14.9362i 0.749627 0.749627i −0.224782 0.974409i \(-0.572167\pi\)
0.974409 + 0.224782i \(0.0721671\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 27.0477i 1.35070i 0.737499 + 0.675349i \(0.236007\pi\)
−0.737499 + 0.675349i \(0.763993\pi\)
\(402\) 0 0
\(403\) −44.0611 44.0611i −2.19484 2.19484i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −21.2038 + 21.2038i −1.05103 + 1.05103i
\(408\) 0 0
\(409\) 4.66540i 0.230689i 0.993326 + 0.115345i \(0.0367973\pi\)
−0.993326 + 0.115345i \(0.963203\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.32484 1.32484i 0.0651911 0.0651911i
\(414\) 0 0
\(415\) 10.8812 29.2040i 0.534136 1.43357i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.43646i 0.119029i −0.998227 0.0595144i \(-0.981045\pi\)
0.998227 0.0595144i \(-0.0189552\pi\)
\(420\) 0 0
\(421\) 9.62136i 0.468916i 0.972126 + 0.234458i \(0.0753316\pi\)
−0.972126 + 0.234458i \(0.924668\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.960298 + 13.2990i 0.0465813 + 0.645098i
\(426\) 0 0
\(427\) −7.49294 + 7.49294i −0.362609 + 0.362609i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 26.4447i 1.27380i −0.770948 0.636898i \(-0.780217\pi\)
0.770948 0.636898i \(-0.219783\pi\)
\(432\) 0 0
\(433\) 5.22850 5.22850i 0.251266 0.251266i −0.570224 0.821490i \(-0.693143\pi\)
0.821490 + 0.570224i \(0.193143\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.42114 + 3.42114i 0.163655 + 0.163655i
\(438\) 0 0
\(439\) 37.3742i 1.78377i 0.452258 + 0.891887i \(0.350619\pi\)
−0.452258 + 0.891887i \(0.649381\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −18.0711 + 18.0711i −0.858585 + 0.858585i −0.991171 0.132587i \(-0.957672\pi\)
0.132587 + 0.991171i \(0.457672\pi\)
\(444\) 0 0
\(445\) −5.93425 + 2.71253i −0.281310 + 0.128586i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −24.4570 −1.15420 −0.577098 0.816675i \(-0.695815\pi\)
−0.577098 + 0.816675i \(0.695815\pi\)
\(450\) 0 0
\(451\) 24.8921i 1.17212i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 21.1307 + 46.2279i 0.990621 + 2.16720i
\(456\) 0 0
\(457\) 5.76322 + 5.76322i 0.269592 + 0.269592i 0.828936 0.559344i \(-0.188947\pi\)
−0.559344 + 0.828936i \(0.688947\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10.6204 −0.494639 −0.247320 0.968934i \(-0.579550\pi\)
−0.247320 + 0.968934i \(0.579550\pi\)
\(462\) 0 0
\(463\) −13.7984 + 13.7984i −0.641268 + 0.641268i −0.950867 0.309599i \(-0.899805\pi\)
0.309599 + 0.950867i \(0.399805\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 11.6749 + 11.6749i 0.540248 + 0.540248i 0.923602 0.383354i \(-0.125231\pi\)
−0.383354 + 0.923602i \(0.625231\pi\)
\(468\) 0 0
\(469\) 6.41933 0.296417
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −0.809762 0.809762i −0.0372329 0.0372329i
\(474\) 0 0
\(475\) −15.1008 + 17.4513i −0.692872 + 0.800721i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.10716 0.233352 0.116676 0.993170i \(-0.462776\pi\)
0.116676 + 0.993170i \(0.462776\pi\)
\(480\) 0 0
\(481\) −49.1768 −2.24227
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −24.0431 8.95824i −1.09174 0.406773i
\(486\) 0 0
\(487\) −3.80542 3.80542i −0.172440 0.172440i 0.615611 0.788050i \(-0.288909\pi\)
−0.788050 + 0.615611i \(0.788909\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −19.3774 −0.874492 −0.437246 0.899342i \(-0.644046\pi\)
−0.437246 + 0.899342i \(0.644046\pi\)
\(492\) 0 0
\(493\) −8.21932 8.21932i −0.370180 0.370180i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 19.0018 19.0018i 0.852349 0.852349i
\(498\) 0 0
\(499\) 21.5723 0.965707 0.482853 0.875701i \(-0.339600\pi\)
0.482853 + 0.875701i \(0.339600\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −0.650945 0.650945i −0.0290242 0.0290242i 0.692446 0.721470i \(-0.256533\pi\)
−0.721470 + 0.692446i \(0.756533\pi\)
\(504\) 0 0
\(505\) 22.4251 10.2505i 0.997906 0.456140i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 9.29371i 0.411937i −0.978559 0.205968i \(-0.933966\pi\)
0.978559 0.205968i \(-0.0660344\pi\)
\(510\) 0 0
\(511\) −2.54090 −0.112403
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 3.19224 8.56766i 0.140667 0.377536i
\(516\) 0 0
\(517\) 13.6753 13.6753i 0.601441 0.601441i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 37.4945i 1.64266i −0.570451 0.821331i \(-0.693232\pi\)
0.570451 0.821331i \(-0.306768\pi\)
\(522\) 0 0
\(523\) 18.0635 + 18.0635i 0.789861 + 0.789861i 0.981471 0.191610i \(-0.0613710\pi\)
−0.191610 + 0.981471i \(0.561371\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 18.2366 18.2366i 0.794400 0.794400i
\(528\) 0 0
\(529\) 21.9012i 0.952225i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 28.8655 28.8655i 1.25030 1.25030i
\(534\) 0 0
\(535\) 15.5243 + 5.78423i 0.671175 + 0.250074i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 21.3999i 0.921758i
\(540\) 0 0
\(541\) 29.6103i 1.27305i 0.771258 + 0.636523i \(0.219628\pi\)
−0.771258 + 0.636523i \(0.780372\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 10.8083 4.94044i 0.462976 0.211625i
\(546\) 0 0
\(547\) −13.8891 + 13.8891i −0.593855 + 0.593855i −0.938670 0.344816i \(-0.887941\pi\)
0.344816 + 0.938670i \(0.387941\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 20.1185i 0.857076i
\(552\) 0 0
\(553\) −3.29101 + 3.29101i −0.139948 + 0.139948i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 16.0818 + 16.0818i 0.681408 + 0.681408i 0.960317 0.278910i \(-0.0899730\pi\)
−0.278910 + 0.960317i \(0.589973\pi\)
\(558\) 0 0
\(559\) 1.87804i 0.0794326i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 11.6731 11.6731i 0.491962 0.491962i −0.416962 0.908924i \(-0.636905\pi\)
0.908924 + 0.416962i \(0.136905\pi\)
\(564\) 0 0
\(565\) −30.6874 11.4339i −1.29103 0.481027i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −26.5009 −1.11098 −0.555488 0.831524i \(-0.687469\pi\)
−0.555488 + 0.831524i \(0.687469\pi\)
\(570\) 0 0
\(571\) 42.2873i 1.76967i 0.465904 + 0.884835i \(0.345729\pi\)
−0.465904 + 0.884835i \(0.654271\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −5.22761 + 0.377476i −0.218006 + 0.0157418i
\(576\) 0 0
\(577\) 10.2682 + 10.2682i 0.427473 + 0.427473i 0.887767 0.460294i \(-0.152256\pi\)
−0.460294 + 0.887767i \(0.652256\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 49.1720 2.04000
\(582\) 0 0
\(583\) 4.00635 4.00635i 0.165926 0.165926i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 18.7596 + 18.7596i 0.774290 + 0.774290i 0.978853 0.204563i \(-0.0655773\pi\)
−0.204563 + 0.978853i \(0.565577\pi\)
\(588\) 0 0
\(589\) 44.6379 1.83927
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.79755 + 1.79755i 0.0738164 + 0.0738164i 0.743051 0.669235i \(-0.233378\pi\)
−0.669235 + 0.743051i \(0.733378\pi\)
\(594\) 0 0
\(595\) −19.1335 + 8.74586i −0.784396 + 0.358545i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 34.7082 1.41814 0.709069 0.705139i \(-0.249115\pi\)
0.709069 + 0.705139i \(0.249115\pi\)
\(600\) 0 0
\(601\) −8.66540 −0.353469 −0.176735 0.984259i \(-0.556553\pi\)
−0.176735 + 0.984259i \(0.556553\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 9.02002 4.12303i 0.366716 0.167625i
\(606\) 0 0
\(607\) 5.31702 + 5.31702i 0.215811 + 0.215811i 0.806731 0.590919i \(-0.201235\pi\)
−0.590919 + 0.806731i \(0.701235\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 31.7165 1.28311
\(612\) 0 0
\(613\) 0.848748 + 0.848748i 0.0342806 + 0.0342806i 0.724039 0.689759i \(-0.242283\pi\)
−0.689759 + 0.724039i \(0.742283\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 16.6187 16.6187i 0.669043 0.669043i −0.288452 0.957494i \(-0.593141\pi\)
0.957494 + 0.288452i \(0.0931405\pi\)
\(618\) 0 0
\(619\) −6.21940 −0.249979 −0.124989 0.992158i \(-0.539890\pi\)
−0.124989 + 0.992158i \(0.539890\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −7.27946 7.27946i −0.291646 0.291646i
\(624\) 0 0
\(625\) −3.59168 24.7407i −0.143667 0.989626i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 20.3540i 0.811567i
\(630\) 0 0
\(631\) −12.0019 −0.477790 −0.238895 0.971045i \(-0.576785\pi\)
−0.238895 + 0.971045i \(0.576785\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3.28543 + 1.22412i 0.130378 + 0.0485778i
\(636\) 0 0
\(637\) −24.8158 + 24.8158i −0.983239 + 0.983239i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 6.27061i 0.247674i 0.992303 + 0.123837i \(0.0395200\pi\)
−0.992303 + 0.123837i \(0.960480\pi\)
\(642\) 0 0
\(643\) 15.3358 + 15.3358i 0.604787 + 0.604787i 0.941579 0.336792i \(-0.109342\pi\)
−0.336792 + 0.941579i \(0.609342\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −28.9583 + 28.9583i −1.13847 + 1.13847i −0.149741 + 0.988725i \(0.547844\pi\)
−0.988725 + 0.149741i \(0.952156\pi\)
\(648\) 0 0
\(649\) 2.08643i 0.0818997i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.21463 2.21463i 0.0866651 0.0866651i −0.662445 0.749110i \(-0.730481\pi\)
0.749110 + 0.662445i \(0.230481\pi\)
\(654\) 0 0
\(655\) 2.02754 0.926783i 0.0792225 0.0362124i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 37.2920i 1.45269i −0.687330 0.726345i \(-0.741218\pi\)
0.687330 0.726345i \(-0.258782\pi\)
\(660\) 0 0
\(661\) 6.19442i 0.240935i 0.992717 + 0.120467i \(0.0384393\pi\)
−0.992717 + 0.120467i \(0.961561\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −34.1202 12.7129i −1.32312 0.492985i
\(666\) 0 0
\(667\) 3.23087 3.23087i 0.125100 0.125100i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 11.8003i 0.455546i
\(672\) 0 0
\(673\) −27.8727 + 27.8727i −1.07441 + 1.07441i −0.0774133 + 0.996999i \(0.524666\pi\)
−0.996999 + 0.0774133i \(0.975334\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10.0200 + 10.0200i 0.385098 + 0.385098i 0.872935 0.487837i \(-0.162214\pi\)
−0.487837 + 0.872935i \(0.662214\pi\)
\(678\) 0 0
\(679\) 40.4823i 1.55357i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −11.5229 + 11.5229i −0.440911 + 0.440911i −0.892318 0.451407i \(-0.850922\pi\)
0.451407 + 0.892318i \(0.350922\pi\)
\(684\) 0 0
\(685\) 1.13977 3.05904i 0.0435485 0.116880i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 9.29173 0.353987
\(690\) 0 0
\(691\) 18.3907i 0.699614i 0.936822 + 0.349807i \(0.113753\pi\)
−0.936822 + 0.349807i \(0.886247\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 34.5380 15.7872i 1.31010 0.598844i
\(696\) 0 0
\(697\) 11.9473 + 11.9473i 0.452535 + 0.452535i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 52.0764 1.96690 0.983449 0.181186i \(-0.0579937\pi\)
0.983449 + 0.181186i \(0.0579937\pi\)
\(702\) 0 0
\(703\) 24.9103 24.9103i 0.939509 0.939509i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 27.5086 + 27.5086i 1.03457 + 1.03457i
\(708\) 0 0
\(709\) −49.8546 −1.87233 −0.936165 0.351561i \(-0.885651\pi\)
−0.936165 + 0.351561i \(0.885651\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 7.16849 + 7.16849i 0.268462 + 0.268462i
\(714\) 0 0
\(715\) 53.0401 + 19.7623i 1.98359 + 0.739068i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −21.3548 −0.796400 −0.398200 0.917299i \(-0.630365\pi\)
−0.398200 + 0.917299i \(0.630365\pi\)
\(720\) 0 0
\(721\) 14.4257 0.537242
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 16.4807 + 14.2609i 0.612079 + 0.529638i
\(726\) 0 0
\(727\) −13.1166 13.1166i −0.486469 0.486469i 0.420721 0.907190i \(-0.361777\pi\)
−0.907190 + 0.420721i \(0.861777\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0.777309 0.0287498
\(732\) 0 0
\(733\) −3.40526 3.40526i −0.125776 0.125776i 0.641417 0.767193i \(-0.278347\pi\)
−0.767193 + 0.641417i \(0.778347\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.05477 5.05477i 0.186195 0.186195i
\(738\) 0 0
\(739\) −6.84745 −0.251887 −0.125944 0.992037i \(-0.540196\pi\)
−0.125944 + 0.992037i \(0.540196\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −9.83167 9.83167i −0.360689 0.360689i 0.503377 0.864067i \(-0.332091\pi\)
−0.864067 + 0.503377i \(0.832091\pi\)
\(744\) 0 0
\(745\) −6.03092 13.1940i −0.220956 0.483389i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 26.1389i 0.955095i
\(750\) 0 0
\(751\) 36.1038 1.31745 0.658723 0.752385i \(-0.271097\pi\)
0.658723 + 0.752385i \(0.271097\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −8.56606 + 3.91553i −0.311751 + 0.142501i
\(756\) 0 0
\(757\) −26.0495 + 26.0495i −0.946785 + 0.946785i −0.998654 0.0518693i \(-0.983482\pi\)
0.0518693 + 0.998654i \(0.483482\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 29.4006i 1.06577i 0.846188 + 0.532885i \(0.178892\pi\)
−0.846188 + 0.532885i \(0.821108\pi\)
\(762\) 0 0
\(763\) 13.2584 + 13.2584i 0.479986 + 0.479986i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.41948 2.41948i 0.0873623 0.0873623i
\(768\) 0 0
\(769\) 39.4234i 1.42164i 0.703372 + 0.710822i \(0.251677\pi\)
−0.703372 + 0.710822i \(0.748323\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 2.76896 2.76896i 0.0995925 0.0995925i −0.655555 0.755147i \(-0.727565\pi\)
0.755147 + 0.655555i \(0.227565\pi\)
\(774\) 0 0
\(775\) −31.6414 + 36.5666i −1.13659 + 1.31351i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 29.2434i 1.04775i
\(780\) 0 0
\(781\) 29.9252i 1.07081i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −0.0407272 + 0.109308i −0.00145362 + 0.00390136i
\(786\) 0 0
\(787\) −20.1445 + 20.1445i −0.718072 + 0.718072i −0.968210 0.250138i \(-0.919524\pi\)
0.250138 + 0.968210i \(0.419524\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 51.6696i 1.83716i
\(792\) 0 0
\(793\) −13.6839 + 13.6839i −0.485931 + 0.485931i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −27.4953 27.4953i −0.973933 0.973933i 0.0257360 0.999669i \(-0.491807\pi\)
−0.999669 + 0.0257360i \(0.991807\pi\)
\(798\) 0 0
\(799\) 13.1273i 0.464410i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2.00078 + 2.00078i −0.0706060 + 0.0706060i
\(804\) 0 0
\(805\) −3.43784 7.52102i −0.121168 0.265081i
\(806\) 0 0
\(807\) 0