Properties

Label 1840.2.m.g.1839.12
Level $1840$
Weight $2$
Character 1840.1839
Analytic conductor $14.692$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.m (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.6924739719\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1839.12
Character \(\chi\) \(=\) 1840.1839
Dual form 1840.2.m.g.1839.9

$q$-expansion

\(f(q)\) \(=\) \(q-2.20329 q^{3} +(1.71768 + 1.43163i) q^{5} -0.642617i q^{7} +1.85447 q^{9} +O(q^{10})\) \(q-2.20329 q^{3} +(1.71768 + 1.43163i) q^{5} -0.642617i q^{7} +1.85447 q^{9} -2.87003 q^{11} -0.405025i q^{13} +(-3.78454 - 3.15430i) q^{15} +4.93021 q^{17} -2.74284 q^{19} +1.41587i q^{21} +(4.71132 - 0.896383i) q^{23} +(0.900844 + 4.91818i) q^{25} +2.52393 q^{27} -1.62882 q^{29} +4.55939i q^{31} +6.32349 q^{33} +(0.919993 - 1.10381i) q^{35} -2.00091 q^{37} +0.892386i q^{39} -4.79334 q^{41} +3.29086i q^{43} +(3.18539 + 2.65493i) q^{45} -3.58875 q^{47} +6.58704 q^{49} -10.8627 q^{51} +0.263678 q^{53} +(-4.92979 - 4.10883i) q^{55} +6.04326 q^{57} -10.3753i q^{59} +9.19418i q^{61} -1.19172i q^{63} +(0.579847 - 0.695702i) q^{65} -2.18044i q^{67} +(-10.3804 + 1.97499i) q^{69} +10.3200i q^{71} -4.43051i q^{73} +(-1.98482 - 10.8362i) q^{75} +1.84433i q^{77} +3.16051 q^{79} -11.1243 q^{81} +9.14874i q^{83} +(8.46852 + 7.05826i) q^{85} +3.58875 q^{87} +14.0324i q^{89} -0.260276 q^{91} -10.0456i q^{93} +(-4.71132 - 3.92674i) q^{95} +10.3665 q^{97} -5.32239 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 80q^{9} + O(q^{10}) \) \( 40q + 80q^{9} - 24q^{25} + 24q^{41} - 16q^{49} + 80q^{69} + 40q^{81} - 8q^{85} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).

\(n\) \(737\) \(1151\) \(1201\) \(1381\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(1\)

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
\(3\) −2.20329 −1.27207 −0.636034 0.771661i \(-0.719426\pi\)
−0.636034 + 0.771661i \(0.719426\pi\)
\(4\) 0 0
\(5\) 1.71768 + 1.43163i 0.768169 + 0.640247i
\(6\) 0 0
\(7\) 0.642617i 0.242886i −0.992598 0.121443i \(-0.961248\pi\)
0.992598 0.121443i \(-0.0387522\pi\)
\(8\) 0 0
\(9\) 1.85447 0.618157
\(10\) 0 0
\(11\) −2.87003 −0.865346 −0.432673 0.901551i \(-0.642429\pi\)
−0.432673 + 0.901551i \(0.642429\pi\)
\(12\) 0 0
\(13\) 0.405025i 0.112334i −0.998421 0.0561668i \(-0.982112\pi\)
0.998421 0.0561668i \(-0.0178879\pi\)
\(14\) 0 0
\(15\) −3.78454 3.15430i −0.977164 0.814437i
\(16\) 0 0
\(17\) 4.93021 1.19575 0.597876 0.801589i \(-0.296011\pi\)
0.597876 + 0.801589i \(0.296011\pi\)
\(18\) 0 0
\(19\) −2.74284 −0.629250 −0.314625 0.949216i \(-0.601879\pi\)
−0.314625 + 0.949216i \(0.601879\pi\)
\(20\) 0 0
\(21\) 1.41587i 0.308968i
\(22\) 0 0
\(23\) 4.71132 0.896383i 0.982377 0.186909i
\(24\) 0 0
\(25\) 0.900844 + 4.91818i 0.180169 + 0.983636i
\(26\) 0 0
\(27\) 2.52393 0.485730
\(28\) 0 0
\(29\) −1.62882 −0.302464 −0.151232 0.988498i \(-0.548324\pi\)
−0.151232 + 0.988498i \(0.548324\pi\)
\(30\) 0 0
\(31\) 4.55939i 0.818890i 0.912335 + 0.409445i \(0.134278\pi\)
−0.912335 + 0.409445i \(0.865722\pi\)
\(32\) 0 0
\(33\) 6.32349 1.10078
\(34\) 0 0
\(35\) 0.919993 1.10381i 0.155507 0.186578i
\(36\) 0 0
\(37\) −2.00091 −0.328947 −0.164474 0.986381i \(-0.552593\pi\)
−0.164474 + 0.986381i \(0.552593\pi\)
\(38\) 0 0
\(39\) 0.892386i 0.142896i
\(40\) 0 0
\(41\) −4.79334 −0.748593 −0.374297 0.927309i \(-0.622116\pi\)
−0.374297 + 0.927309i \(0.622116\pi\)
\(42\) 0 0
\(43\) 3.29086i 0.501852i 0.968006 + 0.250926i \(0.0807351\pi\)
−0.968006 + 0.250926i \(0.919265\pi\)
\(44\) 0 0
\(45\) 3.18539 + 2.65493i 0.474850 + 0.395773i
\(46\) 0 0
\(47\) −3.58875 −0.523473 −0.261736 0.965139i \(-0.584295\pi\)
−0.261736 + 0.965139i \(0.584295\pi\)
\(48\) 0 0
\(49\) 6.58704 0.941006
\(50\) 0 0
\(51\) −10.8627 −1.52108
\(52\) 0 0
\(53\) 0.263678 0.0362190 0.0181095 0.999836i \(-0.494235\pi\)
0.0181095 + 0.999836i \(0.494235\pi\)
\(54\) 0 0
\(55\) −4.92979 4.10883i −0.664732 0.554035i
\(56\) 0 0
\(57\) 6.04326 0.800449
\(58\) 0 0
\(59\) 10.3753i 1.35074i −0.737478 0.675372i \(-0.763983\pi\)
0.737478 0.675372i \(-0.236017\pi\)
\(60\) 0 0
\(61\) 9.19418i 1.17719i 0.808427 + 0.588597i \(0.200319\pi\)
−0.808427 + 0.588597i \(0.799681\pi\)
\(62\) 0 0
\(63\) 1.19172i 0.150142i
\(64\) 0 0
\(65\) 0.579847 0.695702i 0.0719212 0.0862913i
\(66\) 0 0
\(67\) 2.18044i 0.266383i −0.991090 0.133192i \(-0.957477\pi\)
0.991090 0.133192i \(-0.0425225\pi\)
\(68\) 0 0
\(69\) −10.3804 + 1.97499i −1.24965 + 0.237761i
\(70\) 0 0
\(71\) 10.3200i 1.22475i 0.790566 + 0.612376i \(0.209786\pi\)
−0.790566 + 0.612376i \(0.790214\pi\)
\(72\) 0 0
\(73\) 4.43051i 0.518552i −0.965803 0.259276i \(-0.916516\pi\)
0.965803 0.259276i \(-0.0834839\pi\)
\(74\) 0 0
\(75\) −1.98482 10.8362i −0.229187 1.25125i
\(76\) 0 0
\(77\) 1.84433i 0.210181i
\(78\) 0 0
\(79\) 3.16051 0.355585 0.177792 0.984068i \(-0.443104\pi\)
0.177792 + 0.984068i \(0.443104\pi\)
\(80\) 0 0
\(81\) −11.1243 −1.23604
\(82\) 0 0
\(83\) 9.14874i 1.00420i 0.864808 + 0.502102i \(0.167440\pi\)
−0.864808 + 0.502102i \(0.832560\pi\)
\(84\) 0 0
\(85\) 8.46852 + 7.05826i 0.918540 + 0.765576i
\(86\) 0 0
\(87\) 3.58875 0.384754
\(88\) 0 0
\(89\) 14.0324i 1.48744i 0.668494 + 0.743718i \(0.266939\pi\)
−0.668494 + 0.743718i \(0.733061\pi\)
\(90\) 0 0
\(91\) −0.260276 −0.0272843
\(92\) 0 0
\(93\) 10.0456i 1.04168i
\(94\) 0 0
\(95\) −4.71132 3.92674i −0.483371 0.402875i
\(96\) 0 0
\(97\) 10.3665 1.05256 0.526278 0.850312i \(-0.323587\pi\)
0.526278 + 0.850312i \(0.323587\pi\)
\(98\) 0 0
\(99\) −5.32239 −0.534920
\(100\) 0 0
\(101\) −12.2075 −1.21469 −0.607346 0.794437i \(-0.707766\pi\)
−0.607346 + 0.794437i \(0.707766\pi\)
\(102\) 0 0
\(103\) 11.3098i 1.11439i 0.830382 + 0.557195i \(0.188122\pi\)
−0.830382 + 0.557195i \(0.811878\pi\)
\(104\) 0 0
\(105\) −2.02701 + 2.43201i −0.197816 + 0.237340i
\(106\) 0 0
\(107\) 15.5211i 1.50048i 0.661167 + 0.750239i \(0.270062\pi\)
−0.661167 + 0.750239i \(0.729938\pi\)
\(108\) 0 0
\(109\) 13.6376i 1.30625i 0.757251 + 0.653124i \(0.226542\pi\)
−0.757251 + 0.653124i \(0.773458\pi\)
\(110\) 0 0
\(111\) 4.40857 0.418443
\(112\) 0 0
\(113\) 7.47503 0.703192 0.351596 0.936152i \(-0.385639\pi\)
0.351596 + 0.936152i \(0.385639\pi\)
\(114\) 0 0
\(115\) 9.37582 + 5.20518i 0.874300 + 0.485386i
\(116\) 0 0
\(117\) 0.751107i 0.0694399i
\(118\) 0 0
\(119\) 3.16824i 0.290432i
\(120\) 0 0
\(121\) −2.76295 −0.251177
\(122\) 0 0
\(123\) 10.5611 0.952262
\(124\) 0 0
\(125\) −5.49368 + 9.73753i −0.491369 + 0.870951i
\(126\) 0 0
\(127\) 0.380884 0.0337980 0.0168990 0.999857i \(-0.494621\pi\)
0.0168990 + 0.999857i \(0.494621\pi\)
\(128\) 0 0
\(129\) 7.25072i 0.638390i
\(130\) 0 0
\(131\) 14.8999i 1.30181i 0.759157 + 0.650907i \(0.225611\pi\)
−0.759157 + 0.650907i \(0.774389\pi\)
\(132\) 0 0
\(133\) 1.76259i 0.152836i
\(134\) 0 0
\(135\) 4.33529 + 3.61334i 0.373123 + 0.310987i
\(136\) 0 0
\(137\) −8.37933 −0.715894 −0.357947 0.933742i \(-0.616523\pi\)
−0.357947 + 0.933742i \(0.616523\pi\)
\(138\) 0 0
\(139\) 3.37882i 0.286588i −0.989680 0.143294i \(-0.954231\pi\)
0.989680 0.143294i \(-0.0457694\pi\)
\(140\) 0 0
\(141\) 7.90704 0.665893
\(142\) 0 0
\(143\) 1.16243i 0.0972074i
\(144\) 0 0
\(145\) −2.79778 2.33187i −0.232343 0.193651i
\(146\) 0 0
\(147\) −14.5131 −1.19702
\(148\) 0 0
\(149\) 17.7280i 1.45233i 0.687519 + 0.726167i \(0.258700\pi\)
−0.687519 + 0.726167i \(0.741300\pi\)
\(150\) 0 0
\(151\) 16.9047i 1.37568i 0.725861 + 0.687841i \(0.241441\pi\)
−0.725861 + 0.687841i \(0.758559\pi\)
\(152\) 0 0
\(153\) 9.14294 0.739163
\(154\) 0 0
\(155\) −6.52738 + 7.83157i −0.524292 + 0.629046i
\(156\) 0 0
\(157\) −11.1520 −0.890027 −0.445013 0.895524i \(-0.646801\pi\)
−0.445013 + 0.895524i \(0.646801\pi\)
\(158\) 0 0
\(159\) −0.580959 −0.0460730
\(160\) 0 0
\(161\) −0.576031 3.02757i −0.0453976 0.238606i
\(162\) 0 0
\(163\) −2.50634 −0.196312 −0.0981559 0.995171i \(-0.531294\pi\)
−0.0981559 + 0.995171i \(0.531294\pi\)
\(164\) 0 0
\(165\) 10.8617 + 9.05293i 0.845585 + 0.704770i
\(166\) 0 0
\(167\) −1.83999 −0.142382 −0.0711912 0.997463i \(-0.522680\pi\)
−0.0711912 + 0.997463i \(0.522680\pi\)
\(168\) 0 0
\(169\) 12.8360 0.987381
\(170\) 0 0
\(171\) −5.08652 −0.388976
\(172\) 0 0
\(173\) 11.2607i 0.856136i −0.903747 0.428068i \(-0.859194\pi\)
0.903747 0.428068i \(-0.140806\pi\)
\(174\) 0 0
\(175\) 3.16051 0.578898i 0.238912 0.0437605i
\(176\) 0 0
\(177\) 22.8597i 1.71824i
\(178\) 0 0
\(179\) 0.613572i 0.0458605i 0.999737 + 0.0229303i \(0.00729957\pi\)
−0.999737 + 0.0229303i \(0.992700\pi\)
\(180\) 0 0
\(181\) 0.527590i 0.0392154i −0.999808 0.0196077i \(-0.993758\pi\)
0.999808 0.0196077i \(-0.00624173\pi\)
\(182\) 0 0
\(183\) 20.2574i 1.49747i
\(184\) 0 0
\(185\) −3.43692 2.86457i −0.252687 0.210607i
\(186\) 0 0
\(187\) −14.1498 −1.03474
\(188\) 0 0
\(189\) 1.62192i 0.117977i
\(190\) 0 0
\(191\) 13.0548 0.944609 0.472304 0.881435i \(-0.343422\pi\)
0.472304 + 0.881435i \(0.343422\pi\)
\(192\) 0 0
\(193\) 20.3324i 1.46356i −0.681541 0.731780i \(-0.738690\pi\)
0.681541 0.731780i \(-0.261310\pi\)
\(194\) 0 0
\(195\) −1.27757 + 1.53283i −0.0914887 + 0.109768i
\(196\) 0 0
\(197\) 15.0465i 1.07202i 0.844213 + 0.536008i \(0.180068\pi\)
−0.844213 + 0.536008i \(0.819932\pi\)
\(198\) 0 0
\(199\) 6.81716 0.483255 0.241628 0.970369i \(-0.422319\pi\)
0.241628 + 0.970369i \(0.422319\pi\)
\(200\) 0 0
\(201\) 4.80413i 0.338857i
\(202\) 0 0
\(203\) 1.04671i 0.0734643i
\(204\) 0 0
\(205\) −8.23341 6.86231i −0.575047 0.479284i
\(206\) 0 0
\(207\) 8.73701 1.66232i 0.607264 0.115539i
\(208\) 0 0
\(209\) 7.87202 0.544519
\(210\) 0 0
\(211\) 2.73591i 0.188348i 0.995556 + 0.0941739i \(0.0300210\pi\)
−0.995556 + 0.0941739i \(0.969979\pi\)
\(212\) 0 0
\(213\) 22.7378i 1.55797i
\(214\) 0 0
\(215\) −4.71132 + 5.65265i −0.321309 + 0.385507i
\(216\) 0 0
\(217\) 2.92994 0.198897
\(218\) 0 0
\(219\) 9.76168i 0.659633i
\(220\) 0 0
\(221\) 1.99686i 0.134323i
\(222\) 0 0
\(223\) 19.6037 1.31276 0.656379 0.754431i \(-0.272087\pi\)
0.656379 + 0.754431i \(0.272087\pi\)
\(224\) 0 0
\(225\) 1.67059 + 9.12063i 0.111373 + 0.608042i
\(226\) 0 0
\(227\) 18.0945i 1.20097i 0.799635 + 0.600487i \(0.205026\pi\)
−0.799635 + 0.600487i \(0.794974\pi\)
\(228\) 0 0
\(229\) 27.1740i 1.79571i −0.440293 0.897854i \(-0.645125\pi\)
0.440293 0.897854i \(-0.354875\pi\)
\(230\) 0 0
\(231\) 4.06359i 0.267364i
\(232\) 0 0
\(233\) 4.25756i 0.278922i −0.990228 0.139461i \(-0.955463\pi\)
0.990228 0.139461i \(-0.0445370\pi\)
\(234\) 0 0
\(235\) −6.16432 5.13778i −0.402116 0.335152i
\(236\) 0 0
\(237\) −6.96350 −0.452328
\(238\) 0 0
\(239\) 18.5247i 1.19826i −0.800651 0.599131i \(-0.795513\pi\)
0.800651 0.599131i \(-0.204487\pi\)
\(240\) 0 0
\(241\) 3.60856i 0.232448i 0.993223 + 0.116224i \(0.0370790\pi\)
−0.993223 + 0.116224i \(0.962921\pi\)
\(242\) 0 0
\(243\) 16.9384 1.08660
\(244\) 0 0
\(245\) 11.3144 + 9.43024i 0.722852 + 0.602476i
\(246\) 0 0
\(247\) 1.11092i 0.0706860i
\(248\) 0 0
\(249\) 20.1573i 1.27742i
\(250\) 0 0
\(251\) −3.81994 −0.241113 −0.120556 0.992706i \(-0.538468\pi\)
−0.120556 + 0.992706i \(0.538468\pi\)
\(252\) 0 0
\(253\) −13.5216 + 2.57264i −0.850096 + 0.161741i
\(254\) 0 0
\(255\) −18.6586 15.5514i −1.16845 0.973865i
\(256\) 0 0
\(257\) 1.24356i 0.0775712i 0.999248 + 0.0387856i \(0.0123489\pi\)
−0.999248 + 0.0387856i \(0.987651\pi\)
\(258\) 0 0
\(259\) 1.28582i 0.0798968i
\(260\) 0 0
\(261\) −3.02059 −0.186970
\(262\) 0 0
\(263\) 10.0562i 0.620094i −0.950721 0.310047i \(-0.899655\pi\)
0.950721 0.310047i \(-0.100345\pi\)
\(264\) 0 0
\(265\) 0.452914 + 0.377491i 0.0278223 + 0.0231891i
\(266\) 0 0
\(267\) 30.9175i 1.89212i
\(268\) 0 0
\(269\) −2.19489 −0.133825 −0.0669125 0.997759i \(-0.521315\pi\)
−0.0669125 + 0.997759i \(0.521315\pi\)
\(270\) 0 0
\(271\) 4.25997i 0.258775i −0.991594 0.129387i \(-0.958699\pi\)
0.991594 0.129387i \(-0.0413010\pi\)
\(272\) 0 0
\(273\) 0.573462 0.0347075
\(274\) 0 0
\(275\) −2.58545 14.1153i −0.155908 0.851185i
\(276\) 0 0
\(277\) 8.87597i 0.533305i −0.963793 0.266653i \(-0.914082\pi\)
0.963793 0.266653i \(-0.0859176\pi\)
\(278\) 0 0
\(279\) 8.45526i 0.506203i
\(280\) 0 0
\(281\) 8.57906i 0.511784i 0.966705 + 0.255892i \(0.0823692\pi\)
−0.966705 + 0.255892i \(0.917631\pi\)
\(282\) 0 0
\(283\) 3.40195i 0.202225i 0.994875 + 0.101113i \(0.0322402\pi\)
−0.994875 + 0.101113i \(0.967760\pi\)
\(284\) 0 0
\(285\) 10.3804 + 8.65174i 0.614881 + 0.512485i
\(286\) 0 0
\(287\) 3.08028i 0.181823i
\(288\) 0 0
\(289\) 7.30700 0.429824
\(290\) 0 0
\(291\) −22.8403 −1.33892
\(292\) 0 0
\(293\) 28.9057 1.68869 0.844344 0.535801i \(-0.179990\pi\)
0.844344 + 0.535801i \(0.179990\pi\)
\(294\) 0 0
\(295\) 14.8536 17.8214i 0.864809 1.03760i
\(296\) 0 0
\(297\) −7.24374 −0.420324
\(298\) 0 0
\(299\) −0.363057 1.90820i −0.0209962 0.110354i
\(300\) 0 0
\(301\) 2.11477 0.121893
\(302\) 0 0
\(303\) 26.8966 1.54517
\(304\) 0 0
\(305\) −13.1627 + 15.7926i −0.753694 + 0.904284i
\(306\) 0 0
\(307\) 3.66239 0.209024 0.104512 0.994524i \(-0.466672\pi\)
0.104512 + 0.994524i \(0.466672\pi\)
\(308\) 0 0
\(309\) 24.9188i 1.41758i
\(310\) 0 0
\(311\) 8.46706i 0.480123i −0.970758 0.240061i \(-0.922832\pi\)
0.970758 0.240061i \(-0.0771676\pi\)
\(312\) 0 0
\(313\) −18.5693 −1.04960 −0.524800 0.851226i \(-0.675860\pi\)
−0.524800 + 0.851226i \(0.675860\pi\)
\(314\) 0 0
\(315\) 1.70610 2.04699i 0.0961280 0.115335i
\(316\) 0 0
\(317\) 0.673248i 0.0378134i 0.999821 + 0.0189067i \(0.00601854\pi\)
−0.999821 + 0.0189067i \(0.993981\pi\)
\(318\) 0 0
\(319\) 4.67475 0.261736
\(320\) 0 0
\(321\) 34.1974i 1.90871i
\(322\) 0 0
\(323\) −13.5228 −0.752427
\(324\) 0 0
\(325\) 1.99198 0.364864i 0.110495 0.0202390i
\(326\) 0 0
\(327\) 30.0476i 1.66164i
\(328\) 0 0
\(329\) 2.30619i 0.127144i
\(330\) 0 0
\(331\) 11.3823i 0.625630i 0.949814 + 0.312815i \(0.101272\pi\)
−0.949814 + 0.312815i \(0.898728\pi\)
\(332\) 0 0
\(333\) −3.71063 −0.203341
\(334\) 0 0
\(335\) 3.12159 3.74530i 0.170551 0.204627i
\(336\) 0 0
\(337\) 2.41570 0.131592 0.0657959 0.997833i \(-0.479041\pi\)
0.0657959 + 0.997833i \(0.479041\pi\)
\(338\) 0 0
\(339\) −16.4696 −0.894508
\(340\) 0 0
\(341\) 13.0856i 0.708623i
\(342\) 0 0
\(343\) 8.73127i 0.471444i
\(344\) 0 0
\(345\) −20.6576 11.4685i −1.11217 0.617444i
\(346\) 0 0
\(347\) −20.0264 −1.07507 −0.537536 0.843241i \(-0.680645\pi\)
−0.537536 + 0.843241i \(0.680645\pi\)
\(348\) 0 0
\(349\) −22.9116 −1.22643 −0.613215 0.789916i \(-0.710124\pi\)
−0.613215 + 0.789916i \(0.710124\pi\)
\(350\) 0 0
\(351\) 1.02225i 0.0545638i
\(352\) 0 0
\(353\) 28.3834i 1.51070i −0.655324 0.755348i \(-0.727468\pi\)
0.655324 0.755348i \(-0.272532\pi\)
\(354\) 0 0
\(355\) −14.7744 + 17.7264i −0.784144 + 0.940818i
\(356\) 0 0
\(357\) 6.98054i 0.369449i
\(358\) 0 0
\(359\) 13.5509 0.715189 0.357595 0.933877i \(-0.383597\pi\)
0.357595 + 0.933877i \(0.383597\pi\)
\(360\) 0 0
\(361\) −11.4768 −0.604044
\(362\) 0 0
\(363\) 6.08756 0.319514
\(364\) 0 0
\(365\) 6.34287 7.61019i 0.332001 0.398336i
\(366\) 0 0
\(367\) 4.18607i 0.218511i −0.994014 0.109256i \(-0.965153\pi\)
0.994014 0.109256i \(-0.0348467\pi\)
\(368\) 0 0
\(369\) −8.88911 −0.462749
\(370\) 0 0
\(371\) 0.169444i 0.00879710i
\(372\) 0 0
\(373\) 13.2025 0.683599 0.341799 0.939773i \(-0.388964\pi\)
0.341799 + 0.939773i \(0.388964\pi\)
\(374\) 0 0
\(375\) 12.1041 21.4546i 0.625055 1.10791i
\(376\) 0 0
\(377\) 0.659711i 0.0339768i
\(378\) 0 0
\(379\) 7.79915 0.400616 0.200308 0.979733i \(-0.435806\pi\)
0.200308 + 0.979733i \(0.435806\pi\)
\(380\) 0 0
\(381\) −0.839197 −0.0429934
\(382\) 0 0
\(383\) 0.691775i 0.0353480i −0.999844 0.0176740i \(-0.994374\pi\)
0.999844 0.0176740i \(-0.00562611\pi\)
\(384\) 0 0
\(385\) −2.64041 + 3.16797i −0.134568 + 0.161454i
\(386\) 0 0
\(387\) 6.10282i 0.310224i
\(388\) 0 0
\(389\) 8.94180i 0.453367i −0.973968 0.226684i \(-0.927212\pi\)
0.973968 0.226684i \(-0.0727883\pi\)
\(390\) 0 0
\(391\) 23.2278 4.41936i 1.17468 0.223497i
\(392\) 0 0
\(393\) 32.8289i 1.65600i
\(394\) 0 0
\(395\) 5.42874 + 4.52469i 0.273149 + 0.227662i
\(396\) 0 0
\(397\) 7.00315i 0.351478i 0.984437 + 0.175739i \(0.0562315\pi\)
−0.984437 + 0.175739i \(0.943768\pi\)
\(398\) 0 0
\(399\) 3.88350i 0.194418i
\(400\) 0 0
\(401\) 1.06280i 0.0530736i −0.999648 0.0265368i \(-0.991552\pi\)
0.999648 0.0265368i \(-0.00844792\pi\)
\(402\) 0 0
\(403\) 1.84666 0.0919889
\(404\) 0 0
\(405\) −19.1081 15.9260i −0.949487 0.791370i
\(406\) 0 0
\(407\) 5.74266 0.284653
\(408\) 0 0
\(409\) 5.85837 0.289678 0.144839 0.989455i \(-0.453734\pi\)
0.144839 + 0.989455i \(0.453734\pi\)
\(410\) 0 0
\(411\) 18.4621 0.910666
\(412\) 0 0
\(413\) −6.66732 −0.328077
\(414\) 0 0
\(415\) −13.0977 + 15.7146i −0.642939 + 0.771399i
\(416\) 0 0
\(417\) 7.44451i 0.364559i
\(418\) 0 0
\(419\) −30.7667 −1.50305 −0.751525 0.659705i \(-0.770681\pi\)
−0.751525 + 0.659705i \(0.770681\pi\)
\(420\) 0 0
\(421\) 37.3043i 1.81810i −0.416687 0.909050i \(-0.636809\pi\)
0.416687 0.909050i \(-0.363191\pi\)
\(422\) 0 0
\(423\) −6.65524 −0.323589
\(424\) 0 0
\(425\) 4.44135 + 24.2477i 0.215437 + 1.17618i
\(426\) 0 0
\(427\) 5.90834 0.285924
\(428\) 0 0
\(429\) 2.56117i 0.123654i
\(430\) 0 0
\(431\) −18.2987 −0.881416 −0.440708 0.897651i \(-0.645273\pi\)
−0.440708 + 0.897651i \(0.645273\pi\)
\(432\) 0 0
\(433\) −31.1511 −1.49702 −0.748512 0.663121i \(-0.769231\pi\)
−0.748512 + 0.663121i \(0.769231\pi\)
\(434\) 0 0
\(435\) 6.16432 + 5.13778i 0.295557 + 0.246338i
\(436\) 0 0
\(437\) −12.9224 + 2.45863i −0.618161 + 0.117612i
\(438\) 0 0
\(439\) 8.87110i 0.423394i 0.977335 + 0.211697i \(0.0678991\pi\)
−0.977335 + 0.211697i \(0.932101\pi\)
\(440\) 0 0
\(441\) 12.2155 0.581690
\(442\) 0 0
\(443\) 34.1696 1.62344 0.811722 0.584044i \(-0.198530\pi\)
0.811722 + 0.584044i \(0.198530\pi\)
\(444\) 0 0
\(445\) −20.0893 + 24.1032i −0.952325 + 1.14260i
\(446\) 0 0
\(447\) 39.0598i 1.84747i
\(448\) 0 0
\(449\) 16.3702 0.772558 0.386279 0.922382i \(-0.373760\pi\)
0.386279 + 0.922382i \(0.373760\pi\)
\(450\) 0 0
\(451\) 13.7570 0.647792
\(452\) 0 0
\(453\) 37.2458i 1.74996i
\(454\) 0 0
\(455\) −0.447070 0.372620i −0.0209590 0.0174687i
\(456\) 0 0
\(457\) −34.4242 −1.61030 −0.805148 0.593074i \(-0.797914\pi\)
−0.805148 + 0.593074i \(0.797914\pi\)
\(458\) 0 0
\(459\) 12.4435 0.580812
\(460\) 0 0
\(461\) 19.6000 0.912861 0.456430 0.889759i \(-0.349128\pi\)
0.456430 + 0.889759i \(0.349128\pi\)
\(462\) 0 0
\(463\) −12.4580 −0.578970 −0.289485 0.957183i \(-0.593484\pi\)
−0.289485 + 0.957183i \(0.593484\pi\)
\(464\) 0 0
\(465\) 14.3817 17.2552i 0.666935 0.800190i
\(466\) 0 0
\(467\) 9.93867i 0.459907i 0.973202 + 0.229953i \(0.0738574\pi\)
−0.973202 + 0.229953i \(0.926143\pi\)
\(468\) 0 0
\(469\) −1.40119 −0.0647008
\(470\) 0 0
\(471\) 24.5711 1.13217
\(472\) 0 0
\(473\) 9.44487i 0.434276i
\(474\) 0 0
\(475\) −2.47087 13.4898i −0.113371 0.618953i
\(476\) 0 0
\(477\) 0.488984 0.0223890
\(478\) 0 0
\(479\) 39.2013 1.79115 0.895576 0.444908i \(-0.146764\pi\)
0.895576 + 0.444908i \(0.146764\pi\)
\(480\) 0 0
\(481\) 0.810417i 0.0369518i
\(482\) 0 0
\(483\) 1.26916 + 6.67061i 0.0577489 + 0.303523i
\(484\) 0 0
\(485\) 17.8063 + 14.8410i 0.808542 + 0.673896i
\(486\) 0 0
\(487\) 31.2472 1.41594 0.707972 0.706241i \(-0.249610\pi\)
0.707972 + 0.706241i \(0.249610\pi\)
\(488\) 0 0
\(489\) 5.52219 0.249722
\(490\) 0 0
\(491\) 28.2058i 1.27291i −0.771313 0.636456i \(-0.780400\pi\)
0.771313 0.636456i \(-0.219600\pi\)
\(492\) 0 0
\(493\) −8.03041 −0.361672
\(494\) 0 0
\(495\) −9.14215 7.61971i −0.410909 0.342481i
\(496\) 0 0
\(497\) 6.63178 0.297476
\(498\) 0 0
\(499\) 15.7217i 0.703800i −0.936038 0.351900i \(-0.885536\pi\)
0.936038 0.351900i \(-0.114464\pi\)
\(500\) 0 0
\(501\) 4.05402 0.181120
\(502\) 0 0
\(503\) 10.7408i 0.478911i 0.970907 + 0.239455i \(0.0769689\pi\)
−0.970907 + 0.239455i \(0.923031\pi\)
\(504\) 0 0
\(505\) −20.9686 17.4767i −0.933090 0.777703i
\(506\) 0 0
\(507\) −28.2813 −1.25602
\(508\) 0 0
\(509\) −17.3015 −0.766874 −0.383437 0.923567i \(-0.625260\pi\)
−0.383437 + 0.923567i \(0.625260\pi\)
\(510\) 0 0
\(511\) −2.84712 −0.125949
\(512\) 0 0
\(513\) −6.92272 −0.305646
\(514\) 0 0
\(515\) −16.1915 + 19.4266i −0.713484 + 0.856040i
\(516\) 0 0
\(517\) 10.2998 0.452985
\(518\) 0 0
\(519\) 24.8106i 1.08906i
\(520\) 0 0
\(521\) 28.2184i 1.23627i 0.786071 + 0.618136i \(0.212112\pi\)
−0.786071 + 0.618136i \(0.787888\pi\)
\(522\) 0 0
\(523\) 22.2167i 0.971467i 0.874107 + 0.485734i \(0.161448\pi\)
−0.874107 + 0.485734i \(0.838552\pi\)
\(524\) 0 0
\(525\) −6.96350 + 1.27548i −0.303912 + 0.0556664i
\(526\) 0 0
\(527\) 22.4788i 0.979190i
\(528\) 0 0
\(529\) 21.3930 8.44629i 0.930130 0.367230i
\(530\) 0 0
\(531\) 19.2406i 0.834972i
\(532\) 0 0
\(533\) 1.94142i 0.0840922i
\(534\) 0 0
\(535\) −22.2205 + 26.6602i −0.960676 + 1.15262i
\(536\) 0 0
\(537\) 1.35188i 0.0583377i
\(538\) 0 0
\(539\) −18.9050 −0.814296
\(540\) 0 0
\(541\) 35.1024 1.50917 0.754585 0.656202i \(-0.227838\pi\)
0.754585 + 0.656202i \(0.227838\pi\)
\(542\) 0 0
\(543\) 1.16243i 0.0498847i
\(544\) 0 0
\(545\) −19.5241 + 23.4251i −0.836320 + 1.00342i
\(546\) 0 0
\(547\) 13.1595 0.562659 0.281329 0.959611i \(-0.409225\pi\)
0.281329 + 0.959611i \(0.409225\pi\)
\(548\) 0 0
\(549\) 17.0503i 0.727691i
\(550\) 0 0
\(551\) 4.46758 0.190325
\(552\) 0 0
\(553\) 2.03100i 0.0863667i
\(554\) 0 0
\(555\) 7.57251 + 6.31147i 0.321435 + 0.267907i
\(556\) 0 0
\(557\) 22.6673 0.960446 0.480223 0.877146i \(-0.340556\pi\)
0.480223 + 0.877146i \(0.340556\pi\)
\(558\) 0 0
\(559\) 1.33288 0.0563749
\(560\) 0 0
\(561\) 31.1762 1.31626
\(562\) 0 0
\(563\) 40.9106i 1.72418i 0.506759 + 0.862088i \(0.330844\pi\)
−0.506759 + 0.862088i \(0.669156\pi\)
\(564\) 0 0
\(565\) 12.8397 + 10.7015i 0.540171 + 0.450216i
\(566\) 0 0
\(567\) 7.14870i 0.300217i
\(568\) 0 0
\(569\) 37.6655i 1.57902i 0.613737 + 0.789510i \(0.289665\pi\)
−0.613737 + 0.789510i \(0.710335\pi\)
\(570\) 0 0
\(571\) 20.1278 0.842322 0.421161 0.906986i \(-0.361623\pi\)
0.421161 + 0.906986i \(0.361623\pi\)
\(572\) 0 0
\(573\) −28.7634 −1.20161
\(574\) 0 0
\(575\) 8.65273 + 22.3636i 0.360844 + 0.932626i
\(576\) 0 0
\(577\) 18.0377i 0.750918i −0.926839 0.375459i \(-0.877485\pi\)
0.926839 0.375459i \(-0.122515\pi\)
\(578\) 0 0
\(579\) 44.7982i 1.86175i
\(580\) 0 0
\(581\) 5.87914 0.243908
\(582\) 0 0
\(583\) −0.756763 −0.0313419
\(584\) 0 0
\(585\) 1.07531 1.29016i 0.0444586 0.0533416i
\(586\) 0 0
\(587\) −32.6326 −1.34689 −0.673446 0.739236i \(-0.735187\pi\)
−0.673446 + 0.739236i \(0.735187\pi\)
\(588\) 0 0
\(589\) 12.5057i 0.515287i
\(590\) 0 0
\(591\) 33.1517i 1.36368i
\(592\) 0 0
\(593\) 25.4394i 1.04467i 0.852740 + 0.522336i \(0.174939\pi\)
−0.852740 + 0.522336i \(0.825061\pi\)
\(594\) 0 0
\(595\) 4.53576 5.44202i 0.185948 0.223101i
\(596\) 0 0
\(597\) −15.0202 −0.614734
\(598\) 0 0
\(599\) 9.29234i 0.379675i −0.981816 0.189837i \(-0.939204\pi\)
0.981816 0.189837i \(-0.0607961\pi\)
\(600\) 0 0
\(601\) −28.2140 −1.15087 −0.575437 0.817846i \(-0.695168\pi\)
−0.575437 + 0.817846i \(0.695168\pi\)
\(602\) 0 0
\(603\) 4.04356i 0.164667i
\(604\) 0 0
\(605\) −4.74585 3.95553i −0.192946 0.160815i
\(606\) 0 0
\(607\) 4.57912 0.185861 0.0929303 0.995673i \(-0.470377\pi\)
0.0929303 + 0.995673i \(0.470377\pi\)
\(608\) 0 0
\(609\) 2.30619i 0.0934516i
\(610\) 0 0
\(611\) 1.45353i 0.0588036i
\(612\) 0 0
\(613\) 43.8068 1.76934 0.884671 0.466217i \(-0.154383\pi\)
0.884671 + 0.466217i \(0.154383\pi\)
\(614\) 0 0
\(615\) 18.1406 + 15.1196i 0.731498 + 0.609682i
\(616\) 0 0
\(617\) −39.1574 −1.57642 −0.788208 0.615409i \(-0.788991\pi\)
−0.788208 + 0.615409i \(0.788991\pi\)
\(618\) 0 0
\(619\) 41.9315 1.68537 0.842685 0.538407i \(-0.180974\pi\)
0.842685 + 0.538407i \(0.180974\pi\)
\(620\) 0 0
\(621\) 11.8910 2.26241i 0.477170 0.0907872i
\(622\) 0 0
\(623\) 9.01749 0.361278
\(624\) 0 0
\(625\) −23.3770 + 8.86102i −0.935078 + 0.354441i
\(626\) 0 0
\(627\) −17.3443 −0.692665
\(628\) 0 0
\(629\) −9.86490 −0.393339
\(630\) 0 0
\(631\) −1.85343 −0.0737840 −0.0368920 0.999319i \(-0.511746\pi\)
−0.0368920 + 0.999319i \(0.511746\pi\)
\(632\) 0 0
\(633\) 6.02799i 0.239591i
\(634\) 0 0
\(635\) 0.654237 + 0.545287i 0.0259626 + 0.0216391i
\(636\) 0 0
\(637\) 2.66792i 0.105707i
\(638\) 0 0
\(639\) 19.1381i 0.757090i
\(640\) 0 0
\(641\) 31.2121i 1.23280i 0.787432 + 0.616401i \(0.211410\pi\)
−0.787432 + 0.616401i \(0.788590\pi\)
\(642\) 0 0
\(643\) 37.3161i 1.47160i −0.677198 0.735801i \(-0.736806\pi\)
0.677198 0.735801i \(-0.263194\pi\)
\(644\) 0 0
\(645\) 10.3804 12.4544i 0.408727 0.490392i
\(646\) 0 0
\(647\) 20.8936 0.821412 0.410706 0.911768i \(-0.365282\pi\)
0.410706 + 0.911768i \(0.365282\pi\)
\(648\) 0 0
\(649\) 29.7773i 1.16886i
\(650\) 0 0
\(651\) −6.45550 −0.253011
\(652\) 0 0
\(653\) 44.2036i 1.72982i −0.501927 0.864910i \(-0.667375\pi\)
0.501927 0.864910i \(-0.332625\pi\)
\(654\) 0 0
\(655\) −21.3313 + 25.5933i −0.833482 + 1.00001i
\(656\) 0 0
\(657\) 8.21626i 0.320547i
\(658\) 0 0
\(659\) −40.9875 −1.59665 −0.798323 0.602229i \(-0.794279\pi\)
−0.798323 + 0.602229i \(0.794279\pi\)
\(660\) 0 0
\(661\) 22.5000i 0.875150i 0.899182 + 0.437575i \(0.144163\pi\)
−0.899182 + 0.437575i \(0.855837\pi\)
\(662\) 0 0
\(663\) 4.39965i 0.170868i
\(664\) 0 0
\(665\) −2.52339 + 3.02757i −0.0978530 + 0.117404i
\(666\) 0 0
\(667\) −7.67387 + 1.46004i −0.297133 + 0.0565331i
\(668\) 0 0
\(669\) −43.1925 −1.66992
\(670\) 0 0
\(671\) 26.3875i 1.01868i
\(672\) 0 0
\(673\) 17.6567i 0.680615i −0.940314 0.340307i \(-0.889469\pi\)
0.940314 0.340307i \(-0.110531\pi\)
\(674\) 0 0
\(675\) 2.27366 + 12.4131i 0.0875133 + 0.477781i
\(676\) 0 0
\(677\) 41.8438 1.60819 0.804093 0.594503i \(-0.202651\pi\)
0.804093 + 0.594503i \(0.202651\pi\)
\(678\) 0 0
\(679\) 6.66168i 0.255652i
\(680\) 0 0
\(681\) 39.8673i 1.52772i
\(682\) 0 0
\(683\) 35.4804 1.35762 0.678809 0.734315i \(-0.262496\pi\)
0.678809 + 0.734315i \(0.262496\pi\)
\(684\) 0 0
\(685\) −14.3930 11.9961i −0.549928 0.458349i
\(686\) 0 0
\(687\) 59.8721i 2.28426i
\(688\) 0 0
\(689\) 0.106796i 0.00406861i
\(690\) 0 0
\(691\) 42.0356i 1.59911i −0.600592 0.799556i \(-0.705068\pi\)
0.600592 0.799556i \(-0.294932\pi\)
\(692\) 0 0
\(693\) 3.42026i 0.129925i
\(694\) 0 0
\(695\) 4.83724 5.80373i 0.183487 0.220148i
\(696\) 0 0
\(697\) −23.6322 −0.895132
\(698\) 0 0
\(699\) 9.38062i 0.354808i
\(700\) 0 0
\(701\) 41.2075i 1.55639i 0.628025 + 0.778193i \(0.283864\pi\)
−0.628025 + 0.778193i \(0.716136\pi\)
\(702\) 0 0
\(703\) 5.48817 0.206990
\(704\) 0 0
\(705\) 13.5818 + 11.3200i 0.511519 + 0.426336i
\(706\) 0 0
\(707\) 7.84476i 0.295032i
\(708\) 0 0
\(709\) 42.1883i 1.58442i −0.610251 0.792208i \(-0.708931\pi\)
0.610251 0.792208i \(-0.291069\pi\)
\(710\) 0 0
\(711\) 5.86107 0.219807
\(712\) 0 0
\(713\) 4.08696 + 21.4807i 0.153058 + 0.804459i
\(714\) 0 0
\(715\) −1.66418 + 1.99668i −0.0622367 + 0.0746718i
\(716\) 0 0
\(717\) 40.8152i 1.52427i
\(718\) 0 0
\(719\) 34.9606i 1.30381i 0.758301 + 0.651905i \(0.226030\pi\)
−0.758301 + 0.651905i \(0.773970\pi\)
\(720\) 0 0
\(721\) 7.26789 0.270670
\(722\) 0 0
\(723\) 7.95069i 0.295689i
\(724\) 0 0
\(725\) −1.46731 8.01081i −0.0544945 0.297514i
\(726\) 0 0
\(727\) 25.1715i 0.933560i −0.884373 0.466780i \(-0.845414\pi\)
0.884373 0.466780i \(-0.154586\pi\)
\(728\) 0 0
\(729\) −3.94700 −0.146185
\(730\) 0 0
\(731\) 16.2247i 0.600091i
\(732\) 0 0
\(733\) 9.42700 0.348194 0.174097 0.984728i \(-0.444299\pi\)
0.174097 + 0.984728i \(0.444299\pi\)
\(734\) 0 0
\(735\) −24.9289 20.7775i −0.919517 0.766390i
\(736\) 0 0
\(737\) 6.25792i 0.230513i
\(738\) 0 0
\(739\) 43.5175i 1.60082i −0.599455 0.800409i \(-0.704616\pi\)
0.599455 0.800409i \(-0.295384\pi\)
\(740\) 0 0
\(741\) 2.44767i 0.0899174i
\(742\) 0 0
\(743\) 35.2929i 1.29477i −0.762162 0.647386i \(-0.775862\pi\)
0.762162 0.647386i \(-0.224138\pi\)
\(744\) 0 0
\(745\) −25.3800 + 30.4510i −0.929852 + 1.11564i
\(746\) 0 0
\(747\) 16.9661i 0.620757i
\(748\) 0 0
\(749\) 9.97410 0.364446
\(750\) 0 0
\(751\) −23.7239 −0.865699 −0.432849 0.901466i \(-0.642492\pi\)
−0.432849 + 0.901466i \(0.642492\pi\)
\(752\) 0 0
\(753\) 8.41642 0.306712
\(754\) 0 0
\(755\) −24.2013 + 29.0368i −0.880776 + 1.05676i
\(756\) 0 0
\(757\) 5.88600 0.213930 0.106965 0.994263i \(-0.465887\pi\)
0.106965 + 0.994263i \(0.465887\pi\)
\(758\) 0 0
\(759\) 29.7920 5.66827i 1.08138 0.205745i
\(760\) 0 0
\(761\) −9.12950 −0.330944 −0.165472 0.986214i \(-0.552915\pi\)
−0.165472 + 0.986214i \(0.552915\pi\)
\(762\) 0 0
\(763\) 8.76377 0.317270
\(764\) 0 0
\(765\) 15.7046 + 13.0894i 0.567803 + 0.473247i
\(766\) 0 0
\(767\) −4.20223 −0.151734
\(768\) 0 0
\(769\) 5.71892i 0.206230i −0.994669 0.103115i \(-0.967119\pi\)
0.994669 0.103115i \(-0.0328809\pi\)
\(770\) 0 0
\(771\) 2.73992i 0.0986758i
\(772\) 0 0
\(773\) 8.00711 0.287996 0.143998 0.989578i \(-0.454004\pi\)
0.143998 + 0.989578i \(0.454004\pi\)
\(774\) 0 0
\(775\) −22.4239 + 4.10730i −0.805490 + 0.147538i
\(776\) 0 0
\(777\) 2.83303i 0.101634i
\(778\) 0 0
\(779\) 13.1473 0.471053
\(780\) 0 0
\(781\) 29.6185i 1.05983i
\(782\) 0 0
\(783\) −4.11101 −0.146916
\(784\) 0 0
\(785\) −19.1556 15.9656i −0.683692 0.569837i
\(786\) 0 0
\(787\) 10.9386i 0.389917i 0.980811 + 0.194959i \(0.0624573\pi\)
−0.980811 + 0.194959i \(0.937543\pi\)
\(788\) 0 0
\(789\) 22.1568i 0.788801i
\(790\) 0 0
\(791\) 4.80358i 0.170796i
\(792\) 0 0
\(793\) 3.72387 0.132238
\(794\) 0 0
\(795\) −0.997900 0.831720i −0.0353919 0.0294981i
\(796\) 0 0
\(797\) 23.0968 0.818132 0.409066 0.912505i \(-0.365855\pi\)
0.409066 + 0.912505i \(0.365855\pi\)
\(798\) 0 0
\(799\) −17.6933 −0.625944
\(800\) 0 0
\(801\) 26.0228i 0.919469i
\(802\) 0 0
\(803\) 12.7157i 0.448727i