Properties

Label 1400.2.x.b.993.4
Level $1400$
Weight $2$
Character 1400.993
Analytic conductor $11.179$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.x (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 993.4
Character \(\chi\) \(=\) 1400.993
Dual form 1400.2.x.b.657.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.03893 + 1.03893i) q^{3} +(-1.58883 + 2.11557i) q^{7} +0.841261i q^{9} +O(q^{10})\) \(q+(-1.03893 + 1.03893i) q^{3} +(-1.58883 + 2.11557i) q^{7} +0.841261i q^{9} -2.34687 q^{11} +(-1.96436 + 1.96436i) q^{13} +(5.15858 + 5.15858i) q^{17} +3.74821 q^{19} +(-0.547244 - 3.84860i) q^{21} +(-6.08007 - 6.08007i) q^{23} +(-3.99079 - 3.99079i) q^{27} -5.89034i q^{29} +1.56648i q^{31} +(2.43823 - 2.43823i) q^{33} +(-1.53441 + 1.53441i) q^{37} -4.08166i q^{39} +9.51977i q^{41} +(-1.86313 - 1.86313i) q^{43} +(-4.59474 - 4.59474i) q^{47} +(-1.95125 - 6.72254i) q^{49} -10.7188 q^{51} +(-3.88128 - 3.88128i) q^{53} +(-3.89412 + 3.89412i) q^{57} -4.62061 q^{59} +2.00065i q^{61} +(-1.77974 - 1.33662i) q^{63} +(-2.69156 + 2.69156i) q^{67} +12.6335 q^{69} -0.392229 q^{71} +(7.08543 - 7.08543i) q^{73} +(3.72878 - 4.96497i) q^{77} +4.98717i q^{79} +5.76850 q^{81} +(9.36651 - 9.36651i) q^{83} +(6.11964 + 6.11964i) q^{87} -9.83200 q^{89} +(-1.03471 - 7.27677i) q^{91} +(-1.62746 - 1.62746i) q^{93} +(-11.8576 - 11.8576i) q^{97} -1.97433i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 4q^{7} + O(q^{10}) \) \( 24q - 4q^{7} + 8q^{11} + 16q^{21} + 32q^{23} + 8q^{37} - 16q^{43} - 24q^{51} + 16q^{53} - 20q^{63} + 32q^{67} - 32q^{71} + 40q^{77} - 72q^{81} - 64q^{91} - 72q^{93} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.03893 + 1.03893i −0.599825 + 0.599825i −0.940266 0.340441i \(-0.889424\pi\)
0.340441 + 0.940266i \(0.389424\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.58883 + 2.11557i −0.600520 + 0.799609i
\(8\) 0 0
\(9\) 0.841261i 0.280420i
\(10\) 0 0
\(11\) −2.34687 −0.707609 −0.353804 0.935319i \(-0.615112\pi\)
−0.353804 + 0.935319i \(0.615112\pi\)
\(12\) 0 0
\(13\) −1.96436 + 1.96436i −0.544816 + 0.544816i −0.924937 0.380121i \(-0.875882\pi\)
0.380121 + 0.924937i \(0.375882\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.15858 + 5.15858i 1.25114 + 1.25114i 0.955210 + 0.295929i \(0.0956291\pi\)
0.295929 + 0.955210i \(0.404371\pi\)
\(18\) 0 0
\(19\) 3.74821 0.859899 0.429949 0.902853i \(-0.358531\pi\)
0.429949 + 0.902853i \(0.358531\pi\)
\(20\) 0 0
\(21\) −0.547244 3.84860i −0.119419 0.839833i
\(22\) 0 0
\(23\) −6.08007 6.08007i −1.26778 1.26778i −0.947232 0.320550i \(-0.896132\pi\)
−0.320550 0.947232i \(-0.603868\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −3.99079 3.99079i −0.768028 0.768028i
\(28\) 0 0
\(29\) 5.89034i 1.09381i −0.837195 0.546905i \(-0.815806\pi\)
0.837195 0.546905i \(-0.184194\pi\)
\(30\) 0 0
\(31\) 1.56648i 0.281348i 0.990056 + 0.140674i \(0.0449270\pi\)
−0.990056 + 0.140674i \(0.955073\pi\)
\(32\) 0 0
\(33\) 2.43823 2.43823i 0.424441 0.424441i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −1.53441 + 1.53441i −0.252256 + 0.252256i −0.821895 0.569639i \(-0.807083\pi\)
0.569639 + 0.821895i \(0.307083\pi\)
\(38\) 0 0
\(39\) 4.08166i 0.653588i
\(40\) 0 0
\(41\) 9.51977i 1.48674i 0.668882 + 0.743369i \(0.266773\pi\)
−0.668882 + 0.743369i \(0.733227\pi\)
\(42\) 0 0
\(43\) −1.86313 1.86313i −0.284125 0.284125i 0.550626 0.834752i \(-0.314389\pi\)
−0.834752 + 0.550626i \(0.814389\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.59474 4.59474i −0.670212 0.670212i 0.287553 0.957765i \(-0.407158\pi\)
−0.957765 + 0.287553i \(0.907158\pi\)
\(48\) 0 0
\(49\) −1.95125 6.72254i −0.278750 0.960364i
\(50\) 0 0
\(51\) −10.7188 −1.50093
\(52\) 0 0
\(53\) −3.88128 3.88128i −0.533135 0.533135i 0.388369 0.921504i \(-0.373039\pi\)
−0.921504 + 0.388369i \(0.873039\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −3.89412 + 3.89412i −0.515789 + 0.515789i
\(58\) 0 0
\(59\) −4.62061 −0.601552 −0.300776 0.953695i \(-0.597246\pi\)
−0.300776 + 0.953695i \(0.597246\pi\)
\(60\) 0 0
\(61\) 2.00065i 0.256156i 0.991764 + 0.128078i \(0.0408808\pi\)
−0.991764 + 0.128078i \(0.959119\pi\)
\(62\) 0 0
\(63\) −1.77974 1.33662i −0.224227 0.168398i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −2.69156 + 2.69156i −0.328827 + 0.328827i −0.852140 0.523314i \(-0.824696\pi\)
0.523314 + 0.852140i \(0.324696\pi\)
\(68\) 0 0
\(69\) 12.6335 1.52089
\(70\) 0 0
\(71\) −0.392229 −0.0465491 −0.0232745 0.999729i \(-0.507409\pi\)
−0.0232745 + 0.999729i \(0.507409\pi\)
\(72\) 0 0
\(73\) 7.08543 7.08543i 0.829287 0.829287i −0.158131 0.987418i \(-0.550547\pi\)
0.987418 + 0.158131i \(0.0505468\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.72878 4.96497i 0.424934 0.565811i
\(78\) 0 0
\(79\) 4.98717i 0.561100i 0.959839 + 0.280550i \(0.0905169\pi\)
−0.959839 + 0.280550i \(0.909483\pi\)
\(80\) 0 0
\(81\) 5.76850 0.640944
\(82\) 0 0
\(83\) 9.36651 9.36651i 1.02811 1.02811i 0.0285148 0.999593i \(-0.490922\pi\)
0.999593 0.0285148i \(-0.00907776\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 6.11964 + 6.11964i 0.656094 + 0.656094i
\(88\) 0 0
\(89\) −9.83200 −1.04219 −0.521095 0.853499i \(-0.674476\pi\)
−0.521095 + 0.853499i \(0.674476\pi\)
\(90\) 0 0
\(91\) −1.03471 7.27677i −0.108467 0.762813i
\(92\) 0 0
\(93\) −1.62746 1.62746i −0.168760 0.168760i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −11.8576 11.8576i −1.20396 1.20396i −0.972952 0.231006i \(-0.925798\pi\)
−0.231006 0.972952i \(-0.574202\pi\)
\(98\) 0 0
\(99\) 1.97433i 0.198428i
\(100\) 0 0
\(101\) 8.41529i 0.837353i −0.908135 0.418676i \(-0.862494\pi\)
0.908135 0.418676i \(-0.137506\pi\)
\(102\) 0 0
\(103\) −8.77874 + 8.77874i −0.864995 + 0.864995i −0.991913 0.126918i \(-0.959491\pi\)
0.126918 + 0.991913i \(0.459491\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −10.3741 + 10.3741i −1.00290 + 1.00290i −0.00290471 + 0.999996i \(0.500925\pi\)
−0.999996 + 0.00290471i \(0.999075\pi\)
\(108\) 0 0
\(109\) 4.92724i 0.471944i −0.971760 0.235972i \(-0.924173\pi\)
0.971760 0.235972i \(-0.0758273\pi\)
\(110\) 0 0
\(111\) 3.18828i 0.302618i
\(112\) 0 0
\(113\) 3.79963 + 3.79963i 0.357439 + 0.357439i 0.862868 0.505429i \(-0.168666\pi\)
−0.505429 + 0.862868i \(0.668666\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.65254 1.65254i −0.152777 0.152777i
\(118\) 0 0
\(119\) −19.1094 + 2.71723i −1.75176 + 0.249088i
\(120\) 0 0
\(121\) −5.49219 −0.499290
\(122\) 0 0
\(123\) −9.89034 9.89034i −0.891782 0.891782i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0.777755 0.777755i 0.0690146 0.0690146i −0.671757 0.740772i \(-0.734460\pi\)
0.740772 + 0.671757i \(0.234460\pi\)
\(128\) 0 0
\(129\) 3.87132 0.340851
\(130\) 0 0
\(131\) 11.0373i 0.964336i −0.876079 0.482168i \(-0.839849\pi\)
0.876079 0.482168i \(-0.160151\pi\)
\(132\) 0 0
\(133\) −5.95526 + 7.92959i −0.516387 + 0.687583i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.65313 + 2.65313i −0.226672 + 0.226672i −0.811301 0.584629i \(-0.801240\pi\)
0.584629 + 0.811301i \(0.301240\pi\)
\(138\) 0 0
\(139\) 7.15451 0.606838 0.303419 0.952857i \(-0.401872\pi\)
0.303419 + 0.952857i \(0.401872\pi\)
\(140\) 0 0
\(141\) 9.54720 0.804019
\(142\) 0 0
\(143\) 4.61011 4.61011i 0.385516 0.385516i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 9.01144 + 4.95702i 0.743251 + 0.408848i
\(148\) 0 0
\(149\) 12.2552i 1.00399i −0.864872 0.501993i \(-0.832600\pi\)
0.864872 0.501993i \(-0.167400\pi\)
\(150\) 0 0
\(151\) −13.2221 −1.07600 −0.537998 0.842946i \(-0.680819\pi\)
−0.537998 + 0.842946i \(0.680819\pi\)
\(152\) 0 0
\(153\) −4.33971 + 4.33971i −0.350845 + 0.350845i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 8.35401 + 8.35401i 0.666723 + 0.666723i 0.956956 0.290233i \(-0.0937329\pi\)
−0.290233 + 0.956956i \(0.593733\pi\)
\(158\) 0 0
\(159\) 8.06474 0.639576
\(160\) 0 0
\(161\) 22.5230 3.20261i 1.77506 0.252401i
\(162\) 0 0
\(163\) −2.21768 2.21768i −0.173702 0.173702i 0.614902 0.788604i \(-0.289196\pi\)
−0.788604 + 0.614902i \(0.789196\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 15.1934 + 15.1934i 1.17570 + 1.17570i 0.980829 + 0.194871i \(0.0624288\pi\)
0.194871 + 0.980829i \(0.437571\pi\)
\(168\) 0 0
\(169\) 5.28257i 0.406352i
\(170\) 0 0
\(171\) 3.15322i 0.241133i
\(172\) 0 0
\(173\) −4.60458 + 4.60458i −0.350080 + 0.350080i −0.860139 0.510059i \(-0.829623\pi\)
0.510059 + 0.860139i \(0.329623\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 4.80047 4.80047i 0.360826 0.360826i
\(178\) 0 0
\(179\) 11.5721i 0.864939i 0.901648 + 0.432470i \(0.142358\pi\)
−0.901648 + 0.432470i \(0.857642\pi\)
\(180\) 0 0
\(181\) 5.28640i 0.392935i 0.980510 + 0.196467i \(0.0629470\pi\)
−0.980510 + 0.196467i \(0.937053\pi\)
\(182\) 0 0
\(183\) −2.07852 2.07852i −0.153649 0.153649i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −12.1065 12.1065i −0.885317 0.885317i
\(188\) 0 0
\(189\) 14.7835 2.10211i 1.07534 0.152906i
\(190\) 0 0
\(191\) −11.6115 −0.840179 −0.420089 0.907483i \(-0.638001\pi\)
−0.420089 + 0.907483i \(0.638001\pi\)
\(192\) 0 0
\(193\) 17.6369 + 17.6369i 1.26954 + 1.26954i 0.946328 + 0.323207i \(0.104761\pi\)
0.323207 + 0.946328i \(0.395239\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 17.2130 17.2130i 1.22637 1.22637i 0.261049 0.965325i \(-0.415931\pi\)
0.965325 0.261049i \(-0.0840685\pi\)
\(198\) 0 0
\(199\) 6.95883 0.493299 0.246649 0.969105i \(-0.420670\pi\)
0.246649 + 0.969105i \(0.420670\pi\)
\(200\) 0 0
\(201\) 5.59267i 0.394477i
\(202\) 0 0
\(203\) 12.4614 + 9.35874i 0.874620 + 0.656855i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 5.11492 5.11492i 0.355512 0.355512i
\(208\) 0 0
\(209\) −8.79658 −0.608472
\(210\) 0 0
\(211\) 9.28431 0.639159 0.319579 0.947560i \(-0.396458\pi\)
0.319579 + 0.947560i \(0.396458\pi\)
\(212\) 0 0
\(213\) 0.407498 0.407498i 0.0279213 0.0279213i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −3.31400 2.48887i −0.224969 0.168955i
\(218\) 0 0
\(219\) 14.7225i 0.994854i
\(220\) 0 0
\(221\) −20.2666 −1.36328
\(222\) 0 0
\(223\) −4.77582 + 4.77582i −0.319813 + 0.319813i −0.848695 0.528882i \(-0.822611\pi\)
0.528882 + 0.848695i \(0.322611\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2.49990 2.49990i −0.165925 0.165925i 0.619261 0.785185i \(-0.287432\pi\)
−0.785185 + 0.619261i \(0.787432\pi\)
\(228\) 0 0
\(229\) −18.0694 −1.19406 −0.597031 0.802218i \(-0.703653\pi\)
−0.597031 + 0.802218i \(0.703653\pi\)
\(230\) 0 0
\(231\) 1.28431 + 9.03217i 0.0845016 + 0.594273i
\(232\) 0 0
\(233\) −9.14278 9.14278i −0.598963 0.598963i 0.341073 0.940037i \(-0.389210\pi\)
−0.940037 + 0.341073i \(0.889210\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −5.18130 5.18130i −0.336562 0.336562i
\(238\) 0 0
\(239\) 11.3719i 0.735590i −0.929907 0.367795i \(-0.880113\pi\)
0.929907 0.367795i \(-0.119887\pi\)
\(240\) 0 0
\(241\) 19.6361i 1.26488i 0.774611 + 0.632438i \(0.217946\pi\)
−0.774611 + 0.632438i \(0.782054\pi\)
\(242\) 0 0
\(243\) 5.97932 5.97932i 0.383574 0.383574i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −7.36284 + 7.36284i −0.468486 + 0.468486i
\(248\) 0 0
\(249\) 19.4622i 1.23337i
\(250\) 0 0
\(251\) 26.2420i 1.65638i 0.560447 + 0.828190i \(0.310629\pi\)
−0.560447 + 0.828190i \(0.689371\pi\)
\(252\) 0 0
\(253\) 14.2691 + 14.2691i 0.897094 + 0.897094i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.93157 + 1.93157i 0.120488 + 0.120488i 0.764780 0.644292i \(-0.222848\pi\)
−0.644292 + 0.764780i \(0.722848\pi\)
\(258\) 0 0
\(259\) −0.808236 5.68406i −0.0502213 0.353191i
\(260\) 0 0
\(261\) 4.95532 0.306726
\(262\) 0 0
\(263\) −2.64248 2.64248i −0.162942 0.162942i 0.620927 0.783869i \(-0.286757\pi\)
−0.783869 + 0.620927i \(0.786757\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 10.2147 10.2147i 0.625131 0.625131i
\(268\) 0 0
\(269\) 1.17948 0.0719143 0.0359572 0.999353i \(-0.488552\pi\)
0.0359572 + 0.999353i \(0.488552\pi\)
\(270\) 0 0
\(271\) 14.7880i 0.898306i 0.893455 + 0.449153i \(0.148274\pi\)
−0.893455 + 0.449153i \(0.851726\pi\)
\(272\) 0 0
\(273\) 8.63502 + 6.48505i 0.522615 + 0.392493i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −11.6478 + 11.6478i −0.699848 + 0.699848i −0.964378 0.264529i \(-0.914783\pi\)
0.264529 + 0.964378i \(0.414783\pi\)
\(278\) 0 0
\(279\) −1.31782 −0.0788957
\(280\) 0 0
\(281\) 20.2153 1.20594 0.602971 0.797763i \(-0.293983\pi\)
0.602971 + 0.797763i \(0.293983\pi\)
\(282\) 0 0
\(283\) −5.53654 + 5.53654i −0.329113 + 0.329113i −0.852249 0.523136i \(-0.824762\pi\)
0.523136 + 0.852249i \(0.324762\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −20.1397 15.1253i −1.18881 0.892816i
\(288\) 0 0
\(289\) 36.2218i 2.13070i
\(290\) 0 0
\(291\) 24.6384 1.44433
\(292\) 0 0
\(293\) 1.12050 1.12050i 0.0654601 0.0654601i −0.673619 0.739079i \(-0.735261\pi\)
0.739079 + 0.673619i \(0.235261\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 9.36588 + 9.36588i 0.543463 + 0.543463i
\(298\) 0 0
\(299\) 23.8869 1.38141
\(300\) 0 0
\(301\) 6.90179 0.981388i 0.397812 0.0565662i
\(302\) 0 0
\(303\) 8.74288 + 8.74288i 0.502265 + 0.502265i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 9.43044 + 9.43044i 0.538224 + 0.538224i 0.923007 0.384783i \(-0.125724\pi\)
−0.384783 + 0.923007i \(0.625724\pi\)
\(308\) 0 0
\(309\) 18.2409i 1.03769i
\(310\) 0 0
\(311\) 14.6035i 0.828090i 0.910256 + 0.414045i \(0.135884\pi\)
−0.910256 + 0.414045i \(0.864116\pi\)
\(312\) 0 0
\(313\) 7.05535 7.05535i 0.398792 0.398792i −0.479015 0.877807i \(-0.659006\pi\)
0.877807 + 0.479015i \(0.159006\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 11.2538 11.2538i 0.632075 0.632075i −0.316513 0.948588i \(-0.602512\pi\)
0.948588 + 0.316513i \(0.102512\pi\)
\(318\) 0 0
\(319\) 13.8239i 0.773989i
\(320\) 0 0
\(321\) 21.5558i 1.20313i
\(322\) 0 0
\(323\) 19.3354 + 19.3354i 1.07585 + 1.07585i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 5.11904 + 5.11904i 0.283084 + 0.283084i
\(328\) 0 0
\(329\) 17.0207 2.42023i 0.938383 0.133432i
\(330\) 0 0
\(331\) −33.6643 −1.85036 −0.925179 0.379531i \(-0.876085\pi\)
−0.925179 + 0.379531i \(0.876085\pi\)
\(332\) 0 0
\(333\) −1.29084 1.29084i −0.0707376 0.0707376i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −12.8298 + 12.8298i −0.698885 + 0.698885i −0.964170 0.265285i \(-0.914534\pi\)
0.265285 + 0.964170i \(0.414534\pi\)
\(338\) 0 0
\(339\) −7.89507 −0.428802
\(340\) 0 0
\(341\) 3.67633i 0.199085i
\(342\) 0 0
\(343\) 17.3222 + 6.55296i 0.935311 + 0.353826i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 20.6439 20.6439i 1.10822 1.10822i 0.114837 0.993384i \(-0.463365\pi\)
0.993384 0.114837i \(-0.0366345\pi\)
\(348\) 0 0
\(349\) −29.3356 −1.57030 −0.785150 0.619306i \(-0.787414\pi\)
−0.785150 + 0.619306i \(0.787414\pi\)
\(350\) 0 0
\(351\) 15.6787 0.836867
\(352\) 0 0
\(353\) −16.5837 + 16.5837i −0.882662 + 0.882662i −0.993805 0.111142i \(-0.964549\pi\)
0.111142 + 0.993805i \(0.464549\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 17.0303 22.6763i 0.901338 1.20016i
\(358\) 0 0
\(359\) 30.4050i 1.60472i 0.596843 + 0.802358i \(0.296421\pi\)
−0.596843 + 0.802358i \(0.703579\pi\)
\(360\) 0 0
\(361\) −4.95092 −0.260575
\(362\) 0 0
\(363\) 5.70598 5.70598i 0.299486 0.299486i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −13.6007 13.6007i −0.709950 0.709950i 0.256574 0.966525i \(-0.417406\pi\)
−0.966525 + 0.256574i \(0.917406\pi\)
\(368\) 0 0
\(369\) −8.00861 −0.416911
\(370\) 0 0
\(371\) 14.3778 2.04443i 0.746459 0.106141i
\(372\) 0 0
\(373\) −13.8626 13.8626i −0.717776 0.717776i 0.250373 0.968149i \(-0.419447\pi\)
−0.968149 + 0.250373i \(0.919447\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 11.5708 + 11.5708i 0.595925 + 0.595925i
\(378\) 0 0
\(379\) 11.8896i 0.610727i 0.952236 + 0.305363i \(0.0987779\pi\)
−0.952236 + 0.305363i \(0.901222\pi\)
\(380\) 0 0
\(381\) 1.61606i 0.0827934i
\(382\) 0 0
\(383\) −16.5186 + 16.5186i −0.844059 + 0.844059i −0.989384 0.145325i \(-0.953577\pi\)
0.145325 + 0.989384i \(0.453577\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.56738 1.56738i 0.0796745 0.0796745i
\(388\) 0 0
\(389\) 9.62098i 0.487803i −0.969800 0.243902i \(-0.921573\pi\)
0.969800 0.243902i \(-0.0784274\pi\)
\(390\) 0 0
\(391\) 62.7290i 3.17234i
\(392\) 0 0
\(393\) 11.4670 + 11.4670i 0.578433 + 0.578433i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 17.5393 + 17.5393i 0.880270 + 0.880270i 0.993562 0.113292i \(-0.0361394\pi\)
−0.113292 + 0.993562i \(0.536139\pi\)
\(398\) 0 0
\(399\) −2.05119 14.4254i −0.102688 0.722171i
\(400\) 0 0
\(401\) −14.2238 −0.710302 −0.355151 0.934809i \(-0.615571\pi\)
−0.355151 + 0.934809i \(0.615571\pi\)
\(402\) 0 0
\(403\) −3.07713 3.07713i −0.153283 0.153283i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.60107 3.60107i 0.178498 0.178498i
\(408\) 0 0
\(409\) 14.2602 0.705123 0.352562 0.935789i \(-0.385311\pi\)
0.352562 + 0.935789i \(0.385311\pi\)
\(410\) 0 0
\(411\) 5.51281i 0.271927i
\(412\) 0 0
\(413\) 7.34135 9.77520i 0.361244 0.481006i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −7.43302 + 7.43302i −0.363996 + 0.363996i
\(418\) 0 0
\(419\) −13.5802 −0.663434 −0.331717 0.943379i \(-0.607628\pi\)
−0.331717 + 0.943379i \(0.607628\pi\)
\(420\) 0 0
\(421\) −12.7805 −0.622884 −0.311442 0.950265i \(-0.600812\pi\)
−0.311442 + 0.950265i \(0.600812\pi\)
\(422\) 0 0
\(423\) 3.86537 3.86537i 0.187941 0.187941i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −4.23250 3.17868i −0.204825 0.153827i
\(428\) 0 0
\(429\) 9.57913i 0.462485i
\(430\) 0 0
\(431\) 37.7947 1.82051 0.910254 0.414049i \(-0.135886\pi\)
0.910254 + 0.414049i \(0.135886\pi\)
\(432\) 0 0
\(433\) −14.2122 + 14.2122i −0.682996 + 0.682996i −0.960674 0.277678i \(-0.910435\pi\)
0.277678 + 0.960674i \(0.410435\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −22.7894 22.7894i −1.09016 1.09016i
\(438\) 0 0
\(439\) −27.7697 −1.32538 −0.662688 0.748896i \(-0.730584\pi\)
−0.662688 + 0.748896i \(0.730584\pi\)
\(440\) 0 0
\(441\) 5.65541 1.64151i 0.269305 0.0781673i
\(442\) 0 0
\(443\) −11.8951 11.8951i −0.565152 0.565152i 0.365615 0.930766i \(-0.380859\pi\)
−0.930766 + 0.365615i \(0.880859\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 12.7323 + 12.7323i 0.602216 + 0.602216i
\(448\) 0 0
\(449\) 3.92227i 0.185104i −0.995708 0.0925518i \(-0.970498\pi\)
0.995708 0.0925518i \(-0.0295024\pi\)
\(450\) 0 0
\(451\) 22.3417i 1.05203i
\(452\) 0 0
\(453\) 13.7367 13.7367i 0.645409 0.645409i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −17.6596 + 17.6596i −0.826083 + 0.826083i −0.986972 0.160889i \(-0.948564\pi\)
0.160889 + 0.986972i \(0.448564\pi\)
\(458\) 0 0
\(459\) 41.1736i 1.92182i
\(460\) 0 0
\(461\) 0.616064i 0.0286930i 0.999897 + 0.0143465i \(0.00456678\pi\)
−0.999897 + 0.0143465i \(0.995433\pi\)
\(462\) 0 0
\(463\) 11.9726 + 11.9726i 0.556413 + 0.556413i 0.928284 0.371871i \(-0.121284\pi\)
−0.371871 + 0.928284i \(0.621284\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 12.8767 + 12.8767i 0.595861 + 0.595861i 0.939208 0.343348i \(-0.111561\pi\)
−0.343348 + 0.939208i \(0.611561\pi\)
\(468\) 0 0
\(469\) −1.41775 9.97061i −0.0654658 0.460400i
\(470\) 0 0
\(471\) −17.3584 −0.799834
\(472\) 0 0
\(473\) 4.37254 + 4.37254i 0.201050 + 0.201050i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 3.26517 3.26517i 0.149502 0.149502i
\(478\) 0 0
\(479\) 8.34016 0.381072 0.190536 0.981680i \(-0.438977\pi\)
0.190536 + 0.981680i \(0.438977\pi\)
\(480\) 0 0
\(481\) 6.02827i 0.274866i
\(482\) 0 0
\(483\) −20.0724 + 26.7270i −0.913328 + 1.21612i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 6.90541 6.90541i 0.312914 0.312914i −0.533123 0.846037i \(-0.678982\pi\)
0.846037 + 0.533123i \(0.178982\pi\)
\(488\) 0 0
\(489\) 4.60801 0.208381
\(490\) 0 0
\(491\) 25.1783 1.13628 0.568140 0.822932i \(-0.307663\pi\)
0.568140 + 0.822932i \(0.307663\pi\)
\(492\) 0 0
\(493\) 30.3858 30.3858i 1.36851 1.36851i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.623185 0.829788i 0.0279537 0.0372211i
\(498\) 0 0
\(499\) 20.8907i 0.935197i −0.883941 0.467599i \(-0.845119\pi\)
0.883941 0.467599i \(-0.154881\pi\)
\(500\) 0 0
\(501\) −31.5696 −1.41043
\(502\) 0 0
\(503\) 0.585795 0.585795i 0.0261193 0.0261193i −0.693927 0.720046i \(-0.744121\pi\)
0.720046 + 0.693927i \(0.244121\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −5.48821 5.48821i −0.243740 0.243740i
\(508\) 0 0
\(509\) 38.2153 1.69386 0.846932 0.531701i \(-0.178447\pi\)
0.846932 + 0.531701i \(0.178447\pi\)
\(510\) 0 0
\(511\) 3.73218 + 26.2472i 0.165102 + 1.16111i
\(512\) 0 0
\(513\) −14.9583 14.9583i −0.660426 0.660426i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 10.7833 + 10.7833i 0.474248 + 0.474248i
\(518\) 0 0
\(519\) 9.56765i 0.419973i
\(520\) 0 0
\(521\) 8.40522i 0.368239i −0.982904 0.184120i \(-0.941057\pi\)
0.982904 0.184120i \(-0.0589434\pi\)
\(522\) 0 0
\(523\) 14.1989 14.1989i 0.620876 0.620876i −0.324879 0.945755i \(-0.605324\pi\)
0.945755 + 0.324879i \(0.105324\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.08081 + 8.08081i −0.352006 + 0.352006i
\(528\) 0 0
\(529\) 50.9344i 2.21454i
\(530\) 0 0
\(531\) 3.88713i 0.168687i
\(532\) 0 0
\(533\) −18.7003 18.7003i −0.809998 0.809998i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −12.0226 12.0226i −0.518812 0.518812i
\(538\) 0 0
\(539\) 4.57934 + 15.7770i 0.197246 + 0.679562i
\(540\) 0 0
\(541\) −38.9363 −1.67400 −0.837001 0.547202i \(-0.815693\pi\)
−0.837001 + 0.547202i \(0.815693\pi\)
\(542\) 0 0
\(543\) −5.49218 5.49218i −0.235692 0.235692i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −2.30390 + 2.30390i −0.0985078 + 0.0985078i −0.754643 0.656135i \(-0.772190\pi\)
0.656135 + 0.754643i \(0.272190\pi\)
\(548\) 0 0
\(549\) −1.68306 −0.0718314
\(550\) 0 0
\(551\) 22.0783i 0.940565i
\(552\) 0 0
\(553\) −10.5507 7.92375i −0.448661 0.336952i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −7.69913 + 7.69913i −0.326223 + 0.326223i −0.851148 0.524926i \(-0.824093\pi\)
0.524926 + 0.851148i \(0.324093\pi\)
\(558\) 0 0
\(559\) 7.31974 0.309592
\(560\) 0 0
\(561\) 25.1556 1.06207
\(562\) 0 0
\(563\) −11.8855 + 11.8855i −0.500914 + 0.500914i −0.911722 0.410808i \(-0.865247\pi\)
0.410808 + 0.911722i \(0.365247\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −9.16515 + 12.2036i −0.384900 + 0.512505i
\(568\) 0 0
\(569\) 3.16924i 0.132861i −0.997791 0.0664307i \(-0.978839\pi\)
0.997791 0.0664307i \(-0.0211611\pi\)
\(570\) 0 0
\(571\) −24.8492 −1.03991 −0.519953 0.854195i \(-0.674050\pi\)
−0.519953 + 0.854195i \(0.674050\pi\)
\(572\) 0 0
\(573\) 12.0635 12.0635i 0.503960 0.503960i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −29.2688 29.2688i −1.21848 1.21848i −0.968166 0.250309i \(-0.919468\pi\)
−0.250309 0.968166i \(-0.580532\pi\)
\(578\) 0 0
\(579\) −36.6470 −1.52300
\(580\) 0 0
\(581\) 4.93372 + 34.6973i 0.204685 + 1.43948i
\(582\) 0 0
\(583\) 9.10888 + 9.10888i 0.377251 + 0.377251i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −16.3313 16.3313i −0.674065 0.674065i 0.284586 0.958651i \(-0.408144\pi\)
−0.958651 + 0.284586i \(0.908144\pi\)
\(588\) 0 0
\(589\) 5.87150i 0.241931i
\(590\) 0 0
\(591\) 35.7661i 1.47122i
\(592\) 0 0
\(593\) −17.5540 + 17.5540i −0.720858 + 0.720858i −0.968780 0.247922i \(-0.920252\pi\)
0.247922 + 0.968780i \(0.420252\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −7.22972 + 7.22972i −0.295893 + 0.295893i
\(598\) 0 0
\(599\) 21.4754i 0.877461i −0.898619 0.438731i \(-0.855428\pi\)
0.898619 0.438731i \(-0.144572\pi\)
\(600\) 0 0
\(601\) 32.4373i 1.32314i 0.749882 + 0.661572i \(0.230110\pi\)
−0.749882 + 0.661572i \(0.769890\pi\)
\(602\) 0 0
\(603\) −2.26431 2.26431i −0.0922096 0.0922096i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 13.4507 + 13.4507i 0.545947 + 0.545947i 0.925266 0.379319i \(-0.123842\pi\)
−0.379319 + 0.925266i \(0.623842\pi\)
\(608\) 0 0
\(609\) −22.6696 + 3.22346i −0.918617 + 0.130621i
\(610\) 0 0
\(611\) 18.0515 0.730284
\(612\) 0 0
\(613\) 1.66986 + 1.66986i 0.0674449 + 0.0674449i 0.740025 0.672580i \(-0.234814\pi\)
−0.672580 + 0.740025i \(0.734814\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 16.0944 16.0944i 0.647938 0.647938i −0.304556 0.952494i \(-0.598508\pi\)
0.952494 + 0.304556i \(0.0985082\pi\)
\(618\) 0 0
\(619\) −0.973019 −0.0391089 −0.0195545 0.999809i \(-0.506225\pi\)
−0.0195545 + 0.999809i \(0.506225\pi\)
\(620\) 0 0
\(621\) 48.5285i 1.94738i
\(622\) 0 0
\(623\) 15.6213 20.8003i 0.625856 0.833345i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 9.13900 9.13900i 0.364977 0.364977i
\(628\) 0 0
\(629\) −15.8308 −0.631213
\(630\) 0 0
\(631\) 17.4830 0.695987 0.347994 0.937497i \(-0.386863\pi\)
0.347994 + 0.937497i \(0.386863\pi\)
\(632\) 0 0
\(633\) −9.64573 + 9.64573i −0.383383 + 0.383383i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 17.0385 + 9.37254i 0.675089 + 0.371353i
\(638\) 0 0
\(639\) 0.329967i 0.0130533i
\(640\) 0 0
\(641\) −25.0710 −0.990244 −0.495122 0.868823i \(-0.664877\pi\)
−0.495122 + 0.868823i \(0.664877\pi\)
\(642\) 0 0
\(643\) 3.86619 3.86619i 0.152468 0.152468i −0.626752 0.779219i \(-0.715616\pi\)
0.779219 + 0.626752i \(0.215616\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −24.4727 24.4727i −0.962119 0.962119i 0.0371889 0.999308i \(-0.488160\pi\)
−0.999308 + 0.0371889i \(0.988160\pi\)
\(648\) 0 0
\(649\) 10.8440 0.425663
\(650\) 0 0
\(651\) 6.02875 0.857248i 0.236285 0.0335982i
\(652\) 0 0
\(653\) −23.1478 23.1478i −0.905845 0.905845i 0.0900885 0.995934i \(-0.471285\pi\)
−0.995934 + 0.0900885i \(0.971285\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 5.96070 + 5.96070i 0.232549 + 0.232549i
\(658\) 0 0
\(659\) 36.1548i 1.40839i −0.710006 0.704195i \(-0.751308\pi\)
0.710006 0.704195i \(-0.248692\pi\)
\(660\) 0 0
\(661\) 33.4541i 1.30121i −0.759415 0.650606i \(-0.774515\pi\)
0.759415 0.650606i \(-0.225485\pi\)
\(662\) 0 0
\(663\) 21.0555 21.0555i 0.817729 0.817729i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −35.8137 + 35.8137i −1.38671 + 1.38671i
\(668\) 0 0
\(669\) 9.92347i 0.383663i
\(670\) 0 0
\(671\) 4.69526i 0.181259i
\(672\) 0 0
\(673\) 6.30998 + 6.30998i 0.243232 + 0.243232i 0.818186 0.574954i \(-0.194980\pi\)
−0.574954 + 0.818186i \(0.694980\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.88730 6.88730i −0.264700 0.264700i 0.562260 0.826960i \(-0.309932\pi\)
−0.826960 + 0.562260i \(0.809932\pi\)
\(678\) 0 0
\(679\) 43.9253 6.24588i 1.68570 0.239695i
\(680\) 0 0
\(681\) 5.19444 0.199051
\(682\) 0 0
\(683\) −1.06740 1.06740i −0.0408430 0.0408430i 0.686390 0.727233i \(-0.259194\pi\)
−0.727233 + 0.686390i \(0.759194\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 18.7728 18.7728i 0.716228 0.716228i
\(688\) 0 0
\(689\) 15.2485 0.580921
\(690\) 0 0
\(691\) 43.8638i 1.66866i 0.551267 + 0.834329i \(0.314145\pi\)
−0.551267 + 0.834329i \(0.685855\pi\)
\(692\) 0 0
\(693\) 4.17683 + 3.13687i 0.158665 + 0.119160i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −49.1085 + 49.1085i −1.86012 + 1.86012i
\(698\) 0 0
\(699\) 18.9974 0.718546
\(700\) 0 0
\(701\) −36.6200 −1.38312 −0.691559 0.722320i \(-0.743076\pi\)
−0.691559 + 0.722320i \(0.743076\pi\)
\(702\) 0 0
\(703\) −5.75130 + 5.75130i −0.216914 + 0.216914i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 17.8031 + 13.3705i 0.669555 + 0.502848i
\(708\) 0 0
\(709\) 30.7975i 1.15662i −0.815816 0.578311i \(-0.803712\pi\)
0.815816 0.578311i \(-0.196288\pi\)
\(710\) 0 0
\(711\) −4.19551 −0.157344
\(712\) 0 0
\(713\) 9.52431 9.52431i 0.356688 0.356688i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 11.8146 + 11.8146i 0.441225 + 0.441225i
\(718\) 0 0
\(719\) 36.9703 1.37876 0.689379 0.724401i \(-0.257883\pi\)
0.689379 + 0.724401i \(0.257883\pi\)
\(720\) 0 0
\(721\) −4.62411 32.5199i −0.172211 1.21111i
\(722\) 0 0
\(723\) −20.4005 20.4005i −0.758704 0.758704i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −4.99011 4.99011i −0.185073 0.185073i 0.608489 0.793562i \(-0.291776\pi\)
−0.793562 + 0.608489i \(0.791776\pi\)
\(728\) 0 0
\(729\) 29.7297i 1.10110i
\(730\) 0 0
\(731\) 19.2222i 0.710960i
\(732\) 0 0
\(733\) −18.9857 + 18.9857i −0.701252 + 0.701252i −0.964679 0.263427i \(-0.915147\pi\)
0.263427 + 0.964679i \(0.415147\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.31675 6.31675i 0.232681 0.232681i
\(738\) 0 0
\(739\) 4.09135i 0.150503i −0.997165 0.0752515i \(-0.976024\pi\)
0.997165 0.0752515i \(-0.0239759\pi\)
\(740\) 0 0
\(741\) 15.2989i 0.562019i
\(742\) 0 0
\(743\) −37.7330 37.7330i −1.38429 1.38429i −0.836838 0.547451i \(-0.815598\pi\)
−0.547451 0.836838i \(-0.684402\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 7.87968 + 7.87968i 0.288302 + 0.288302i
\(748\) 0 0
\(749\) −5.46444 38.4297i −0.199666 1.40419i
\(750\) 0 0
\(751\) −21.3975 −0.780805 −0.390403 0.920644i \(-0.627664\pi\)
−0.390403 + 0.920644i \(0.627664\pi\)
\(752\) 0 0
\(753\) −27.2635 27.2635i −0.993538 0.993538i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −24.8160 + 24.8160i −0.901952 + 0.901952i −0.995605 0.0936529i \(-0.970146\pi\)
0.0936529 + 0.995605i \(0.470146\pi\)
\(758\) 0 0
\(759\) −29.6492 −1.07620
\(760\) 0 0
\(761\) 20.4451i 0.741135i −0.928806 0.370567i \(-0.879163\pi\)
0.928806 0.370567i \(-0.120837\pi\)
\(762\) 0 0
\(763\) 10.4239 + 7.82853i 0.377371 + 0.283412i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9.07654 9.07654i 0.327735 0.327735i
\(768\) 0 0
\(769\) 6.20785 0.223861 0.111930 0.993716i \(-0.464297\pi\)
0.111930 + 0.993716i \(0.464297\pi\)
\(770\) 0 0
\(771\) −4.01351 −0.144543
\(772\) 0 0
\(773\) −12.7179 + 12.7179i −0.457430 + 0.457430i −0.897811 0.440381i \(-0.854843\pi\)
0.440381 + 0.897811i \(0.354843\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 6.74503 + 5.06563i 0.241976 + 0.181728i
\(778\) 0 0
\(779\) 35.6821i 1.27844i
\(780\) 0 0
\(781\) 0.920513 0.0329385
\(782\) 0 0
\(783\) −23.5071 + 23.5071i −0.840076 + 0.840076i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 32.6842 + 32.6842i 1.16506 + 1.16506i 0.983352 + 0.181713i \(0.0581642\pi\)
0.181713 + 0.983352i \(0.441836\pi\)
\(788\) 0 0
\(789\) 5.49068 0.195474
\(790\) 0 0
\(791\) −14.0753 + 2.00142i −0.500461 + 0.0711622i
\(792\) 0 0
\(793\) −3.92999 3.92999i −0.139558 0.139558i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −8.76878 8.76878i −0.310606 0.310606i 0.534538 0.845144i \(-0.320486\pi\)
−0.845144 + 0.534538i \(0.820486\pi\)
\(798\) 0 0
\(799\) 47.4046i 1.67706i
\(800\) 0 0
\(801\) 8.27127i 0.292251i
\(802\) 0 0
\(803\) −16.6286 + 16.6286i −0.586811 + 0.586811i
\(804\)