Properties

Label 2028.2.i.g.529.1
Level $2028$
Weight $2$
Character 2028.529
Analytic conductor $16.194$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2028.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(16.1936615299\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 156)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 529.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2028.529
Dual form 2028.2.i.g.2005.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +4.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +4.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} +(2.00000 - 3.46410i) q^{15} +(-1.00000 - 1.73205i) q^{17} +(-1.00000 - 1.73205i) q^{19} -2.00000 q^{21} +11.0000 q^{25} -1.00000 q^{27} +(3.00000 - 5.19615i) q^{29} +10.0000 q^{31} +(2.00000 + 3.46410i) q^{33} +(-4.00000 - 6.92820i) q^{35} +(5.00000 - 8.66025i) q^{37} +(4.00000 - 6.92820i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(-2.00000 - 3.46410i) q^{45} +4.00000 q^{47} +(1.50000 - 2.59808i) q^{49} -2.00000 q^{51} -10.0000 q^{53} +(-8.00000 + 13.8564i) q^{55} -2.00000 q^{57} +(-4.00000 - 6.92820i) q^{59} +(7.00000 + 12.1244i) q^{61} +(-1.00000 + 1.73205i) q^{63} +(1.00000 - 1.73205i) q^{67} +(8.00000 + 13.8564i) q^{71} +10.0000 q^{73} +(5.50000 - 9.52628i) q^{75} +8.00000 q^{77} -16.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.00000 - 6.92820i) q^{85} +(-3.00000 - 5.19615i) q^{87} +(-2.00000 + 3.46410i) q^{89} +(5.00000 - 8.66025i) q^{93} +(-4.00000 - 6.92820i) q^{95} +(-1.00000 - 1.73205i) q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} + 8q^{5} - 2q^{7} - q^{9} + O(q^{10}) \) \( 2q + q^{3} + 8q^{5} - 2q^{7} - q^{9} - 4q^{11} + 4q^{15} - 2q^{17} - 2q^{19} - 4q^{21} + 22q^{25} - 2q^{27} + 6q^{29} + 20q^{31} + 4q^{33} - 8q^{35} + 10q^{37} + 8q^{41} - 4q^{43} - 4q^{45} + 8q^{47} + 3q^{49} - 4q^{51} - 20q^{53} - 16q^{55} - 4q^{57} - 8q^{59} + 14q^{61} - 2q^{63} + 2q^{67} + 16q^{71} + 20q^{73} + 11q^{75} + 16q^{77} - 32q^{79} - q^{81} - 8q^{85} - 6q^{87} - 4q^{89} + 10q^{93} - 8q^{95} - 2q^{97} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2028\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(1015\) \(1861\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0 0
\(5\) 4.00000 1.78885 0.894427 0.447214i \(-0.147584\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(6\) 0 0
\(7\) −1.00000 1.73205i −0.377964 0.654654i 0.612801 0.790237i \(-0.290043\pi\)
−0.990766 + 0.135583i \(0.956709\pi\)
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −2.00000 + 3.46410i −0.603023 + 1.04447i 0.389338 + 0.921095i \(0.372704\pi\)
−0.992361 + 0.123371i \(0.960630\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) 0 0
\(15\) 2.00000 3.46410i 0.516398 0.894427i
\(16\) 0 0
\(17\) −1.00000 1.73205i −0.242536 0.420084i 0.718900 0.695113i \(-0.244646\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) 0 0
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 0 0
\(21\) −2.00000 −0.436436
\(22\) 0 0
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) 11.0000 2.20000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 3.00000 5.19615i 0.557086 0.964901i −0.440652 0.897678i \(-0.645253\pi\)
0.997738 0.0672232i \(-0.0214140\pi\)
\(30\) 0 0
\(31\) 10.0000 1.79605 0.898027 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) 0 0
\(33\) 2.00000 + 3.46410i 0.348155 + 0.603023i
\(34\) 0 0
\(35\) −4.00000 6.92820i −0.676123 1.17108i
\(36\) 0 0
\(37\) 5.00000 8.66025i 0.821995 1.42374i −0.0821995 0.996616i \(-0.526194\pi\)
0.904194 0.427121i \(-0.140472\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 4.00000 6.92820i 0.624695 1.08200i −0.363905 0.931436i \(-0.618557\pi\)
0.988600 0.150567i \(-0.0481100\pi\)
\(42\) 0 0
\(43\) −2.00000 3.46410i −0.304997 0.528271i 0.672264 0.740312i \(-0.265322\pi\)
−0.977261 + 0.212041i \(0.931989\pi\)
\(44\) 0 0
\(45\) −2.00000 3.46410i −0.298142 0.516398i
\(46\) 0 0
\(47\) 4.00000 0.583460 0.291730 0.956501i \(-0.405769\pi\)
0.291730 + 0.956501i \(0.405769\pi\)
\(48\) 0 0
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) 0 0
\(51\) −2.00000 −0.280056
\(52\) 0 0
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) 0 0
\(55\) −8.00000 + 13.8564i −1.07872 + 1.86840i
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) 0 0
\(59\) −4.00000 6.92820i −0.520756 0.901975i −0.999709 0.0241347i \(-0.992317\pi\)
0.478953 0.877841i \(-0.341016\pi\)
\(60\) 0 0
\(61\) 7.00000 + 12.1244i 0.896258 + 1.55236i 0.832240 + 0.554416i \(0.187058\pi\)
0.0640184 + 0.997949i \(0.479608\pi\)
\(62\) 0 0
\(63\) −1.00000 + 1.73205i −0.125988 + 0.218218i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 1.00000 1.73205i 0.122169 0.211604i −0.798454 0.602056i \(-0.794348\pi\)
0.920623 + 0.390453i \(0.127682\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.00000 + 13.8564i 0.949425 + 1.64445i 0.746639 + 0.665230i \(0.231667\pi\)
0.202787 + 0.979223i \(0.435000\pi\)
\(72\) 0 0
\(73\) 10.0000 1.17041 0.585206 0.810885i \(-0.301014\pi\)
0.585206 + 0.810885i \(0.301014\pi\)
\(74\) 0 0
\(75\) 5.50000 9.52628i 0.635085 1.10000i
\(76\) 0 0
\(77\) 8.00000 0.911685
\(78\) 0 0
\(79\) −16.0000 −1.80014 −0.900070 0.435745i \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −4.00000 6.92820i −0.433861 0.751469i
\(86\) 0 0
\(87\) −3.00000 5.19615i −0.321634 0.557086i
\(88\) 0 0
\(89\) −2.00000 + 3.46410i −0.212000 + 0.367194i −0.952340 0.305038i \(-0.901331\pi\)
0.740341 + 0.672232i \(0.234664\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 5.00000 8.66025i 0.518476 0.898027i
\(94\) 0 0
\(95\) −4.00000 6.92820i −0.410391 0.710819i
\(96\) 0 0
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) −5.00000 + 8.66025i −0.497519 + 0.861727i −0.999996 0.00286291i \(-0.999089\pi\)
0.502477 + 0.864590i \(0.332422\pi\)
\(102\) 0 0
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 0 0
\(105\) −8.00000 −0.780720
\(106\) 0 0
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) 0 0
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) −5.00000 8.66025i −0.474579 0.821995i
\(112\) 0 0
\(113\) −3.00000 5.19615i −0.282216 0.488813i 0.689714 0.724082i \(-0.257736\pi\)
−0.971930 + 0.235269i \(0.924403\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.00000 + 3.46410i −0.183340 + 0.317554i
\(120\) 0 0
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) 0 0
\(123\) −4.00000 6.92820i −0.360668 0.624695i
\(124\) 0 0
\(125\) 24.0000 2.14663
\(126\) 0 0
\(127\) −6.00000 + 10.3923i −0.532414 + 0.922168i 0.466870 + 0.884326i \(0.345382\pi\)
−0.999284 + 0.0378419i \(0.987952\pi\)
\(128\) 0 0
\(129\) −4.00000 −0.352180
\(130\) 0 0
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 0 0
\(133\) −2.00000 + 3.46410i −0.173422 + 0.300376i
\(134\) 0 0
\(135\) −4.00000 −0.344265
\(136\) 0 0
\(137\) 4.00000 + 6.92820i 0.341743 + 0.591916i 0.984757 0.173939i \(-0.0556494\pi\)
−0.643013 + 0.765855i \(0.722316\pi\)
\(138\) 0 0
\(139\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(140\) 0 0
\(141\) 2.00000 3.46410i 0.168430 0.291730i
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 12.0000 20.7846i 0.996546 1.72607i
\(146\) 0 0
\(147\) −1.50000 2.59808i −0.123718 0.214286i
\(148\) 0 0
\(149\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(150\) 0 0
\(151\) −18.0000 −1.46482 −0.732410 0.680864i \(-0.761604\pi\)
−0.732410 + 0.680864i \(0.761604\pi\)
\(152\) 0 0
\(153\) −1.00000 + 1.73205i −0.0808452 + 0.140028i
\(154\) 0 0
\(155\) 40.0000 3.21288
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 0 0
\(159\) −5.00000 + 8.66025i −0.396526 + 0.686803i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 1.00000 + 1.73205i 0.0783260 + 0.135665i 0.902528 0.430632i \(-0.141709\pi\)
−0.824202 + 0.566296i \(0.808376\pi\)
\(164\) 0 0
\(165\) 8.00000 + 13.8564i 0.622799 + 1.07872i
\(166\) 0 0
\(167\) −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i \(-0.987025\pi\)
0.534875 + 0.844931i \(0.320359\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) −1.00000 + 1.73205i −0.0764719 + 0.132453i
\(172\) 0 0
\(173\) −1.00000 1.73205i −0.0760286 0.131685i 0.825505 0.564396i \(-0.190891\pi\)
−0.901533 + 0.432710i \(0.857557\pi\)
\(174\) 0 0
\(175\) −11.0000 19.0526i −0.831522 1.44024i
\(176\) 0 0
\(177\) −8.00000 −0.601317
\(178\) 0 0
\(179\) −6.00000 + 10.3923i −0.448461 + 0.776757i −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 14.0000 1.03491
\(184\) 0 0
\(185\) 20.0000 34.6410i 1.47043 2.54686i
\(186\) 0 0
\(187\) 8.00000 0.585018
\(188\) 0 0
\(189\) 1.00000 + 1.73205i 0.0727393 + 0.125988i
\(190\) 0 0
\(191\) 4.00000 + 6.92820i 0.289430 + 0.501307i 0.973674 0.227946i \(-0.0732010\pi\)
−0.684244 + 0.729253i \(0.739868\pi\)
\(192\) 0 0
\(193\) −7.00000 + 12.1244i −0.503871 + 0.872730i 0.496119 + 0.868255i \(0.334758\pi\)
−0.999990 + 0.00447566i \(0.998575\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.00000 + 10.3923i −0.427482 + 0.740421i −0.996649 0.0818013i \(-0.973933\pi\)
0.569166 + 0.822222i \(0.307266\pi\)
\(198\) 0 0
\(199\) −2.00000 3.46410i −0.141776 0.245564i 0.786389 0.617731i \(-0.211948\pi\)
−0.928166 + 0.372168i \(0.878615\pi\)
\(200\) 0 0
\(201\) −1.00000 1.73205i −0.0705346 0.122169i
\(202\) 0 0
\(203\) −12.0000 −0.842235
\(204\) 0 0
\(205\) 16.0000 27.7128i 1.11749 1.93555i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 8.00000 0.553372
\(210\) 0 0
\(211\) 6.00000 10.3923i 0.413057 0.715436i −0.582165 0.813070i \(-0.697794\pi\)
0.995222 + 0.0976347i \(0.0311277\pi\)
\(212\) 0 0
\(213\) 16.0000 1.09630
\(214\) 0 0
\(215\) −8.00000 13.8564i −0.545595 0.944999i
\(216\) 0 0
\(217\) −10.0000 17.3205i −0.678844 1.17579i
\(218\) 0 0
\(219\) 5.00000 8.66025i 0.337869 0.585206i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 7.00000 12.1244i 0.468755 0.811907i −0.530607 0.847618i \(-0.678036\pi\)
0.999362 + 0.0357107i \(0.0113695\pi\)
\(224\) 0 0
\(225\) −5.50000 9.52628i −0.366667 0.635085i
\(226\) 0 0
\(227\) −2.00000 3.46410i −0.132745 0.229920i 0.791989 0.610535i \(-0.209046\pi\)
−0.924734 + 0.380615i \(0.875712\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 0 0
\(231\) 4.00000 6.92820i 0.263181 0.455842i
\(232\) 0 0
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 0 0
\(235\) 16.0000 1.04372
\(236\) 0 0
\(237\) −8.00000 + 13.8564i −0.519656 + 0.900070i
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) −1.00000 1.73205i −0.0644157 0.111571i 0.832019 0.554747i \(-0.187185\pi\)
−0.896435 + 0.443176i \(0.853852\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 6.00000 10.3923i 0.383326 0.663940i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 10.0000 + 17.3205i 0.631194 + 1.09326i 0.987308 + 0.158818i \(0.0507683\pi\)
−0.356113 + 0.934443i \(0.615898\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −8.00000 −0.500979
\(256\) 0 0
\(257\) −15.0000 + 25.9808i −0.935674 + 1.62064i −0.162247 + 0.986750i \(0.551874\pi\)
−0.773427 + 0.633885i \(0.781459\pi\)
\(258\) 0 0
\(259\) −20.0000 −1.24274
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 0 0
\(263\) 8.00000 13.8564i 0.493301 0.854423i −0.506669 0.862141i \(-0.669123\pi\)
0.999970 + 0.00771799i \(0.00245674\pi\)
\(264\) 0 0
\(265\) −40.0000 −2.45718
\(266\) 0 0
\(267\) 2.00000 + 3.46410i 0.122398 + 0.212000i
\(268\) 0 0
\(269\) 7.00000 + 12.1244i 0.426798 + 0.739235i 0.996586 0.0825561i \(-0.0263084\pi\)
−0.569789 + 0.821791i \(0.692975\pi\)
\(270\) 0 0
\(271\) −5.00000 + 8.66025i −0.303728 + 0.526073i −0.976977 0.213343i \(-0.931565\pi\)
0.673249 + 0.739416i \(0.264898\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −22.0000 + 38.1051i −1.32665 + 2.29783i
\(276\) 0 0
\(277\) −11.0000 19.0526i −0.660926 1.14476i −0.980373 0.197153i \(-0.936830\pi\)
0.319447 0.947604i \(-0.396503\pi\)
\(278\) 0 0
\(279\) −5.00000 8.66025i −0.299342 0.518476i
\(280\) 0 0
\(281\) 8.00000 0.477240 0.238620 0.971113i \(-0.423305\pi\)
0.238620 + 0.971113i \(0.423305\pi\)
\(282\) 0 0
\(283\) 8.00000 13.8564i 0.475551 0.823678i −0.524057 0.851683i \(-0.675582\pi\)
0.999608 + 0.0280052i \(0.00891551\pi\)
\(284\) 0 0
\(285\) −8.00000 −0.473879
\(286\) 0 0
\(287\) −16.0000 −0.944450
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 0 0
\(291\) −2.00000 −0.117242
\(292\) 0 0
\(293\) 4.00000 + 6.92820i 0.233682 + 0.404750i 0.958889 0.283782i \(-0.0915890\pi\)
−0.725206 + 0.688531i \(0.758256\pi\)
\(294\) 0 0
\(295\) −16.0000 27.7128i −0.931556 1.61350i
\(296\) 0 0
\(297\) 2.00000 3.46410i 0.116052 0.201008i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −4.00000 + 6.92820i −0.230556 + 0.399335i
\(302\) 0 0
\(303\) 5.00000 + 8.66025i 0.287242 + 0.497519i
\(304\) 0 0
\(305\) 28.0000 + 48.4974i 1.60328 + 2.77695i
\(306\) 0 0
\(307\) −22.0000 −1.25561 −0.627803 0.778372i \(-0.716046\pi\)
−0.627803 + 0.778372i \(0.716046\pi\)
\(308\) 0 0
\(309\) −4.00000 + 6.92820i −0.227552 + 0.394132i
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) −6.00000 −0.339140 −0.169570 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 0 0
\(315\) −4.00000 + 6.92820i −0.225374 + 0.390360i
\(316\) 0 0
\(317\) 12.0000 0.673987 0.336994 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) 0 0
\(319\) 12.0000 + 20.7846i 0.671871 + 1.16371i
\(320\) 0 0
\(321\) 6.00000 + 10.3923i 0.334887 + 0.580042i
\(322\) 0 0
\(323\) −2.00000 + 3.46410i −0.111283 + 0.192748i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1.00000 1.73205i 0.0553001 0.0957826i
\(328\) 0 0
\(329\) −4.00000 6.92820i −0.220527 0.381964i
\(330\) 0 0
\(331\) 1.00000 + 1.73205i 0.0549650 + 0.0952021i 0.892199 0.451643i \(-0.149162\pi\)
−0.837234 + 0.546845i \(0.815829\pi\)
\(332\) 0 0
\(333\) −10.0000 −0.547997
\(334\) 0 0
\(335\) 4.00000 6.92820i 0.218543 0.378528i
\(336\) 0 0
\(337\) −30.0000 −1.63420 −0.817102 0.576493i \(-0.804421\pi\)
−0.817102 + 0.576493i \(0.804421\pi\)
\(338\) 0 0
\(339\) −6.00000 −0.325875
\(340\) 0 0
\(341\) −20.0000 + 34.6410i −1.08306 + 1.87592i
\(342\) 0 0
\(343\) −20.0000 −1.07990
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 0 0
\(349\) 9.00000 15.5885i 0.481759 0.834431i −0.518022 0.855367i \(-0.673331\pi\)
0.999781 + 0.0209364i \(0.00666475\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −8.00000 + 13.8564i −0.425797 + 0.737502i −0.996495 0.0836583i \(-0.973340\pi\)
0.570697 + 0.821160i \(0.306673\pi\)
\(354\) 0 0
\(355\) 32.0000 + 55.4256i 1.69838 + 2.94169i
\(356\) 0 0
\(357\) 2.00000 + 3.46410i 0.105851 + 0.183340i
\(358\) 0 0
\(359\) 12.0000 0.633336 0.316668 0.948536i \(-0.397436\pi\)
0.316668 + 0.948536i \(0.397436\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 0 0
\(363\) −5.00000 −0.262432
\(364\) 0 0
\(365\) 40.0000 2.09370
\(366\) 0 0
\(367\) −2.00000 + 3.46410i −0.104399 + 0.180825i −0.913493 0.406855i \(-0.866625\pi\)
0.809093 + 0.587680i \(0.199959\pi\)
\(368\) 0 0
\(369\) −8.00000 −0.416463
\(370\) 0 0
\(371\) 10.0000 + 17.3205i 0.519174 + 0.899236i
\(372\) 0 0
\(373\) 9.00000 + 15.5885i 0.466002 + 0.807140i 0.999246 0.0388219i \(-0.0123605\pi\)
−0.533244 + 0.845962i \(0.679027\pi\)
\(374\) 0 0
\(375\) 12.0000 20.7846i 0.619677 1.07331i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 3.00000 5.19615i 0.154100 0.266908i −0.778631 0.627482i \(-0.784086\pi\)
0.932731 + 0.360573i \(0.117419\pi\)
\(380\) 0 0
\(381\) 6.00000 + 10.3923i 0.307389 + 0.532414i
\(382\) 0 0
\(383\) 6.00000 + 10.3923i 0.306586 + 0.531022i 0.977613 0.210411i \(-0.0674801\pi\)
−0.671027 + 0.741433i \(0.734147\pi\)
\(384\) 0 0
\(385\) 32.0000 1.63087
\(386\) 0 0
\(387\) −2.00000 + 3.46410i −0.101666 + 0.176090i
\(388\) 0 0
\(389\) −26.0000 −1.31825 −0.659126 0.752032i \(-0.729074\pi\)
−0.659126 + 0.752032i \(0.729074\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 2.00000 3.46410i 0.100887 0.174741i
\(394\) 0 0
\(395\) −64.0000 −3.22019
\(396\) 0 0
\(397\) 9.00000 + 15.5885i 0.451697 + 0.782362i 0.998492 0.0549046i \(-0.0174855\pi\)
−0.546795 + 0.837267i \(0.684152\pi\)
\(398\) 0 0
\(399\) 2.00000 + 3.46410i 0.100125 + 0.173422i
\(400\) 0 0
\(401\) −6.00000 + 10.3923i −0.299626 + 0.518967i −0.976050 0.217545i \(-0.930195\pi\)
0.676425 + 0.736512i \(0.263528\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −2.00000 + 3.46410i −0.0993808 + 0.172133i
\(406\) 0 0
\(407\) 20.0000 + 34.6410i 0.991363 + 1.71709i
\(408\) 0 0
\(409\) 7.00000 + 12.1244i 0.346128 + 0.599511i 0.985558 0.169338i \(-0.0541630\pi\)
−0.639430 + 0.768849i \(0.720830\pi\)
\(410\) 0 0
\(411\) 8.00000 0.394611
\(412\) 0 0
\(413\) −8.00000 + 13.8564i −0.393654 + 0.681829i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10.0000 17.3205i 0.488532 0.846162i −0.511381 0.859354i \(-0.670866\pi\)
0.999913 + 0.0131919i \(0.00419923\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 0 0
\(423\) −2.00000 3.46410i −0.0972433 0.168430i
\(424\) 0 0
\(425\) −11.0000 19.0526i −0.533578 0.924185i
\(426\) 0 0
\(427\) 14.0000 24.2487i 0.677507 1.17348i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −10.0000 + 17.3205i −0.481683 + 0.834300i −0.999779 0.0210230i \(-0.993308\pi\)
0.518096 + 0.855323i \(0.326641\pi\)
\(432\) 0 0
\(433\) 9.00000 + 15.5885i 0.432512 + 0.749133i 0.997089 0.0762473i \(-0.0242938\pi\)
−0.564577 + 0.825381i \(0.690961\pi\)
\(434\) 0 0
\(435\) −12.0000 20.7846i −0.575356 0.996546i
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −8.00000 + 13.8564i −0.381819 + 0.661330i −0.991322 0.131453i \(-0.958036\pi\)
0.609503 + 0.792784i \(0.291369\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 0 0
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) 0 0
\(445\) −8.00000 + 13.8564i −0.379236 + 0.656857i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6.00000 + 10.3923i 0.283158 + 0.490443i 0.972161 0.234315i \(-0.0752847\pi\)
−0.689003 + 0.724758i \(0.741951\pi\)
\(450\) 0 0
\(451\) 16.0000 + 27.7128i 0.753411 + 1.30495i
\(452\) 0 0
\(453\) −9.00000 + 15.5885i −0.422857 + 0.732410i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −9.00000 + 15.5885i −0.421002 + 0.729197i −0.996038 0.0889312i \(-0.971655\pi\)
0.575036 + 0.818128i \(0.304988\pi\)
\(458\) 0 0
\(459\) 1.00000 + 1.73205i 0.0466760 + 0.0808452i
\(460\) 0 0
\(461\) 6.00000 + 10.3923i 0.279448 + 0.484018i 0.971248 0.238071i \(-0.0765153\pi\)
−0.691800 + 0.722089i \(0.743182\pi\)
\(462\) 0 0
\(463\) −22.0000 −1.02243 −0.511213 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) 0 0
\(465\) 20.0000 34.6410i 0.927478 1.60644i
\(466\) 0 0
\(467\) −28.0000 −1.29569 −0.647843 0.761774i \(-0.724329\pi\)
−0.647843 + 0.761774i \(0.724329\pi\)
\(468\) 0 0
\(469\) −4.00000 −0.184703
\(470\) 0 0
\(471\) 1.00000 1.73205i 0.0460776 0.0798087i
\(472\) 0 0
\(473\) 16.0000 0.735681
\(474\) 0 0
\(475\) −11.0000 19.0526i −0.504715 0.874191i
\(476\) 0 0
\(477\) 5.00000 + 8.66025i 0.228934 + 0.396526i
\(478\) 0 0
\(479\) −8.00000 + 13.8564i −0.365529 + 0.633115i −0.988861 0.148842i \(-0.952445\pi\)
0.623332 + 0.781958i \(0.285779\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.00000 6.92820i −0.181631 0.314594i
\(486\) 0 0
\(487\) −13.0000 22.5167i −0.589086 1.02033i −0.994352 0.106129i \(-0.966154\pi\)
0.405266 0.914199i \(-0.367179\pi\)
\(488\) 0 0
\(489\) 2.00000 0.0904431
\(490\) 0 0
\(491\) −6.00000 + 10.3923i −0.270776 + 0.468998i −0.969061 0.246822i \(-0.920614\pi\)
0.698285 + 0.715820i \(0.253947\pi\)
\(492\) 0 0
\(493\) −12.0000 −0.540453
\(494\) 0 0
\(495\) 16.0000 0.719147
\(496\) 0 0
\(497\) 16.0000 27.7128i 0.717698 1.24309i
\(498\) 0 0
\(499\) 6.00000 0.268597 0.134298 0.990941i \(-0.457122\pi\)
0.134298 + 0.990941i \(0.457122\pi\)
\(500\) 0 0
\(501\) 6.00000 + 10.3923i 0.268060 + 0.464294i
\(502\) 0 0
\(503\) −8.00000 13.8564i −0.356702 0.617827i 0.630705 0.776022i \(-0.282766\pi\)
−0.987408 + 0.158196i \(0.949432\pi\)
\(504\) 0 0
\(505\) −20.0000 + 34.6410i −0.889988 + 1.54150i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 6.00000 10.3923i 0.265945 0.460631i −0.701866 0.712309i \(-0.747649\pi\)
0.967811 + 0.251679i \(0.0809826\pi\)
\(510\) 0 0
\(511\) −10.0000 17.3205i −0.442374 0.766214i
\(512\) 0 0
\(513\) 1.00000 + 1.73205i 0.0441511 + 0.0764719i
\(514\) 0 0
\(515\) −32.0000 −1.41009
\(516\) 0 0
\(517\) −8.00000 + 13.8564i −0.351840 + 0.609404i
\(518\) 0 0
\(519\) −2.00000 −0.0877903
\(520\) 0 0
\(521\) −2.00000 −0.0876216 −0.0438108 0.999040i \(-0.513950\pi\)
−0.0438108 + 0.999040i \(0.513950\pi\)
\(522\) 0 0
\(523\) −8.00000 + 13.8564i −0.349816 + 0.605898i −0.986216 0.165460i \(-0.947089\pi\)
0.636401 + 0.771358i \(0.280422\pi\)
\(524\) 0 0
\(525\) −22.0000 −0.960159
\(526\) 0 0
\(527\) −10.0000 17.3205i −0.435607 0.754493i
\(528\) 0 0
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) −4.00000 + 6.92820i −0.173585 + 0.300658i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −24.0000 + 41.5692i −1.03761 + 1.79719i
\(536\) 0 0
\(537\) 6.00000 + 10.3923i 0.258919 + 0.448461i
\(538\) 0 0
\(539\) 6.00000 + 10.3923i 0.258438 + 0.447628i
\(540\) 0 0
\(541\) −38.0000 −1.63375 −0.816874 0.576816i \(-0.804295\pi\)
−0.816874 + 0.576816i \(0.804295\pi\)
\(542\) 0 0
\(543\) 1.00000 1.73205i 0.0429141 0.0743294i
\(544\) 0 0
\(545\) 8.00000 0.342682
\(546\) 0 0
\(547\) 32.0000 1.36822 0.684111 0.729378i \(-0.260191\pi\)
0.684111 + 0.729378i \(0.260191\pi\)
\(548\) 0 0
\(549\) 7.00000 12.1244i 0.298753 0.517455i
\(550\) 0 0
\(551\) −12.0000 −0.511217
\(552\) 0 0
\(553\) 16.0000 + 27.7128i 0.680389 + 1.17847i
\(554\) 0 0
\(555\) −20.0000 34.6410i −0.848953 1.47043i
\(556\) 0 0
\(557\) 12.0000 20.7846i 0.508456 0.880672i −0.491496 0.870880i \(-0.663550\pi\)
0.999952 0.00979220i \(-0.00311700\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 4.00000 6.92820i 0.168880 0.292509i
\(562\) 0 0
\(563\) −14.0000 24.2487i −0.590030 1.02196i −0.994228 0.107290i \(-0.965783\pi\)
0.404198 0.914671i \(-0.367551\pi\)
\(564\) 0 0
\(565\) −12.0000 20.7846i −0.504844 0.874415i
\(566\) 0 0
\(567\) 2.00000 0.0839921
\(568\) 0 0
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) 0 0
\(571\) −8.00000 −0.334790 −0.167395 0.985890i \(-0.553535\pi\)
−0.167395 + 0.985890i \(0.553535\pi\)
\(572\) 0 0
\(573\) 8.00000 0.334205
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 30.0000 1.24892 0.624458 0.781058i \(-0.285320\pi\)
0.624458 + 0.781058i \(0.285320\pi\)
\(578\) 0 0
\(579\) 7.00000 + 12.1244i 0.290910 + 0.503871i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 20.0000 34.6410i 0.828315 1.43468i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −4.00000 + 6.92820i −0.165098 + 0.285958i −0.936690 0.350160i \(-0.886127\pi\)
0.771592 + 0.636117i \(0.219461\pi\)
\(588\) 0 0
\(589\) −10.0000 17.3205i −0.412043 0.713679i
\(590\) 0 0
\(591\) 6.00000 + 10.3923i 0.246807 + 0.427482i
\(592\) 0 0
\(593\) 36.0000 1.47834 0.739171 0.673517i \(-0.235217\pi\)
0.739171 + 0.673517i \(0.235217\pi\)
\(594\) 0 0
\(595\) −8.00000 + 13.8564i −0.327968 + 0.568057i
\(596\) 0 0
\(597\) −4.00000 −0.163709
\(598\) 0 0
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 0 0
\(601\) 11.0000 19.0526i 0.448699 0.777170i −0.549602 0.835426i \(-0.685221\pi\)
0.998302 + 0.0582563i \(0.0185541\pi\)
\(602\) 0 0
\(603\) −2.00000 −0.0814463
\(604\) 0 0
\(605\) −10.0000 17.3205i −0.406558 0.704179i
\(606\) 0 0
\(607\) 2.00000 + 3.46410i 0.0811775 + 0.140604i 0.903756 0.428048i \(-0.140799\pi\)
−0.822578 + 0.568652i \(0.807465\pi\)
\(608\) 0 0
\(609\) −6.00000 + 10.3923i −0.243132 + 0.421117i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −7.00000 + 12.1244i −0.282727 + 0.489698i −0.972056 0.234751i \(-0.924572\pi\)
0.689328 + 0.724449i \(0.257906\pi\)
\(614\) 0 0
\(615\) −16.0000 27.7128i −0.645182 1.11749i
\(616\) 0 0
\(617\) −24.0000 41.5692i −0.966204 1.67351i −0.706346 0.707867i \(-0.749658\pi\)
−0.259858 0.965647i \(-0.583676\pi\)
\(618\) 0 0
\(619\) −14.0000 −0.562708 −0.281354 0.959604i \(-0.590783\pi\)
−0.281354 + 0.959604i \(0.590783\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 8.00000 0.320513
\(624\) 0 0
\(625\) 41.0000 1.64000
\(626\) 0 0
\(627\) 4.00000 6.92820i 0.159745 0.276686i
\(628\) 0 0
\(629\) −20.0000 −0.797452
\(630\) 0 0
\(631\) −15.0000 25.9808i −0.597141 1.03428i −0.993241 0.116071i \(-0.962970\pi\)
0.396100 0.918207i \(-0.370363\pi\)
\(632\) 0 0
\(633\) −6.00000 10.3923i −0.238479 0.413057i
\(634\) 0 0
\(635\) −24.0000 + 41.5692i −0.952411 + 1.64962i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 8.00000 13.8564i 0.316475 0.548151i
\(640\) 0 0
\(641\) −13.0000 22.5167i −0.513469 0.889355i −0.999878 0.0156233i \(-0.995027\pi\)
0.486409 0.873731i \(-0.338307\pi\)
\(642\) 0 0
\(643\) 13.0000 + 22.5167i 0.512670 + 0.887970i 0.999892 + 0.0146923i \(0.00467688\pi\)
−0.487222 + 0.873278i \(0.661990\pi\)
\(644\) 0 0
\(645\) −16.0000 −0.629999
\(646\) 0 0
\(647\) 12.0000 20.7846i 0.471769 0.817127i −0.527710 0.849425i \(-0.676949\pi\)
0.999478 + 0.0322975i \(0.0102824\pi\)
\(648\) 0 0
\(649\) 32.0000 1.25611
\(650\) 0 0
\(651\) −20.0000 −0.783862
\(652\) 0 0
\(653\) 23.0000 39.8372i 0.900060 1.55895i 0.0726446 0.997358i \(-0.476856\pi\)
0.827415 0.561591i \(-0.189811\pi\)
\(654\) 0 0
\(655\) 16.0000 0.625172
\(656\) 0 0
\(657\) −5.00000 8.66025i −0.195069 0.337869i
\(658\) 0 0
\(659\) 6.00000 + 10.3923i 0.233727 + 0.404827i 0.958902 0.283738i \(-0.0915745\pi\)
−0.725175 + 0.688565i \(0.758241\pi\)
\(660\) 0 0
\(661\) 5.00000 8.66025i 0.194477 0.336845i −0.752252 0.658876i \(-0.771032\pi\)
0.946729 + 0.322031i \(0.104366\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −8.00000 + 13.8564i −0.310227 + 0.537328i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −7.00000 12.1244i −0.270636 0.468755i
\(670\) 0 0
\(671\) −56.0000 −2.16186
\(672\) 0 0
\(673\) −11.0000 + 19.0526i −0.424019 + 0.734422i −0.996328 0.0856156i \(-0.972714\pi\)
0.572309 + 0.820038i \(0.306048\pi\)
\(674\) 0 0
\(675\) −11.0000 −0.423390
\(676\) 0 0
\(677\) 38.0000 1.46046 0.730229 0.683202i \(-0.239413\pi\)
0.730229 + 0.683202i \(0.239413\pi\)
\(678\) 0 0
\(679\) −2.00000 + 3.46410i −0.0767530 + 0.132940i
\(680\) 0 0
\(681\) −4.00000 −0.153280
\(682\) 0 0
\(683\) 10.0000 + 17.3205i 0.382639 + 0.662751i 0.991439 0.130573i \(-0.0416818\pi\)
−0.608799 + 0.793324i \(0.708349\pi\)
\(684\) 0 0
\(685\) 16.0000 + 27.7128i 0.611329 + 1.05885i
\(686\) 0 0
\(687\) 1.00000 1.73205i 0.0381524 0.0660819i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 5.00000 8.66025i 0.190209 0.329452i −0.755110 0.655598i \(-0.772417\pi\)
0.945319 + 0.326146i \(0.105750\pi\)
\(692\) 0 0
\(693\) −4.00000 6.92820i −0.151947 0.263181i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −16.0000 −0.606043
\(698\) 0 0
\(699\) −9.00000 + 15.5885i −0.340411 + 0.589610i
\(700\) 0 0
\(701\) −2.00000 −0.0755390 −0.0377695 0.999286i \(-0.512025\pi\)
−0.0377695 + 0.999286i \(0.512025\pi\)
\(702\) 0 0
\(703\) −20.0000 −0.754314
\(704\) 0 0
\(705\) 8.00000 13.8564i 0.301297 0.521862i
\(706\) 0 0
\(707\) 20.0000 0.752177
\(708\) 0 0
\(709\) 3.00000 + 5.19615i 0.112667 + 0.195146i 0.916845 0.399244i \(-0.130727\pi\)
−0.804178 + 0.594389i \(0.797394\pi\)
\(710\) 0 0
\(711\) 8.00000 + 13.8564i 0.300023 + 0.519656i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 12.0000 20.7846i 0.448148 0.776215i
\(718\) 0 0
\(719\) 24.0000 + 41.5692i 0.895049 + 1.55027i 0.833744 + 0.552151i \(0.186193\pi\)
0.0613050 + 0.998119i \(0.480474\pi\)
\(720\) 0 0
\(721\) 8.00000 + 13.8564i 0.297936 + 0.516040i
\(722\) 0 0
\(723\) −2.00000 −0.0743808
\(724\) 0 0
\(725\) 33.0000 57.1577i 1.22559 2.12278i
\(726\) 0 0
\(727\) 44.0000 1.63187 0.815935 0.578144i \(-0.196223\pi\)
0.815935 + 0.578144i \(0.196223\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −4.00000 + 6.92820i −0.147945 + 0.256249i
\(732\) 0 0
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) 0 0
\(735\) −6.00000 10.3923i −0.221313 0.383326i
\(736\) 0 0
\(737\) 4.00000 + 6.92820i 0.147342 + 0.255204i
\(738\) 0 0
\(739\) 11.0000 19.0526i 0.404642 0.700860i −0.589638 0.807668i \(-0.700730\pi\)
0.994280 + 0.106808i \(0.0340630\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0000 41.5692i 0.880475 1.52503i 0.0296605 0.999560i \(-0.490557\pi\)
0.850814 0.525467i \(-0.176109\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 24.0000 0.876941
\(750\) 0 0
\(751\) −4.00000 + 6.92820i −0.145962 + 0.252814i −0.929731 0.368238i \(-0.879961\pi\)
0.783769 + 0.621052i \(0.213294\pi\)
\(752\) 0 0
\(753\) 20.0000 0.728841
\(754\) 0 0
\(755\) −72.0000 −2.62035
\(756\) 0 0
\(757\) −9.00000 + 15.5885i −0.327111 + 0.566572i −0.981937 0.189207i \(-0.939408\pi\)
0.654827 + 0.755779i \(0.272742\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 20.0000 + 34.6410i 0.724999 + 1.25574i 0.958974 + 0.283493i \(0.0914933\pi\)
−0.233975 + 0.972243i \(0.575173\pi\)
\(762\) 0 0
\(763\) −2.00000 3.46410i −0.0724049 0.125409i
\(764\) 0 0
\(765\) −4.00000 + 6.92820i −0.144620 + 0.250490i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −11.0000 + 19.0526i −0.396670 + 0.687053i −0.993313 0.115454i \(-0.963168\pi\)
0.596643 + 0.802507i \(0.296501\pi\)
\(770\) 0 0
\(771\) 15.0000 + 25.9808i 0.540212 + 0.935674i
\(772\) 0 0
\(773\) −24.0000 41.5692i −0.863220 1.49514i −0.868804 0.495156i \(-0.835111\pi\)
0.00558380 0.999984i \(-0.498223\pi\)
\(774\) 0 0
\(775\) 110.000 3.95132
\(776\) 0 0
\(777\) −10.0000 + 17.3205i −0.358748 + 0.621370i
\(778\) 0 0
\(779\) −16.0000 −0.573259
\(780\) 0 0
\(781\) −64.0000 −2.29010
\(782\) 0 0
\(783\) −3.00000 + 5.19615i −0.107211 + 0.185695i
\(784\) 0 0
\(785\) 8.00000 0.285532
\(786\) 0 0
\(787\) −25.0000 43.3013i −0.891154 1.54352i −0.838494 0.544911i \(-0.816563\pi\)
−0.0526599 0.998613i \(-0.516770\pi\)
\(788\) 0 0
\(789\) −8.00000 13.8564i −0.284808 0.493301i
\(790\) 0 0
\(791\) −6.00000 + 10.3923i −0.213335 + 0.369508i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −20.0000 + 34.6410i −0.709327 + 1.22859i
\(796\) 0 0
\(797\) 13.0000 + 22.5167i 0.460484 + 0.797581i 0.998985 0.0450436i \(-0.0143427\pi\)
−0.538501 + 0.842625i \(0.681009\pi\)
\(798\) 0 0