Properties

Label 416.2.i.d.321.1
Level $416$
Weight $2$
Character 416.321
Analytic conductor $3.322$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [416,2,Mod(289,416)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(416, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("416.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 416 = 2^{5} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 416.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.32177672409\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 11x^{2} + 121 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 321.1
Root \(-1.65831 + 2.87228i\) of defining polynomial
Character \(\chi\) \(=\) 416.321
Dual form 416.2.i.d.289.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.65831 + 2.87228i) q^{3} +(-1.65831 - 2.87228i) q^{7} +(-4.00000 - 6.92820i) q^{9} +O(q^{10})\) \(q+(-1.65831 + 2.87228i) q^{3} +(-1.65831 - 2.87228i) q^{7} +(-4.00000 - 6.92820i) q^{9} +(-1.65831 + 2.87228i) q^{11} +(-1.00000 - 3.46410i) q^{13} +(1.50000 + 2.59808i) q^{17} +(-1.65831 - 2.87228i) q^{19} +11.0000 q^{21} +(1.65831 - 2.87228i) q^{23} -5.00000 q^{25} +16.5831 q^{27} +(2.50000 - 4.33013i) q^{29} +(-5.50000 - 9.52628i) q^{33} +(-4.50000 + 7.79423i) q^{37} +(11.6082 + 2.87228i) q^{39} +(1.50000 - 2.59808i) q^{41} +(-4.97494 - 8.61684i) q^{43} -6.63325 q^{47} +(-2.00000 + 3.46410i) q^{49} -9.94987 q^{51} -8.00000 q^{53} +11.0000 q^{57} +(-1.65831 - 2.87228i) q^{59} +(4.50000 + 7.79423i) q^{61} +(-13.2665 + 22.9783i) q^{63} +(-4.97494 + 8.61684i) q^{67} +(5.50000 + 9.52628i) q^{69} +(-4.97494 - 8.61684i) q^{71} -4.00000 q^{73} +(8.29156 - 14.3614i) q^{75} +11.0000 q^{77} +6.63325 q^{79} +(-15.5000 + 26.8468i) q^{81} -13.2665 q^{83} +(8.29156 + 14.3614i) q^{87} +(0.500000 - 0.866025i) q^{89} +(-8.29156 + 8.61684i) q^{91} +(-3.50000 - 6.06218i) q^{97} +26.5330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 16 q^{9} - 4 q^{13} + 6 q^{17} + 44 q^{21} - 20 q^{25} + 10 q^{29} - 22 q^{33} - 18 q^{37} + 6 q^{41} - 8 q^{49} - 32 q^{53} + 44 q^{57} + 18 q^{61} + 22 q^{69} - 16 q^{73} + 44 q^{77} - 62 q^{81} + 2 q^{89} - 14 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/416\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(287\) \(353\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −1.65831 + 2.87228i −0.957427 + 1.65831i −0.228714 + 0.973494i \(0.573452\pi\)
−0.728714 + 0.684819i \(0.759881\pi\)
\(4\) 0 0
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) −1.65831 2.87228i −0.626783 1.08562i −0.988193 0.153213i \(-0.951038\pi\)
0.361410 0.932407i \(-0.382295\pi\)
\(8\) 0 0
\(9\) −4.00000 6.92820i −1.33333 2.30940i
\(10\) 0 0
\(11\) −1.65831 + 2.87228i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) −1.00000 3.46410i −0.277350 0.960769i
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 0 0
\(19\) −1.65831 2.87228i −0.380443 0.658947i 0.610683 0.791875i \(-0.290895\pi\)
−0.991126 + 0.132929i \(0.957562\pi\)
\(20\) 0 0
\(21\) 11.0000 2.40040
\(22\) 0 0
\(23\) 1.65831 2.87228i 0.345782 0.598912i −0.639713 0.768613i \(-0.720947\pi\)
0.985496 + 0.169701i \(0.0542803\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) 16.5831 3.19142
\(28\) 0 0
\(29\) 2.50000 4.33013i 0.464238 0.804084i −0.534928 0.844897i \(-0.679661\pi\)
0.999167 + 0.0408130i \(0.0129948\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) −5.50000 9.52628i −0.957427 1.65831i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −4.50000 + 7.79423i −0.739795 + 1.28136i 0.212792 + 0.977098i \(0.431744\pi\)
−0.952587 + 0.304266i \(0.901589\pi\)
\(38\) 0 0
\(39\) 11.6082 + 2.87228i 1.85880 + 0.459933i
\(40\) 0 0
\(41\) 1.50000 2.59808i 0.234261 0.405751i −0.724797 0.688963i \(-0.758066\pi\)
0.959058 + 0.283211i \(0.0913998\pi\)
\(42\) 0 0
\(43\) −4.97494 8.61684i −0.758671 1.31406i −0.943529 0.331291i \(-0.892516\pi\)
0.184858 0.982765i \(-0.440818\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.63325 −0.967559 −0.483779 0.875190i \(-0.660736\pi\)
−0.483779 + 0.875190i \(0.660736\pi\)
\(48\) 0 0
\(49\) −2.00000 + 3.46410i −0.285714 + 0.494872i
\(50\) 0 0
\(51\) −9.94987 −1.39326
\(52\) 0 0
\(53\) −8.00000 −1.09888 −0.549442 0.835532i \(-0.685160\pi\)
−0.549442 + 0.835532i \(0.685160\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 11.0000 1.45699
\(58\) 0 0
\(59\) −1.65831 2.87228i −0.215894 0.373939i 0.737655 0.675178i \(-0.235933\pi\)
−0.953549 + 0.301239i \(0.902600\pi\)
\(60\) 0 0
\(61\) 4.50000 + 7.79423i 0.576166 + 0.997949i 0.995914 + 0.0903080i \(0.0287851\pi\)
−0.419748 + 0.907641i \(0.637882\pi\)
\(62\) 0 0
\(63\) −13.2665 + 22.9783i −1.67142 + 2.89499i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −4.97494 + 8.61684i −0.607785 + 1.05272i 0.383819 + 0.923408i \(0.374609\pi\)
−0.991605 + 0.129307i \(0.958725\pi\)
\(68\) 0 0
\(69\) 5.50000 + 9.52628i 0.662122 + 1.14683i
\(70\) 0 0
\(71\) −4.97494 8.61684i −0.590416 1.02263i −0.994176 0.107766i \(-0.965630\pi\)
0.403760 0.914865i \(-0.367703\pi\)
\(72\) 0 0
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 0 0
\(75\) 8.29156 14.3614i 0.957427 1.65831i
\(76\) 0 0
\(77\) 11.0000 1.25357
\(78\) 0 0
\(79\) 6.63325 0.746299 0.373149 0.927771i \(-0.378278\pi\)
0.373149 + 0.927771i \(0.378278\pi\)
\(80\) 0 0
\(81\) −15.5000 + 26.8468i −1.72222 + 2.98298i
\(82\) 0 0
\(83\) −13.2665 −1.45619 −0.728094 0.685478i \(-0.759593\pi\)
−0.728094 + 0.685478i \(0.759593\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 8.29156 + 14.3614i 0.888949 + 1.53970i
\(88\) 0 0
\(89\) 0.500000 0.866025i 0.0529999 0.0917985i −0.838308 0.545197i \(-0.816455\pi\)
0.891308 + 0.453398i \(0.149788\pi\)
\(90\) 0 0
\(91\) −8.29156 + 8.61684i −0.869192 + 0.903291i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −3.50000 6.06218i −0.355371 0.615521i 0.631810 0.775123i \(-0.282312\pi\)
−0.987181 + 0.159602i \(0.948979\pi\)
\(98\) 0 0
\(99\) 26.5330 2.66667
\(100\) 0 0
\(101\) 7.50000 12.9904i 0.746278 1.29259i −0.203317 0.979113i \(-0.565172\pi\)
0.949595 0.313478i \(-0.101494\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.65831 + 2.87228i −0.160315 + 0.277674i −0.934982 0.354696i \(-0.884584\pi\)
0.774667 + 0.632370i \(0.217918\pi\)
\(108\) 0 0
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) −14.9248 25.8505i −1.41660 2.45362i
\(112\) 0 0
\(113\) 5.50000 + 9.52628i 0.517396 + 0.896157i 0.999796 + 0.0202056i \(0.00643208\pi\)
−0.482399 + 0.875951i \(0.660235\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −20.0000 + 20.7846i −1.84900 + 1.92154i
\(118\) 0 0
\(119\) 4.97494 8.61684i 0.456052 0.789905i
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 4.97494 + 8.61684i 0.448575 + 0.776955i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 4.97494 8.61684i 0.441454 0.764621i −0.556343 0.830952i \(-0.687796\pi\)
0.997798 + 0.0663312i \(0.0211294\pi\)
\(128\) 0 0
\(129\) 33.0000 2.90549
\(130\) 0 0
\(131\) 13.2665 1.15910 0.579550 0.814937i \(-0.303228\pi\)
0.579550 + 0.814937i \(0.303228\pi\)
\(132\) 0 0
\(133\) −5.50000 + 9.52628i −0.476910 + 0.826033i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.50000 + 7.79423i 0.384461 + 0.665906i 0.991694 0.128618i \(-0.0410540\pi\)
−0.607233 + 0.794524i \(0.707721\pi\)
\(138\) 0 0
\(139\) −1.65831 2.87228i −0.140656 0.243624i 0.787088 0.616841i \(-0.211588\pi\)
−0.927744 + 0.373217i \(0.878255\pi\)
\(140\) 0 0
\(141\) 11.0000 19.0526i 0.926367 1.60451i
\(142\) 0 0
\(143\) 11.6082 + 2.87228i 0.970725 + 0.240192i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −6.63325 11.4891i −0.547101 0.947607i
\(148\) 0 0
\(149\) 0.500000 + 0.866025i 0.0409616 + 0.0709476i 0.885779 0.464107i \(-0.153625\pi\)
−0.844818 + 0.535054i \(0.820291\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 12.0000 20.7846i 0.970143 1.68034i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −8.00000 −0.638470 −0.319235 0.947676i \(-0.603426\pi\)
−0.319235 + 0.947676i \(0.603426\pi\)
\(158\) 0 0
\(159\) 13.2665 22.9783i 1.05210 1.82229i
\(160\) 0 0
\(161\) −11.0000 −0.866921
\(162\) 0 0
\(163\) 8.29156 + 14.3614i 0.649445 + 1.12487i 0.983256 + 0.182232i \(0.0583322\pi\)
−0.333810 + 0.942640i \(0.608335\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.65831 2.87228i 0.128324 0.222264i −0.794703 0.606998i \(-0.792374\pi\)
0.923027 + 0.384734i \(0.125707\pi\)
\(168\) 0 0
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) 0 0
\(171\) −13.2665 + 22.9783i −1.01451 + 1.75719i
\(172\) 0 0
\(173\) −3.50000 6.06218i −0.266100 0.460899i 0.701751 0.712422i \(-0.252402\pi\)
−0.967851 + 0.251523i \(0.919068\pi\)
\(174\) 0 0
\(175\) 8.29156 + 14.3614i 0.626783 + 1.08562i
\(176\) 0 0
\(177\) 11.0000 0.826811
\(178\) 0 0
\(179\) −1.65831 + 2.87228i −0.123948 + 0.214684i −0.921321 0.388802i \(-0.872889\pi\)
0.797373 + 0.603487i \(0.206222\pi\)
\(180\) 0 0
\(181\) −8.00000 −0.594635 −0.297318 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 0 0
\(183\) −29.8496 −2.20655
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −9.94987 −0.727607
\(188\) 0 0
\(189\) −27.5000 47.6314i −2.00033 3.46467i
\(190\) 0 0
\(191\) 11.6082 + 20.1060i 0.839939 + 1.45482i 0.889945 + 0.456068i \(0.150743\pi\)
−0.0500060 + 0.998749i \(0.515924\pi\)
\(192\) 0 0
\(193\) −6.50000 + 11.2583i −0.467880 + 0.810392i −0.999326 0.0366998i \(-0.988315\pi\)
0.531446 + 0.847092i \(0.321649\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.50000 11.2583i 0.463106 0.802123i −0.536008 0.844213i \(-0.680068\pi\)
0.999114 + 0.0420901i \(0.0134016\pi\)
\(198\) 0 0
\(199\) −4.97494 8.61684i −0.352664 0.610832i 0.634051 0.773291i \(-0.281391\pi\)
−0.986715 + 0.162459i \(0.948057\pi\)
\(200\) 0 0
\(201\) −16.5000 28.5788i −1.16382 2.01580i
\(202\) 0 0
\(203\) −16.5831 −1.16391
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −26.5330 −1.84417
\(208\) 0 0
\(209\) 11.0000 0.760886
\(210\) 0 0
\(211\) −1.65831 + 2.87228i −0.114163 + 0.197736i −0.917445 0.397863i \(-0.869752\pi\)
0.803282 + 0.595599i \(0.203085\pi\)
\(212\) 0 0
\(213\) 33.0000 2.26112
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 6.63325 11.4891i 0.448233 0.776363i
\(220\) 0 0
\(221\) 7.50000 7.79423i 0.504505 0.524297i
\(222\) 0 0
\(223\) 1.65831 2.87228i 0.111049 0.192342i −0.805145 0.593079i \(-0.797912\pi\)
0.916193 + 0.400736i \(0.131246\pi\)
\(224\) 0 0
\(225\) 20.0000 + 34.6410i 1.33333 + 2.30940i
\(226\) 0 0
\(227\) −1.65831 2.87228i −0.110066 0.190640i 0.805731 0.592282i \(-0.201773\pi\)
−0.915797 + 0.401642i \(0.868440\pi\)
\(228\) 0 0
\(229\) 8.00000 0.528655 0.264327 0.964433i \(-0.414850\pi\)
0.264327 + 0.964433i \(0.414850\pi\)
\(230\) 0 0
\(231\) −18.2414 + 31.5951i −1.20020 + 2.07880i
\(232\) 0 0
\(233\) 4.00000 0.262049 0.131024 0.991379i \(-0.458173\pi\)
0.131024 + 0.991379i \(0.458173\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −11.0000 + 19.0526i −0.714527 + 1.23760i
\(238\) 0 0
\(239\) 26.5330 1.71628 0.858138 0.513418i \(-0.171621\pi\)
0.858138 + 0.513418i \(0.171621\pi\)
\(240\) 0 0
\(241\) −6.50000 11.2583i −0.418702 0.725213i 0.577107 0.816668i \(-0.304181\pi\)
−0.995809 + 0.0914555i \(0.970848\pi\)
\(242\) 0 0
\(243\) −26.5330 45.9565i −1.70209 2.94811i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −8.29156 + 8.61684i −0.527579 + 0.548277i
\(248\) 0 0
\(249\) 22.0000 38.1051i 1.39419 2.41481i
\(250\) 0 0
\(251\) 8.29156 + 14.3614i 0.523359 + 0.906484i 0.999630 + 0.0271858i \(0.00865456\pi\)
−0.476272 + 0.879298i \(0.658012\pi\)
\(252\) 0 0
\(253\) 5.50000 + 9.52628i 0.345782 + 0.598912i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.50000 + 11.2583i −0.405459 + 0.702275i −0.994375 0.105919i \(-0.966222\pi\)
0.588916 + 0.808194i \(0.299555\pi\)
\(258\) 0 0
\(259\) 29.8496 1.85477
\(260\) 0 0
\(261\) −40.0000 −2.47594
\(262\) 0 0
\(263\) −11.6082 + 20.1060i −0.715791 + 1.23979i 0.246862 + 0.969051i \(0.420601\pi\)
−0.962653 + 0.270737i \(0.912733\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 1.65831 + 2.87228i 0.101487 + 0.175781i
\(268\) 0 0
\(269\) −14.5000 25.1147i −0.884081 1.53127i −0.846764 0.531969i \(-0.821452\pi\)
−0.0373168 0.999303i \(-0.511881\pi\)
\(270\) 0 0
\(271\) 14.9248 25.8505i 0.906618 1.57031i 0.0878869 0.996130i \(-0.471989\pi\)
0.818731 0.574178i \(-0.194678\pi\)
\(272\) 0 0
\(273\) −11.0000 38.1051i −0.665750 2.30623i
\(274\) 0 0
\(275\) 8.29156 14.3614i 0.500000 0.866025i
\(276\) 0 0
\(277\) −2.50000 4.33013i −0.150210 0.260172i 0.781094 0.624413i \(-0.214662\pi\)
−0.931305 + 0.364241i \(0.881328\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 20.0000 1.19310 0.596550 0.802576i \(-0.296538\pi\)
0.596550 + 0.802576i \(0.296538\pi\)
\(282\) 0 0
\(283\) 11.6082 20.1060i 0.690035 1.19518i −0.281791 0.959476i \(-0.590928\pi\)
0.971826 0.235700i \(-0.0757383\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −9.94987 −0.587323
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 23.2164 1.36097
\(292\) 0 0
\(293\) −3.50000 6.06218i −0.204472 0.354156i 0.745492 0.666514i \(-0.232214\pi\)
−0.949964 + 0.312358i \(0.898881\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −27.5000 + 47.6314i −1.59571 + 2.76385i
\(298\) 0 0
\(299\) −11.6082 2.87228i −0.671319 0.166108i
\(300\) 0 0
\(301\) −16.5000 + 28.5788i −0.951044 + 1.64726i
\(302\) 0 0
\(303\) 24.8747 + 43.0842i 1.42901 + 2.47512i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 13.2665 0.757159 0.378580 0.925569i \(-0.376413\pi\)
0.378580 + 0.925569i \(0.376413\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 26.5330 1.50455 0.752274 0.658850i \(-0.228957\pi\)
0.752274 + 0.658850i \(0.228957\pi\)
\(312\) 0 0
\(313\) 4.00000 0.226093 0.113047 0.993590i \(-0.463939\pi\)
0.113047 + 0.993590i \(0.463939\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 18.0000 1.01098 0.505490 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 0 0
\(319\) 8.29156 + 14.3614i 0.464238 + 0.804084i
\(320\) 0 0
\(321\) −5.50000 9.52628i −0.306980 0.531705i
\(322\) 0 0
\(323\) 4.97494 8.61684i 0.276813 0.479454i
\(324\) 0 0
\(325\) 5.00000 + 17.3205i 0.277350 + 0.960769i
\(326\) 0 0
\(327\) 26.5330 45.9565i 1.46728 2.54140i
\(328\) 0 0
\(329\) 11.0000 + 19.0526i 0.606450 + 1.05040i
\(330\) 0 0
\(331\) −4.97494 8.61684i −0.273447 0.473625i 0.696295 0.717756i \(-0.254831\pi\)
−0.969742 + 0.244131i \(0.921497\pi\)
\(332\) 0 0
\(333\) 72.0000 3.94558
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −12.0000 −0.653682 −0.326841 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(338\) 0 0
\(339\) −36.4829 −1.98148
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −9.94987 −0.537243
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 8.29156 + 14.3614i 0.445114 + 0.770961i 0.998060 0.0622565i \(-0.0198297\pi\)
−0.552946 + 0.833217i \(0.686496\pi\)
\(348\) 0 0
\(349\) −0.500000 + 0.866025i −0.0267644 + 0.0463573i −0.879097 0.476642i \(-0.841854\pi\)
0.852333 + 0.523000i \(0.175187\pi\)
\(350\) 0 0
\(351\) −16.5831 57.4456i −0.885142 3.06622i
\(352\) 0 0
\(353\) −15.5000 + 26.8468i −0.824982 + 1.42891i 0.0769515 + 0.997035i \(0.475481\pi\)
−0.901933 + 0.431875i \(0.857852\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 16.5000 + 28.5788i 0.873273 + 1.51255i
\(358\) 0 0
\(359\) −26.5330 −1.40036 −0.700179 0.713967i \(-0.746897\pi\)
−0.700179 + 0.713967i \(0.746897\pi\)
\(360\) 0 0
\(361\) 4.00000 6.92820i 0.210526 0.364642i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −11.6082 + 20.1060i −0.605942 + 1.04952i 0.385959 + 0.922516i \(0.373870\pi\)
−0.991902 + 0.127007i \(0.959463\pi\)
\(368\) 0 0
\(369\) −24.0000 −1.24939
\(370\) 0 0
\(371\) 13.2665 + 22.9783i 0.688762 + 1.19297i
\(372\) 0 0
\(373\) −6.50000 11.2583i −0.336557 0.582934i 0.647225 0.762299i \(-0.275929\pi\)
−0.983783 + 0.179364i \(0.942596\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −17.5000 4.33013i −0.901296 0.223013i
\(378\) 0 0
\(379\) −14.9248 + 25.8505i −0.766636 + 1.32785i 0.172741 + 0.984967i \(0.444738\pi\)
−0.939377 + 0.342885i \(0.888596\pi\)
\(380\) 0 0
\(381\) 16.5000 + 28.5788i 0.845321 + 1.46414i
\(382\) 0 0
\(383\) −1.65831 2.87228i −0.0847358 0.146767i 0.820543 0.571585i \(-0.193671\pi\)
−0.905279 + 0.424818i \(0.860338\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −39.7995 + 68.9348i −2.02312 + 3.50415i
\(388\) 0 0
\(389\) −10.0000 −0.507020 −0.253510 0.967333i \(-0.581585\pi\)
−0.253510 + 0.967333i \(0.581585\pi\)
\(390\) 0 0
\(391\) 9.94987 0.503187
\(392\) 0 0
\(393\) −22.0000 + 38.1051i −1.10975 + 1.92215i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −2.50000 4.33013i −0.125471 0.217323i 0.796446 0.604710i \(-0.206711\pi\)
−0.921917 + 0.387387i \(0.873378\pi\)
\(398\) 0 0
\(399\) −18.2414 31.5951i −0.913214 1.58173i
\(400\) 0 0
\(401\) 5.50000 9.52628i 0.274657 0.475720i −0.695392 0.718631i \(-0.744769\pi\)
0.970049 + 0.242911i \(0.0781024\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −14.9248 25.8505i −0.739795 1.28136i
\(408\) 0 0
\(409\) −6.50000 11.2583i −0.321404 0.556689i 0.659374 0.751815i \(-0.270822\pi\)
−0.980778 + 0.195127i \(0.937488\pi\)
\(410\) 0 0
\(411\) −29.8496 −1.47237
\(412\) 0 0
\(413\) −5.50000 + 9.52628i −0.270637 + 0.468758i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 11.0000 0.538672
\(418\) 0 0
\(419\) 8.29156 14.3614i 0.405069 0.701601i −0.589260 0.807943i \(-0.700581\pi\)
0.994330 + 0.106343i \(0.0339141\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) 26.5330 + 45.9565i 1.29008 + 2.23448i
\(424\) 0 0
\(425\) −7.50000 12.9904i −0.363803 0.630126i
\(426\) 0 0
\(427\) 14.9248 25.8505i 0.722262 1.25099i
\(428\) 0 0
\(429\) −27.5000 + 28.5788i −1.32771 + 1.37980i
\(430\) 0 0
\(431\) −8.29156 + 14.3614i −0.399390 + 0.691765i −0.993651 0.112508i \(-0.964112\pi\)
0.594260 + 0.804273i \(0.297445\pi\)
\(432\) 0 0
\(433\) −10.5000 18.1865i −0.504598 0.873989i −0.999986 0.00531724i \(-0.998307\pi\)
0.495388 0.868672i \(-0.335026\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −11.0000 −0.526201
\(438\) 0 0
\(439\) −8.29156 + 14.3614i −0.395735 + 0.685433i −0.993195 0.116466i \(-0.962843\pi\)
0.597460 + 0.801899i \(0.296177\pi\)
\(440\) 0 0
\(441\) 32.0000 1.52381
\(442\) 0 0
\(443\) −13.2665 −0.630310 −0.315155 0.949040i \(-0.602057\pi\)
−0.315155 + 0.949040i \(0.602057\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −3.31662 −0.156871
\(448\) 0 0
\(449\) 1.50000 + 2.59808i 0.0707894 + 0.122611i 0.899247 0.437440i \(-0.144115\pi\)
−0.828458 + 0.560051i \(0.810782\pi\)
\(450\) 0 0
\(451\) 4.97494 + 8.61684i 0.234261 + 0.405751i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.500000 0.866025i 0.0233890 0.0405110i −0.854094 0.520119i \(-0.825888\pi\)
0.877483 + 0.479608i \(0.159221\pi\)
\(458\) 0 0
\(459\) 24.8747 + 43.0842i 1.16105 + 2.01100i
\(460\) 0 0
\(461\) 1.50000 + 2.59808i 0.0698620 + 0.121004i 0.898840 0.438276i \(-0.144411\pi\)
−0.828978 + 0.559281i \(0.811077\pi\)
\(462\) 0 0
\(463\) −26.5330 −1.23309 −0.616547 0.787318i \(-0.711469\pi\)
−0.616547 + 0.787318i \(0.711469\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 19.8997 0.920851 0.460425 0.887698i \(-0.347697\pi\)
0.460425 + 0.887698i \(0.347697\pi\)
\(468\) 0 0
\(469\) 33.0000 1.52380
\(470\) 0 0
\(471\) 13.2665 22.9783i 0.611288 1.05878i
\(472\) 0 0
\(473\) 33.0000 1.51734
\(474\) 0 0
\(475\) 8.29156 + 14.3614i 0.380443 + 0.658947i
\(476\) 0 0
\(477\) 32.0000 + 55.4256i 1.46518 + 2.53777i
\(478\) 0 0
\(479\) 4.97494 8.61684i 0.227311 0.393714i −0.729700 0.683768i \(-0.760340\pi\)
0.957010 + 0.290054i \(0.0936734\pi\)
\(480\) 0 0
\(481\) 31.5000 + 7.79423i 1.43628 + 0.355386i
\(482\) 0 0
\(483\) 18.2414 31.5951i 0.830014 1.43763i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −4.97494 8.61684i −0.225436 0.390466i 0.731014 0.682362i \(-0.239047\pi\)
−0.956450 + 0.291896i \(0.905714\pi\)
\(488\) 0 0
\(489\) −55.0000 −2.48719
\(490\) 0 0
\(491\) 8.29156 14.3614i 0.374193 0.648121i −0.616013 0.787736i \(-0.711253\pi\)
0.990206 + 0.139615i \(0.0445864\pi\)
\(492\) 0 0
\(493\) 15.0000 0.675566
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −16.5000 + 28.5788i −0.740126 + 1.28194i
\(498\) 0 0
\(499\) −13.2665 −0.593890 −0.296945 0.954895i \(-0.595968\pi\)
−0.296945 + 0.954895i \(0.595968\pi\)
\(500\) 0 0
\(501\) 5.50000 + 9.52628i 0.245722 + 0.425603i
\(502\) 0 0
\(503\) −1.65831 2.87228i −0.0739405 0.128069i 0.826685 0.562666i \(-0.190224\pi\)
−0.900625 + 0.434597i \(0.856891\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.65831 43.0842i −0.0736482 1.91344i
\(508\) 0 0
\(509\) 19.5000 33.7750i 0.864322 1.49705i −0.00339621 0.999994i \(-0.501081\pi\)
0.867719 0.497056i \(-0.165586\pi\)
\(510\) 0 0
\(511\) 6.63325 + 11.4891i 0.293438 + 0.508249i
\(512\) 0 0
\(513\) −27.5000 47.6314i −1.21415 2.10298i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 11.0000 19.0526i 0.483779 0.837931i
\(518\) 0 0
\(519\) 23.2164 1.01909
\(520\) 0 0
\(521\) −12.0000 −0.525730 −0.262865 0.964833i \(-0.584667\pi\)
−0.262865 + 0.964833i \(0.584667\pi\)
\(522\) 0 0
\(523\) 8.29156 14.3614i 0.362565 0.627980i −0.625817 0.779970i \(-0.715235\pi\)
0.988382 + 0.151989i \(0.0485679\pi\)
\(524\) 0 0
\(525\) −55.0000 −2.40040
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 6.00000 + 10.3923i 0.260870 + 0.451839i
\(530\) 0 0
\(531\) −13.2665 + 22.9783i −0.575717 + 0.997171i
\(532\) 0 0
\(533\) −10.5000 2.59808i −0.454805 0.112535i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −5.50000 9.52628i −0.237343 0.411089i
\(538\) 0 0
\(539\) −6.63325 11.4891i −0.285714 0.494872i
\(540\) 0 0
\(541\) −18.0000 −0.773880 −0.386940 0.922105i \(-0.626468\pi\)
−0.386940 + 0.922105i \(0.626468\pi\)
\(542\) 0 0
\(543\) 13.2665 22.9783i 0.569320 0.986091i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −13.2665 −0.567235 −0.283617 0.958938i \(-0.591535\pi\)
−0.283617 + 0.958938i \(0.591535\pi\)
\(548\) 0 0
\(549\) 36.0000 62.3538i 1.53644 2.66120i
\(550\) 0 0
\(551\) −16.5831 −0.706465
\(552\) 0 0
\(553\) −11.0000 19.0526i −0.467768 0.810197i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 18.5000 32.0429i 0.783870 1.35770i −0.145802 0.989314i \(-0.546576\pi\)
0.929672 0.368389i \(-0.120091\pi\)
\(558\) 0 0
\(559\) −24.8747 + 25.8505i −1.05209 + 1.09336i
\(560\) 0 0
\(561\) 16.5000 28.5788i 0.696631 1.20660i
\(562\) 0 0
\(563\) −1.65831 2.87228i −0.0698895 0.121052i 0.828963 0.559303i \(-0.188931\pi\)
−0.898853 + 0.438251i \(0.855598\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 102.815 4.31784
\(568\) 0 0
\(569\) −7.50000 + 12.9904i −0.314416 + 0.544585i −0.979313 0.202350i \(-0.935142\pi\)
0.664897 + 0.746935i \(0.268475\pi\)
\(570\) 0 0
\(571\) 13.2665 0.555186 0.277593 0.960699i \(-0.410463\pi\)
0.277593 + 0.960699i \(0.410463\pi\)
\(572\) 0 0
\(573\) −77.0000 −3.21672
\(574\) 0 0
\(575\) −8.29156 + 14.3614i −0.345782 + 0.598912i
\(576\) 0 0
\(577\) 20.0000 0.832611 0.416305 0.909225i \(-0.363325\pi\)
0.416305 + 0.909225i \(0.363325\pi\)
\(578\) 0 0
\(579\) −21.5581 37.3397i −0.895922 1.55178i
\(580\) 0 0
\(581\) 22.0000 + 38.1051i 0.912714 + 1.58087i
\(582\) 0 0
\(583\) 13.2665 22.9783i 0.549442 0.951662i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 21.5581 37.3397i 0.889796 1.54117i 0.0496808 0.998765i \(-0.484180\pi\)
0.840116 0.542407i \(-0.182487\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 21.5581 + 37.3397i 0.886780 + 1.53595i
\(592\) 0 0
\(593\) −36.0000 −1.47834 −0.739171 0.673517i \(-0.764783\pi\)
−0.739171 + 0.673517i \(0.764783\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 33.0000 1.35060
\(598\) 0 0
\(599\) −33.1662 −1.35514 −0.677568 0.735460i \(-0.736966\pi\)
−0.677568 + 0.735460i \(0.736966\pi\)
\(600\) 0 0
\(601\) −14.5000 + 25.1147i −0.591467 + 1.02445i 0.402568 + 0.915390i \(0.368118\pi\)
−0.994035 + 0.109061i \(0.965216\pi\)
\(602\) 0 0
\(603\) 79.5990 3.24152
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −4.97494 8.61684i −0.201926 0.349747i 0.747223 0.664574i \(-0.231387\pi\)
−0.949149 + 0.314827i \(0.898054\pi\)
\(608\) 0 0
\(609\) 27.5000 47.6314i 1.11436 1.93012i
\(610\) 0 0
\(611\) 6.63325 + 22.9783i 0.268353 + 0.929601i
\(612\) 0 0
\(613\) 3.50000 6.06218i 0.141364 0.244849i −0.786647 0.617403i \(-0.788185\pi\)
0.928010 + 0.372554i \(0.121518\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 8.50000 + 14.7224i 0.342197 + 0.592703i 0.984840 0.173463i \(-0.0554956\pi\)
−0.642643 + 0.766165i \(0.722162\pi\)
\(618\) 0 0
\(619\) −39.7995 −1.59968 −0.799838 0.600215i \(-0.795082\pi\)
−0.799838 + 0.600215i \(0.795082\pi\)
\(620\) 0 0
\(621\) 27.5000 47.6314i 1.10354 1.91138i
\(622\) 0 0
\(623\) −3.31662 −0.132878
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) −18.2414 + 31.5951i −0.728493 + 1.26179i
\(628\) 0 0
\(629\) −27.0000 −1.07656
\(630\) 0 0
\(631\) −4.97494 8.61684i −0.198049 0.343031i 0.749847 0.661612i \(-0.230127\pi\)
−0.947896 + 0.318580i \(0.896794\pi\)
\(632\) 0 0
\(633\) −5.50000 9.52628i −0.218605 0.378636i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 14.0000 + 3.46410i 0.554700 + 0.137253i
\(638\) 0 0
\(639\) −39.7995 + 68.9348i −1.57444 + 2.72702i
\(640\) 0 0
\(641\) −10.5000 18.1865i −0.414725 0.718325i 0.580674 0.814136i \(-0.302789\pi\)
−0.995400 + 0.0958109i \(0.969456\pi\)
\(642\) 0 0
\(643\) −18.2414 31.5951i −0.719372 1.24599i −0.961249 0.275682i \(-0.911096\pi\)
0.241877 0.970307i \(-0.422237\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4.97494 8.61684i 0.195585 0.338763i −0.751507 0.659725i \(-0.770673\pi\)
0.947092 + 0.320962i \(0.104006\pi\)
\(648\) 0 0
\(649\) 11.0000 0.431788
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 7.50000 12.9904i 0.293498 0.508353i −0.681137 0.732156i \(-0.738514\pi\)
0.974634 + 0.223803i \(0.0718474\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 16.0000 + 27.7128i 0.624219 + 1.08118i
\(658\) 0 0
\(659\) 21.5581 + 37.3397i 0.839783 + 1.45455i 0.890076 + 0.455812i \(0.150651\pi\)
−0.0502932 + 0.998734i \(0.516016\pi\)
\(660\) 0 0
\(661\) −8.50000 + 14.7224i −0.330612 + 0.572636i −0.982632 0.185565i \(-0.940588\pi\)
0.652020 + 0.758202i \(0.273922\pi\)
\(662\) 0 0
\(663\) 9.94987 + 34.4674i 0.386421 + 1.33860i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −8.29156 14.3614i −0.321051 0.556076i
\(668\) 0 0
\(669\) 5.50000 + 9.52628i 0.212642 + 0.368307i
\(670\) 0 0
\(671\) −29.8496 −1.15233
\(672\) 0 0
\(673\) 24.5000 42.4352i 0.944406 1.63576i 0.187469 0.982271i \(-0.439972\pi\)
0.756937 0.653488i \(-0.226695\pi\)
\(674\) 0 0
\(675\) −82.9156 −3.19142
\(676\) 0 0
\(677\) −24.0000 −0.922395 −0.461197 0.887298i \(-0.652580\pi\)
−0.461197 + 0.887298i \(0.652580\pi\)
\(678\) 0 0
\(679\) −11.6082 + 20.1060i −0.445481 + 0.771596i
\(680\) 0 0
\(681\) 11.0000 0.421521
\(682\) 0 0
\(683\) −14.9248 25.8505i −0.571082 0.989143i −0.996455 0.0841251i \(-0.973190\pi\)
0.425373 0.905018i \(-0.360143\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −13.2665 + 22.9783i −0.506149 + 0.876675i
\(688\) 0 0
\(689\) 8.00000 + 27.7128i 0.304776 + 1.05577i
\(690\) 0 0
\(691\) 11.6082 20.1060i 0.441596 0.764867i −0.556212 0.831041i \(-0.687746\pi\)
0.997808 + 0.0661734i \(0.0210790\pi\)
\(692\) 0 0
\(693\) −44.0000 76.2102i −1.67142 2.89499i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 9.00000 0.340899
\(698\) 0 0
\(699\) −6.63325 + 11.4891i −0.250893 + 0.434559i
\(700\) 0 0
\(701\) −32.0000 −1.20862 −0.604312 0.796748i \(-0.706552\pi\)
−0.604312 + 0.796748i \(0.706552\pi\)
\(702\) 0 0
\(703\) 29.8496 1.12580
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −49.7494 −1.87102
\(708\) 0 0
\(709\) −14.5000 25.1147i −0.544559 0.943204i −0.998635 0.0522406i \(-0.983364\pi\)
0.454076 0.890963i \(-0.349970\pi\)
\(710\) 0 0
\(711\) −26.5330 45.9565i −0.995065 1.72350i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −44.0000 + 76.2102i −1.64321 + 2.84612i
\(718\) 0 0
\(719\) −14.9248 25.8505i −0.556602 0.964062i −0.997777 0.0666413i \(-0.978772\pi\)
0.441175 0.897421i \(-0.354562\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 43.1161 1.60351
\(724\) 0 0
\(725\) −12.5000 + 21.6506i −0.464238 + 0.804084i
\(726\) 0 0
\(727\) −26.5330 −0.984054 −0.492027 0.870580i \(-0.663744\pi\)
−0.492027 + 0.870580i \(0.663744\pi\)
\(728\) 0 0
\(729\) 83.0000 3.07407
\(730\) 0 0
\(731\) 14.9248 25.8505i 0.552014 0.956116i
\(732\) 0 0
\(733\) 18.0000 0.664845 0.332423 0.943131i \(-0.392134\pi\)
0.332423 + 0.943131i \(0.392134\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −16.5000 28.5788i −0.607785 1.05272i
\(738\) 0 0
\(739\) −4.97494 + 8.61684i −0.183006 + 0.316976i −0.942903 0.333068i \(-0.891916\pi\)
0.759897 + 0.650044i \(0.225249\pi\)
\(740\) 0 0
\(741\) −11.0000 38.1051i −0.404095 1.39983i
\(742\) 0 0
\(743\) −21.5581 + 37.3397i −0.790889 + 1.36986i 0.134529 + 0.990910i \(0.457048\pi\)
−0.925417 + 0.378949i \(0.876285\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 53.0660 + 91.9130i 1.94158 + 3.36292i
\(748\) 0 0
\(749\) 11.0000 0.401931
\(750\) 0 0
\(751\) 14.9248 25.8505i 0.544614 0.943299i −0.454017 0.890993i \(-0.650009\pi\)
0.998631 0.0523063i \(-0.0166572\pi\)
\(752\) 0 0
\(753\) −55.0000 −2.00431
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 3.50000 6.06218i 0.127210 0.220334i −0.795385 0.606105i \(-0.792731\pi\)
0.922595 + 0.385771i \(0.126065\pi\)
\(758\) 0 0
\(759\) −36.4829 −1.32424
\(760\) 0 0
\(761\) 13.5000 + 23.3827i 0.489375 + 0.847622i 0.999925 0.0122260i \(-0.00389175\pi\)
−0.510551 + 0.859848i \(0.670558\pi\)
\(762\) 0 0
\(763\) 26.5330 + 45.9565i 0.960559 + 1.66374i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8.29156 + 8.61684i −0.299391 + 0.311136i
\(768\) 0 0
\(769\) 13.5000 23.3827i 0.486822 0.843201i −0.513063 0.858351i \(-0.671489\pi\)
0.999885 + 0.0151499i \(0.00482254\pi\)
\(770\) 0 0
\(771\) −21.5581 37.3397i −0.776395 1.34475i
\(772\) 0 0
\(773\) −10.5000 18.1865i −0.377659 0.654124i 0.613062 0.790034i \(-0.289937\pi\)
−0.990721 + 0.135910i \(0.956604\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −49.5000 + 85.7365i −1.77580 + 3.07578i
\(778\) 0 0
\(779\) −9.94987 −0.356491
\(780\) 0 0
\(781\) 33.0000 1.18083
\(782\) 0 0
\(783\) 41.4578 71.8070i 1.48158 2.56617i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −4.97494 8.61684i −0.177337 0.307157i 0.763630 0.645654i \(-0.223415\pi\)
−0.940968 + 0.338496i \(0.890082\pi\)
\(788\) 0 0
\(789\) −38.5000 66.6840i −1.37064 2.37401i
\(790\) 0 0
\(791\) 18.2414 31.5951i 0.648591 1.12339i
\(792\) 0 0
\(793\) 22.5000 23.3827i 0.798998 0.830344i