Properties

Label 880.2.b.j.529.3
Level $880$
Weight $2$
Character 880.529
Analytic conductor $7.027$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [880,2,Mod(529,880)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(880, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("880.529");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.b (of order \(2\), degree \(1\), not 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: \(7.02683537787\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.47985531136.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 19x^{6} + 91x^{4} + 45x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 440)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 529.3
Root \(-0.655762i\) of defining polynomial
Character \(\chi\) \(=\) 880.529
Dual form 880.2.b.j.529.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.655762i q^{3} +(-2.23285 + 0.119978i) q^{5} -0.415806i q^{7} +2.56998 q^{9} +O(q^{10})\) \(q-0.655762i q^{3} +(-2.23285 + 0.119978i) q^{5} -0.415806i q^{7} +2.56998 q^{9} -1.00000 q^{11} +4.00000i q^{13} +(0.0786769 + 1.46422i) q^{15} +6.51558i q^{17} +5.20406 q^{19} -0.272670 q^{21} -8.54830i q^{23} +(4.97121 - 0.535784i) q^{25} -3.65258i q^{27} -0.895717 q^{29} +6.73836 q^{31} +0.655762i q^{33} +(0.0498875 + 0.928432i) q^{35} -8.96410i q^{37} +2.62305 q^{39} +10.0998 q^{41} +4.78825i q^{43} +(-5.73836 + 0.308340i) q^{45} +5.61986i q^{47} +6.82711 q^{49} +4.27267 q^{51} +10.0357i q^{53} +(2.23285 - 0.119978i) q^{55} -3.41262i q^{57} -1.63408 q^{59} +7.10428 q^{61} -1.06861i q^{63} +(-0.479911 - 8.93139i) q^{65} +10.6914i q^{67} -5.60565 q^{69} +6.19302 q^{71} +3.16839i q^{73} +(-0.351347 - 3.25993i) q^{75} +0.415806i q^{77} -11.2682 q^{79} +5.31471 q^{81} -16.2429i q^{83} +(-0.781725 - 14.5483i) q^{85} +0.587377i q^{87} -9.56998 q^{89} +1.66323 q^{91} -4.41876i q^{93} +(-11.6199 + 0.624371i) q^{95} -0.591657i q^{97} -2.56998 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 14 q^{9} - 8 q^{11} + 12 q^{15} - 18 q^{19} - 14 q^{21} - 2 q^{25} - 6 q^{29} + 30 q^{31} - 30 q^{35} + 8 q^{39} + 20 q^{41} - 22 q^{45} - 18 q^{49} + 46 q^{51} + 12 q^{59} + 58 q^{61} - 8 q^{65} + 60 q^{69} + 2 q^{71} - 26 q^{75} - 40 q^{79} + 88 q^{81} - 26 q^{85} - 42 q^{89} - 8 q^{91} - 28 q^{95} + 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).

\(n\) \(111\) \(177\) \(321\) \(661\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.655762i 0.378604i −0.981919 0.189302i \(-0.939377\pi\)
0.981919 0.189302i \(-0.0606226\pi\)
\(4\) 0 0
\(5\) −2.23285 + 0.119978i −0.998559 + 0.0536557i
\(6\) 0 0
\(7\) 0.415806i 0.157160i −0.996908 0.0785800i \(-0.974961\pi\)
0.996908 0.0785800i \(-0.0250386\pi\)
\(8\) 0 0
\(9\) 2.56998 0.856659
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) 4.00000i 1.10940i 0.832050 + 0.554700i \(0.187167\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) 0.0786769 + 1.46422i 0.0203143 + 0.378059i
\(16\) 0 0
\(17\) 6.51558i 1.58026i 0.612939 + 0.790130i \(0.289987\pi\)
−0.612939 + 0.790130i \(0.710013\pi\)
\(18\) 0 0
\(19\) 5.20406 1.19389 0.596946 0.802281i \(-0.296381\pi\)
0.596946 + 0.802281i \(0.296381\pi\)
\(20\) 0 0
\(21\) −0.272670 −0.0595015
\(22\) 0 0
\(23\) 8.54830i 1.78244i −0.453568 0.891221i \(-0.649849\pi\)
0.453568 0.891221i \(-0.350151\pi\)
\(24\) 0 0
\(25\) 4.97121 0.535784i 0.994242 0.107157i
\(26\) 0 0
\(27\) 3.65258i 0.702939i
\(28\) 0 0
\(29\) −0.895717 −0.166331 −0.0831653 0.996536i \(-0.526503\pi\)
−0.0831653 + 0.996536i \(0.526503\pi\)
\(30\) 0 0
\(31\) 6.73836 1.21025 0.605123 0.796132i \(-0.293124\pi\)
0.605123 + 0.796132i \(0.293124\pi\)
\(32\) 0 0
\(33\) 0.655762i 0.114153i
\(34\) 0 0
\(35\) 0.0498875 + 0.928432i 0.00843253 + 0.156934i
\(36\) 0 0
\(37\) 8.96410i 1.47369i −0.676062 0.736845i \(-0.736315\pi\)
0.676062 0.736845i \(-0.263685\pi\)
\(38\) 0 0
\(39\) 2.62305 0.420024
\(40\) 0 0
\(41\) 10.0998 1.57732 0.788660 0.614830i \(-0.210775\pi\)
0.788660 + 0.614830i \(0.210775\pi\)
\(42\) 0 0
\(43\) 4.78825i 0.730201i 0.930968 + 0.365101i \(0.118965\pi\)
−0.930968 + 0.365101i \(0.881035\pi\)
\(44\) 0 0
\(45\) −5.73836 + 0.308340i −0.855425 + 0.0459646i
\(46\) 0 0
\(47\) 5.61986i 0.819741i 0.912144 + 0.409871i \(0.134426\pi\)
−0.912144 + 0.409871i \(0.865574\pi\)
\(48\) 0 0
\(49\) 6.82711 0.975301
\(50\) 0 0
\(51\) 4.27267 0.598293
\(52\) 0 0
\(53\) 10.0357i 1.37851i 0.724521 + 0.689253i \(0.242061\pi\)
−0.724521 + 0.689253i \(0.757939\pi\)
\(54\) 0 0
\(55\) 2.23285 0.119978i 0.301077 0.0161778i
\(56\) 0 0
\(57\) 3.41262i 0.452013i
\(58\) 0 0
\(59\) −1.63408 −0.212739 −0.106370 0.994327i \(-0.533923\pi\)
−0.106370 + 0.994327i \(0.533923\pi\)
\(60\) 0 0
\(61\) 7.10428 0.909610 0.454805 0.890591i \(-0.349709\pi\)
0.454805 + 0.890591i \(0.349709\pi\)
\(62\) 0 0
\(63\) 1.06861i 0.134633i
\(64\) 0 0
\(65\) −0.479911 8.93139i −0.0595257 1.10780i
\(66\) 0 0
\(67\) 10.6914i 1.30617i 0.757286 + 0.653083i \(0.226525\pi\)
−0.757286 + 0.653083i \(0.773475\pi\)
\(68\) 0 0
\(69\) −5.60565 −0.674841
\(70\) 0 0
\(71\) 6.19302 0.734977 0.367488 0.930028i \(-0.380218\pi\)
0.367488 + 0.930028i \(0.380218\pi\)
\(72\) 0 0
\(73\) 3.16839i 0.370832i 0.982660 + 0.185416i \(0.0593632\pi\)
−0.982660 + 0.185416i \(0.940637\pi\)
\(74\) 0 0
\(75\) −0.351347 3.25993i −0.0405700 0.376424i
\(76\) 0 0
\(77\) 0.415806i 0.0473855i
\(78\) 0 0
\(79\) −11.2682 −1.26777 −0.633884 0.773428i \(-0.718540\pi\)
−0.633884 + 0.773428i \(0.718540\pi\)
\(80\) 0 0
\(81\) 5.31471 0.590523
\(82\) 0 0
\(83\) 16.2429i 1.78289i −0.453128 0.891446i \(-0.649692\pi\)
0.453128 0.891446i \(-0.350308\pi\)
\(84\) 0 0
\(85\) −0.781725 14.5483i −0.0847900 1.57798i
\(86\) 0 0
\(87\) 0.587377i 0.0629735i
\(88\) 0 0
\(89\) −9.56998 −1.01442 −0.507208 0.861824i \(-0.669322\pi\)
−0.507208 + 0.861824i \(0.669322\pi\)
\(90\) 0 0
\(91\) 1.66323 0.174353
\(92\) 0 0
\(93\) 4.41876i 0.458204i
\(94\) 0 0
\(95\) −11.6199 + 0.624371i −1.19217 + 0.0640591i
\(96\) 0 0
\(97\) 0.591657i 0.0600737i −0.999549 0.0300368i \(-0.990438\pi\)
0.999549 0.0300368i \(-0.00956246\pi\)
\(98\) 0 0
\(99\) −2.56998 −0.258292
\(100\) 0 0
\(101\) −4.62305 −0.460010 −0.230005 0.973189i \(-0.573874\pi\)
−0.230005 + 0.973189i \(0.573874\pi\)
\(102\) 0 0
\(103\) 8.24291i 0.812198i 0.913829 + 0.406099i \(0.133111\pi\)
−0.913829 + 0.406099i \(0.866889\pi\)
\(104\) 0 0
\(105\) 0.608830 0.0327143i 0.0594157 0.00319259i
\(106\) 0 0
\(107\) 17.6199i 1.70338i 0.524049 + 0.851688i \(0.324421\pi\)
−0.524049 + 0.851688i \(0.675579\pi\)
\(108\) 0 0
\(109\) −3.66323 −0.350873 −0.175437 0.984491i \(-0.556134\pi\)
−0.175437 + 0.984491i \(0.556134\pi\)
\(110\) 0 0
\(111\) −5.87832 −0.557945
\(112\) 0 0
\(113\) 11.4797i 1.07992i −0.841691 0.539959i \(-0.818440\pi\)
0.841691 0.539959i \(-0.181560\pi\)
\(114\) 0 0
\(115\) 1.02561 + 19.0870i 0.0956382 + 1.77988i
\(116\) 0 0
\(117\) 10.2799i 0.950378i
\(118\) 0 0
\(119\) 2.70922 0.248354
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 6.62305i 0.597180i
\(124\) 0 0
\(125\) −11.0357 + 1.79276i −0.987060 + 0.160349i
\(126\) 0 0
\(127\) 9.13995i 0.811040i −0.914086 0.405520i \(-0.867091\pi\)
0.914086 0.405520i \(-0.132909\pi\)
\(128\) 0 0
\(129\) 3.13995 0.276457
\(130\) 0 0
\(131\) 2.48123 0.216787 0.108393 0.994108i \(-0.465429\pi\)
0.108393 + 0.994108i \(0.465429\pi\)
\(132\) 0 0
\(133\) 2.16388i 0.187632i
\(134\) 0 0
\(135\) 0.438228 + 8.15565i 0.0377167 + 0.701926i
\(136\) 0 0
\(137\) 7.40834i 0.632937i −0.948603 0.316469i \(-0.897503\pi\)
0.948603 0.316469i \(-0.102497\pi\)
\(138\) 0 0
\(139\) −1.69166 −0.143485 −0.0717424 0.997423i \(-0.522856\pi\)
−0.0717424 + 0.997423i \(0.522856\pi\)
\(140\) 0 0
\(141\) 3.68529 0.310358
\(142\) 0 0
\(143\) 4.00000i 0.334497i
\(144\) 0 0
\(145\) 2.00000 0.107466i 0.166091 0.00892458i
\(146\) 0 0
\(147\) 4.47696i 0.369253i
\(148\) 0 0
\(149\) −3.74940 −0.307163 −0.153581 0.988136i \(-0.549081\pi\)
−0.153581 + 0.988136i \(0.549081\pi\)
\(150\) 0 0
\(151\) 15.1400 1.23207 0.616036 0.787718i \(-0.288738\pi\)
0.616036 + 0.787718i \(0.288738\pi\)
\(152\) 0 0
\(153\) 16.7449i 1.35374i
\(154\) 0 0
\(155\) −15.0457 + 0.808454i −1.20850 + 0.0649366i
\(156\) 0 0
\(157\) 11.5871i 0.924755i −0.886683 0.462378i \(-0.846996\pi\)
0.886683 0.462378i \(-0.153004\pi\)
\(158\) 0 0
\(159\) 6.58101 0.521908
\(160\) 0 0
\(161\) −3.55444 −0.280129
\(162\) 0 0
\(163\) 6.82392i 0.534491i −0.963629 0.267245i \(-0.913887\pi\)
0.963629 0.267245i \(-0.0861134\pi\)
\(164\) 0 0
\(165\) −0.0786769 1.46422i −0.00612499 0.113989i
\(166\) 0 0
\(167\) 7.10428i 0.549746i 0.961481 + 0.274873i \(0.0886358\pi\)
−0.961481 + 0.274873i \(0.911364\pi\)
\(168\) 0 0
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) 13.3743 1.02276
\(172\) 0 0
\(173\) 9.31152i 0.707942i 0.935256 + 0.353971i \(0.115169\pi\)
−0.935256 + 0.353971i \(0.884831\pi\)
\(174\) 0 0
\(175\) −0.222782 2.06706i −0.0168408 0.156255i
\(176\) 0 0
\(177\) 1.07157i 0.0805440i
\(178\) 0 0
\(179\) −26.6368 −1.99093 −0.995464 0.0951359i \(-0.969671\pi\)
−0.995464 + 0.0951359i \(0.969671\pi\)
\(180\) 0 0
\(181\) 1.01103 0.0751495 0.0375748 0.999294i \(-0.488037\pi\)
0.0375748 + 0.999294i \(0.488037\pi\)
\(182\) 0 0
\(183\) 4.65872i 0.344382i
\(184\) 0 0
\(185\) 1.07549 + 20.0155i 0.0790718 + 1.47157i
\(186\) 0 0
\(187\) 6.51558i 0.476466i
\(188\) 0 0
\(189\) −1.51877 −0.110474
\(190\) 0 0
\(191\) −10.5655 −0.764490 −0.382245 0.924061i \(-0.624849\pi\)
−0.382245 + 0.924061i \(0.624849\pi\)
\(192\) 0 0
\(193\) 11.8271i 0.851334i 0.904880 + 0.425667i \(0.139960\pi\)
−0.904880 + 0.425667i \(0.860040\pi\)
\(194\) 0 0
\(195\) −5.85686 + 0.314707i −0.419419 + 0.0225367i
\(196\) 0 0
\(197\) 1.31152i 0.0934422i 0.998908 + 0.0467211i \(0.0148772\pi\)
−0.998908 + 0.0467211i \(0.985123\pi\)
\(198\) 0 0
\(199\) −11.8271 −0.838401 −0.419201 0.907894i \(-0.637690\pi\)
−0.419201 + 0.907894i \(0.637690\pi\)
\(200\) 0 0
\(201\) 7.01103 0.494520
\(202\) 0 0
\(203\) 0.372445i 0.0261405i
\(204\) 0 0
\(205\) −22.5513 + 1.21175i −1.57505 + 0.0846322i
\(206\) 0 0
\(207\) 21.9689i 1.52695i
\(208\) 0 0
\(209\) −5.20406 −0.359972
\(210\) 0 0
\(211\) 8.37244 0.576383 0.288191 0.957573i \(-0.406946\pi\)
0.288191 + 0.957573i \(0.406946\pi\)
\(212\) 0 0
\(213\) 4.06115i 0.278265i
\(214\) 0 0
\(215\) −0.574484 10.6914i −0.0391795 0.729150i
\(216\) 0 0
\(217\) 2.80185i 0.190202i
\(218\) 0 0
\(219\) 2.07771 0.140398
\(220\) 0 0
\(221\) −26.0623 −1.75314
\(222\) 0 0
\(223\) 22.1461i 1.48301i 0.670946 + 0.741506i \(0.265888\pi\)
−0.670946 + 0.741506i \(0.734112\pi\)
\(224\) 0 0
\(225\) 12.7759 1.37695i 0.851726 0.0917968i
\(226\) 0 0
\(227\) 21.8194i 1.44821i −0.689692 0.724103i \(-0.742254\pi\)
0.689692 0.724103i \(-0.257746\pi\)
\(228\) 0 0
\(229\) −2.80247 −0.185192 −0.0925962 0.995704i \(-0.529517\pi\)
−0.0925962 + 0.995704i \(0.529517\pi\)
\(230\) 0 0
\(231\) 0.272670 0.0179404
\(232\) 0 0
\(233\) 8.24424i 0.540098i 0.962847 + 0.270049i \(0.0870399\pi\)
−0.962847 + 0.270049i \(0.912960\pi\)
\(234\) 0 0
\(235\) −0.674259 12.5483i −0.0439838 0.818561i
\(236\) 0 0
\(237\) 7.38923i 0.479982i
\(238\) 0 0
\(239\) −11.2682 −0.728877 −0.364438 0.931227i \(-0.618739\pi\)
−0.364438 + 0.931227i \(0.618739\pi\)
\(240\) 0 0
\(241\) 22.3860 1.44201 0.721006 0.692929i \(-0.243680\pi\)
0.721006 + 0.692929i \(0.243680\pi\)
\(242\) 0 0
\(243\) 14.4429i 0.926514i
\(244\) 0 0
\(245\) −15.2439 + 0.819101i −0.973896 + 0.0523304i
\(246\) 0 0
\(247\) 20.8162i 1.32451i
\(248\) 0 0
\(249\) −10.6515 −0.675010
\(250\) 0 0
\(251\) −3.84265 −0.242546 −0.121273 0.992619i \(-0.538698\pi\)
−0.121273 + 0.992619i \(0.538698\pi\)
\(252\) 0 0
\(253\) 8.54830i 0.537427i
\(254\) 0 0
\(255\) −9.54022 + 0.512626i −0.597432 + 0.0321019i
\(256\) 0 0
\(257\) 10.6230i 0.662648i −0.943517 0.331324i \(-0.892505\pi\)
0.943517 0.331324i \(-0.107495\pi\)
\(258\) 0 0
\(259\) −3.72733 −0.231605
\(260\) 0 0
\(261\) −2.30197 −0.142489
\(262\) 0 0
\(263\) 5.79276i 0.357197i −0.983922 0.178598i \(-0.942844\pi\)
0.983922 0.178598i \(-0.0571563\pi\)
\(264\) 0 0
\(265\) −1.20406 22.4081i −0.0739647 1.37652i
\(266\) 0 0
\(267\) 6.27563i 0.384062i
\(268\) 0 0
\(269\) 8.20857 0.500485 0.250243 0.968183i \(-0.419490\pi\)
0.250243 + 0.968183i \(0.419490\pi\)
\(270\) 0 0
\(271\) −27.3111 −1.65903 −0.829515 0.558485i \(-0.811383\pi\)
−0.829515 + 0.558485i \(0.811383\pi\)
\(272\) 0 0
\(273\) 1.09068i 0.0660109i
\(274\) 0 0
\(275\) −4.97121 + 0.535784i −0.299775 + 0.0323090i
\(276\) 0 0
\(277\) 14.4735i 0.869631i 0.900520 + 0.434815i \(0.143186\pi\)
−0.900520 + 0.434815i \(0.856814\pi\)
\(278\) 0 0
\(279\) 17.3174 1.03677
\(280\) 0 0
\(281\) 16.2799 0.971178 0.485589 0.874187i \(-0.338605\pi\)
0.485589 + 0.874187i \(0.338605\pi\)
\(282\) 0 0
\(283\) 10.5169i 0.625165i −0.949891 0.312583i \(-0.898806\pi\)
0.949891 0.312583i \(-0.101194\pi\)
\(284\) 0 0
\(285\) 0.409439 + 7.61986i 0.0242531 + 0.451362i
\(286\) 0 0
\(287\) 4.19955i 0.247892i
\(288\) 0 0
\(289\) −25.4528 −1.49722
\(290\) 0 0
\(291\) −0.387986 −0.0227441
\(292\) 0 0
\(293\) 9.37695i 0.547807i −0.961757 0.273904i \(-0.911685\pi\)
0.961757 0.273904i \(-0.0883150\pi\)
\(294\) 0 0
\(295\) 3.64865 0.196053i 0.212433 0.0114147i
\(296\) 0 0
\(297\) 3.65258i 0.211944i
\(298\) 0 0
\(299\) 34.1932 1.97744
\(300\) 0 0
\(301\) 1.99099 0.114758
\(302\) 0 0
\(303\) 3.03162i 0.174162i
\(304\) 0 0
\(305\) −15.8628 + 0.852356i −0.908300 + 0.0488058i
\(306\) 0 0
\(307\) 2.09978i 0.119840i 0.998203 + 0.0599202i \(0.0190846\pi\)
−0.998203 + 0.0599202i \(0.980915\pi\)
\(308\) 0 0
\(309\) 5.40539 0.307502
\(310\) 0 0
\(311\) 20.3724 1.15522 0.577608 0.816314i \(-0.303986\pi\)
0.577608 + 0.816314i \(0.303986\pi\)
\(312\) 0 0
\(313\) 23.8968i 1.35073i −0.737485 0.675364i \(-0.763987\pi\)
0.737485 0.675364i \(-0.236013\pi\)
\(314\) 0 0
\(315\) 0.128210 + 2.38605i 0.00722380 + 0.134439i
\(316\) 0 0
\(317\) 5.86114i 0.329195i 0.986361 + 0.164597i \(0.0526325\pi\)
−0.986361 + 0.164597i \(0.947368\pi\)
\(318\) 0 0
\(319\) 0.895717 0.0501506
\(320\) 0 0
\(321\) 11.5544 0.644906
\(322\) 0 0
\(323\) 33.9075i 1.88666i
\(324\) 0 0
\(325\) 2.14314 + 19.8848i 0.118880 + 1.10301i
\(326\) 0 0
\(327\) 2.40220i 0.132842i
\(328\) 0 0
\(329\) 2.33677 0.128831
\(330\) 0 0
\(331\) 0.574484 0.0315765 0.0157882 0.999875i \(-0.494974\pi\)
0.0157882 + 0.999875i \(0.494974\pi\)
\(332\) 0 0
\(333\) 23.0375i 1.26245i
\(334\) 0 0
\(335\) −1.28273 23.8723i −0.0700833 1.30428i
\(336\) 0 0
\(337\) 4.10747i 0.223748i 0.993722 + 0.111874i \(0.0356853\pi\)
−0.993722 + 0.111874i \(0.964315\pi\)
\(338\) 0 0
\(339\) −7.52794 −0.408862
\(340\) 0 0
\(341\) −6.73836 −0.364903
\(342\) 0 0
\(343\) 5.74940i 0.310438i
\(344\) 0 0
\(345\) 12.5166 0.672553i 0.673868 0.0362090i
\(346\) 0 0
\(347\) 8.30834i 0.446015i −0.974817 0.223008i \(-0.928413\pi\)
0.974817 0.223008i \(-0.0715875\pi\)
\(348\) 0 0
\(349\) 18.4858 0.989523 0.494762 0.869029i \(-0.335255\pi\)
0.494762 + 0.869029i \(0.335255\pi\)
\(350\) 0 0
\(351\) 14.6103 0.779841
\(352\) 0 0
\(353\) 26.5199i 1.41151i 0.708456 + 0.705755i \(0.249392\pi\)
−0.708456 + 0.705755i \(0.750608\pi\)
\(354\) 0 0
\(355\) −13.8281 + 0.743025i −0.733918 + 0.0394357i
\(356\) 0 0
\(357\) 1.77660i 0.0940278i
\(358\) 0 0
\(359\) −18.8226 −0.993419 −0.496709 0.867917i \(-0.665459\pi\)
−0.496709 + 0.867917i \(0.665459\pi\)
\(360\) 0 0
\(361\) 8.08222 0.425380
\(362\) 0 0
\(363\) 0.655762i 0.0344186i
\(364\) 0 0
\(365\) −0.380136 7.07452i −0.0198972 0.370298i
\(366\) 0 0
\(367\) 10.2115i 0.533037i −0.963830 0.266519i \(-0.914127\pi\)
0.963830 0.266519i \(-0.0858734\pi\)
\(368\) 0 0
\(369\) 25.9562 1.35122
\(370\) 0 0
\(371\) 4.17289 0.216646
\(372\) 0 0
\(373\) 32.3363i 1.67431i −0.546965 0.837156i \(-0.684217\pi\)
0.546965 0.837156i \(-0.315783\pi\)
\(374\) 0 0
\(375\) 1.17562 + 7.23677i 0.0607089 + 0.373705i
\(376\) 0 0
\(377\) 3.58287i 0.184527i
\(378\) 0 0
\(379\) 15.3686 0.789434 0.394717 0.918803i \(-0.370843\pi\)
0.394717 + 0.918803i \(0.370843\pi\)
\(380\) 0 0
\(381\) −5.99363 −0.307063
\(382\) 0 0
\(383\) 13.6662i 0.698309i 0.937065 + 0.349155i \(0.113531\pi\)
−0.937065 + 0.349155i \(0.886469\pi\)
\(384\) 0 0
\(385\) −0.0498875 0.928432i −0.00254250 0.0473173i
\(386\) 0 0
\(387\) 12.3057i 0.625534i
\(388\) 0 0
\(389\) 9.01103 0.456878 0.228439 0.973558i \(-0.426638\pi\)
0.228439 + 0.973558i \(0.426638\pi\)
\(390\) 0 0
\(391\) 55.6971 2.81672
\(392\) 0 0
\(393\) 1.62710i 0.0820763i
\(394\) 0 0
\(395\) 25.1601 1.35193i 1.26594 0.0680229i
\(396\) 0 0
\(397\) 3.45466i 0.173384i 0.996235 + 0.0866922i \(0.0276297\pi\)
−0.996235 + 0.0866922i \(0.972370\pi\)
\(398\) 0 0
\(399\) −1.41899 −0.0710384
\(400\) 0 0
\(401\) −1.62756 −0.0812762 −0.0406381 0.999174i \(-0.512939\pi\)
−0.0406381 + 0.999174i \(0.512939\pi\)
\(402\) 0 0
\(403\) 26.9535i 1.34265i
\(404\) 0 0
\(405\) −11.8669 + 0.637647i −0.589672 + 0.0316849i
\(406\) 0 0
\(407\) 8.96410i 0.444334i
\(408\) 0 0
\(409\) −6.54534 −0.323646 −0.161823 0.986820i \(-0.551737\pi\)
−0.161823 + 0.986820i \(0.551737\pi\)
\(410\) 0 0
\(411\) −4.85811 −0.239633
\(412\) 0 0
\(413\) 0.679461i 0.0334341i
\(414\) 0 0
\(415\) 1.94879 + 36.2679i 0.0956623 + 1.78032i
\(416\) 0 0
\(417\) 1.10933i 0.0543239i
\(418\) 0 0
\(419\) −34.4795 −1.68443 −0.842216 0.539141i \(-0.818749\pi\)
−0.842216 + 0.539141i \(0.818749\pi\)
\(420\) 0 0
\(421\) 6.54534 0.319000 0.159500 0.987198i \(-0.449012\pi\)
0.159500 + 0.987198i \(0.449012\pi\)
\(422\) 0 0
\(423\) 14.4429i 0.702239i
\(424\) 0 0
\(425\) 3.49094 + 32.3903i 0.169336 + 1.57116i
\(426\) 0 0
\(427\) 2.95401i 0.142954i
\(428\) 0 0
\(429\) −2.62305 −0.126642
\(430\) 0 0
\(431\) −36.1711 −1.74230 −0.871151 0.491016i \(-0.836626\pi\)
−0.871151 + 0.491016i \(0.836626\pi\)
\(432\) 0 0
\(433\) 38.1027i 1.83110i −0.402204 0.915550i \(-0.631756\pi\)
0.402204 0.915550i \(-0.368244\pi\)
\(434\) 0 0
\(435\) −0.0704722 1.31152i −0.00337889 0.0628828i
\(436\) 0 0
\(437\) 44.4858i 2.12805i
\(438\) 0 0
\(439\) 12.1282 0.578848 0.289424 0.957201i \(-0.406536\pi\)
0.289424 + 0.957201i \(0.406536\pi\)
\(440\) 0 0
\(441\) 17.5455 0.835500
\(442\) 0 0
\(443\) 16.5483i 0.786233i 0.919489 + 0.393117i \(0.128603\pi\)
−0.919489 + 0.393117i \(0.871397\pi\)
\(444\) 0 0
\(445\) 21.3683 1.14818i 1.01295 0.0544292i
\(446\) 0 0
\(447\) 2.45871i 0.116293i
\(448\) 0 0
\(449\) −15.6056 −0.736476 −0.368238 0.929732i \(-0.620039\pi\)
−0.368238 + 0.929732i \(0.620039\pi\)
\(450\) 0 0
\(451\) −10.0998 −0.475580
\(452\) 0 0
\(453\) 9.92820i 0.466468i
\(454\) 0 0
\(455\) −3.71373 + 0.199550i −0.174102 + 0.00935505i
\(456\) 0 0
\(457\) 5.87761i 0.274943i 0.990506 + 0.137471i \(0.0438975\pi\)
−0.990506 + 0.137471i \(0.956102\pi\)
\(458\) 0 0
\(459\) 23.7987 1.11083
\(460\) 0 0
\(461\) 36.7495 1.71159 0.855797 0.517312i \(-0.173067\pi\)
0.855797 + 0.517312i \(0.173067\pi\)
\(462\) 0 0
\(463\) 19.3081i 0.897324i 0.893702 + 0.448662i \(0.148099\pi\)
−0.893702 + 0.448662i \(0.851901\pi\)
\(464\) 0 0
\(465\) 0.530153 + 9.86642i 0.0245853 + 0.457544i
\(466\) 0 0
\(467\) 11.4129i 0.528127i −0.964505 0.264064i \(-0.914937\pi\)
0.964505 0.264064i \(-0.0850629\pi\)
\(468\) 0 0
\(469\) 4.44556 0.205277
\(470\) 0 0
\(471\) −7.59841 −0.350116
\(472\) 0 0
\(473\) 4.78825i 0.220164i
\(474\) 0 0
\(475\) 25.8705 2.78825i 1.18702 0.127934i
\(476\) 0 0
\(477\) 25.7914i 1.18091i
\(478\) 0 0
\(479\) 29.2307 1.33559 0.667793 0.744347i \(-0.267239\pi\)
0.667793 + 0.744347i \(0.267239\pi\)
\(480\) 0 0
\(481\) 35.8564 1.63491
\(482\) 0 0
\(483\) 2.33086i 0.106058i
\(484\) 0 0
\(485\) 0.0709857 + 1.32108i 0.00322329 + 0.0599871i
\(486\) 0 0
\(487\) 33.2932i 1.50866i −0.656496 0.754329i \(-0.727962\pi\)
0.656496 0.754329i \(-0.272038\pi\)
\(488\) 0 0
\(489\) −4.47487 −0.202361
\(490\) 0 0
\(491\) 24.5151 1.10635 0.553176 0.833064i \(-0.313416\pi\)
0.553176 + 0.833064i \(0.313416\pi\)
\(492\) 0 0
\(493\) 5.83612i 0.262846i
\(494\) 0 0
\(495\) 5.73836 0.308340i 0.257920 0.0138589i
\(496\) 0 0
\(497\) 2.57510i 0.115509i
\(498\) 0 0
\(499\) −18.9093 −0.846497 −0.423249 0.906014i \(-0.639110\pi\)
−0.423249 + 0.906014i \(0.639110\pi\)
\(500\) 0 0
\(501\) 4.65872 0.208136
\(502\) 0 0
\(503\) 9.42031i 0.420031i −0.977698 0.210016i \(-0.932649\pi\)
0.977698 0.210016i \(-0.0673515\pi\)
\(504\) 0 0
\(505\) 10.3226 0.554663i 0.459348 0.0246822i
\(506\) 0 0
\(507\) 1.96729i 0.0873702i
\(508\) 0 0
\(509\) 16.7804 0.743778 0.371889 0.928277i \(-0.378710\pi\)
0.371889 + 0.928277i \(0.378710\pi\)
\(510\) 0 0
\(511\) 1.31744 0.0582799
\(512\) 0 0
\(513\) 19.0082i 0.839234i
\(514\) 0 0
\(515\) −0.988966 18.4052i −0.0435791 0.811028i
\(516\) 0 0
\(517\) 5.61986i 0.247161i
\(518\) 0 0
\(519\) 6.10614 0.268030
\(520\) 0 0
\(521\) −37.8273 −1.65724 −0.828621 0.559810i \(-0.810874\pi\)
−0.828621 + 0.559810i \(0.810874\pi\)
\(522\) 0 0
\(523\) 10.0998i 0.441632i 0.975315 + 0.220816i \(0.0708721\pi\)
−0.975315 + 0.220816i \(0.929128\pi\)
\(524\) 0 0
\(525\) −1.35550 + 0.146092i −0.0591589 + 0.00637599i
\(526\) 0 0
\(527\) 43.9044i 1.91250i
\(528\) 0 0
\(529\) −50.0734 −2.17710
\(530\) 0 0
\(531\) −4.19955 −0.182245
\(532\) 0 0
\(533\) 40.3991i 1.74988i
\(534\) 0 0
\(535\) −2.11399 39.3425i −0.0913959 1.70092i
\(536\) 0 0
\(537\) 17.4674i 0.753774i
\(538\) 0 0
\(539\) −6.82711 −0.294064
\(540\) 0 0
\(541\) −29.9269 −1.28666 −0.643329 0.765590i \(-0.722447\pi\)
−0.643329 + 0.765590i \(0.722447\pi\)
\(542\) 0 0
\(543\) 0.662997i 0.0284519i
\(544\) 0 0
\(545\) 8.17942 0.439506i 0.350368 0.0188264i
\(546\) 0 0
\(547\) 23.7630i 1.01603i −0.861347 0.508016i \(-0.830379\pi\)
0.861347 0.508016i \(-0.169621\pi\)
\(548\) 0 0
\(549\) 18.2578 0.779226
\(550\) 0 0
\(551\) −4.66137 −0.198581
\(552\) 0 0
\(553\) 4.68537i 0.199242i
\(554\) 0 0
\(555\) 13.1254 0.705267i 0.557141 0.0299369i
\(556\) 0 0
\(557\) 24.3363i 1.03116i −0.856841 0.515581i \(-0.827576\pi\)
0.856841 0.515581i \(-0.172424\pi\)
\(558\) 0 0
\(559\) −19.1530 −0.810086
\(560\) 0 0
\(561\) −4.27267 −0.180392
\(562\) 0 0
\(563\) 8.85368i 0.373138i −0.982442 0.186569i \(-0.940263\pi\)
0.982442 0.186569i \(-0.0597368\pi\)
\(564\) 0 0
\(565\) 1.37731 + 25.6324i 0.0579437 + 1.07836i
\(566\) 0 0
\(567\) 2.20989i 0.0928066i
\(568\) 0 0
\(569\) −26.3860 −1.10616 −0.553080 0.833128i \(-0.686548\pi\)
−0.553080 + 0.833128i \(0.686548\pi\)
\(570\) 0 0
\(571\) −6.45280 −0.270041 −0.135021 0.990843i \(-0.543110\pi\)
−0.135021 + 0.990843i \(0.543110\pi\)
\(572\) 0 0
\(573\) 6.92843i 0.289439i
\(574\) 0 0
\(575\) −4.58004 42.4954i −0.191001 1.77218i
\(576\) 0 0
\(577\) 12.1745i 0.506832i 0.967357 + 0.253416i \(0.0815542\pi\)
−0.967357 + 0.253416i \(0.918446\pi\)
\(578\) 0 0
\(579\) 7.75576 0.322319
\(580\) 0 0
\(581\) −6.75390 −0.280199
\(582\) 0 0
\(583\) 10.0357i 0.415635i
\(584\) 0 0
\(585\) −1.23336 22.9535i −0.0509932 0.949009i
\(586\) 0 0
\(587\) 22.9521i 0.947336i 0.880704 + 0.473668i \(0.157070\pi\)
−0.880704 + 0.473668i \(0.842930\pi\)
\(588\) 0 0
\(589\) 35.0668 1.44490
\(590\) 0 0
\(591\) 0.860047 0.0353776
\(592\) 0 0
\(593\) 10.4081i 0.427410i −0.976898 0.213705i \(-0.931447\pi\)
0.976898 0.213705i \(-0.0685531\pi\)
\(594\) 0 0
\(595\) −6.04927 + 0.325046i −0.247996 + 0.0133256i
\(596\) 0 0
\(597\) 7.75576i 0.317422i
\(598\) 0 0
\(599\) −8.98913 −0.367286 −0.183643 0.982993i \(-0.558789\pi\)
−0.183643 + 0.982993i \(0.558789\pi\)
\(600\) 0 0
\(601\) −3.57650 −0.145889 −0.0729443 0.997336i \(-0.523240\pi\)
−0.0729443 + 0.997336i \(0.523240\pi\)
\(602\) 0 0
\(603\) 27.4767i 1.11894i
\(604\) 0 0
\(605\) −2.23285 + 0.119978i −0.0907781 + 0.00487779i
\(606\) 0 0
\(607\) 27.0235i 1.09685i −0.836200 0.548424i \(-0.815228\pi\)
0.836200 0.548424i \(-0.184772\pi\)
\(608\) 0 0
\(609\) 0.244235 0.00989691
\(610\) 0 0
\(611\) −22.4795 −0.909421
\(612\) 0 0
\(613\) 44.5572i 1.79965i 0.436254 + 0.899823i \(0.356305\pi\)
−0.436254 + 0.899823i \(0.643695\pi\)
\(614\) 0 0
\(615\) 0.794619 + 14.7883i 0.0320421 + 0.596320i
\(616\) 0 0
\(617\) 15.2966i 0.615818i −0.951416 0.307909i \(-0.900371\pi\)
0.951416 0.307909i \(-0.0996292\pi\)
\(618\) 0 0
\(619\) 14.5655 0.585436 0.292718 0.956199i \(-0.405440\pi\)
0.292718 + 0.956199i \(0.405440\pi\)
\(620\) 0 0
\(621\) −31.2233 −1.25295
\(622\) 0 0
\(623\) 3.97926i 0.159426i
\(624\) 0 0
\(625\) 24.4259 5.32699i 0.977035 0.213080i
\(626\) 0 0
\(627\) 3.41262i 0.136287i
\(628\) 0 0
\(629\) 58.4063 2.32881
\(630\) 0 0
\(631\) 22.0779 0.878906 0.439453 0.898266i \(-0.355172\pi\)
0.439453 + 0.898266i \(0.355172\pi\)
\(632\) 0 0
\(633\) 5.49033i 0.218221i
\(634\) 0 0
\(635\) 1.09659 + 20.4081i 0.0435169 + 0.809871i
\(636\) 0 0
\(637\) 27.3084i 1.08200i
\(638\) 0 0
\(639\) 15.9159 0.629624
\(640\) 0 0
\(641\) −31.2152 −1.23293 −0.616463 0.787384i \(-0.711435\pi\)
−0.616463 + 0.787384i \(0.711435\pi\)
\(642\) 0 0
\(643\) 10.4498i 0.412102i −0.978541 0.206051i \(-0.933939\pi\)
0.978541 0.206051i \(-0.0660612\pi\)
\(644\) 0 0
\(645\) −7.01103 + 0.376725i −0.276059 + 0.0148335i
\(646\) 0 0
\(647\) 26.1307i 1.02730i −0.857999 0.513652i \(-0.828292\pi\)
0.857999 0.513652i \(-0.171708\pi\)
\(648\) 0 0
\(649\) 1.63408 0.0641433
\(650\) 0 0
\(651\) −1.83735 −0.0720114
\(652\) 0 0
\(653\) 44.2097i 1.73006i −0.501719 0.865030i \(-0.667299\pi\)
0.501719 0.865030i \(-0.332701\pi\)
\(654\) 0 0
\(655\) −5.54022 + 0.297693i −0.216474 + 0.0116318i
\(656\) 0 0
\(657\) 8.14268i 0.317676i
\(658\) 0 0
\(659\) 6.96706 0.271398 0.135699 0.990750i \(-0.456672\pi\)
0.135699 + 0.990750i \(0.456672\pi\)
\(660\) 0 0
\(661\) −9.19753 −0.357743 −0.178871 0.983872i \(-0.557245\pi\)
−0.178871 + 0.983872i \(0.557245\pi\)
\(662\) 0 0
\(663\) 17.0907i 0.663747i
\(664\) 0 0
\(665\) 0.259618 + 4.83161i 0.0100675 + 0.187362i
\(666\) 0 0
\(667\) 7.65686i 0.296475i
\(668\) 0 0
\(669\) 14.5226 0.561475
\(670\) 0 0
\(671\) −7.10428 −0.274258
\(672\) 0 0
\(673\) 8.72415i 0.336291i 0.985762 + 0.168146i \(0.0537779\pi\)
−0.985762 + 0.168146i \(0.946222\pi\)
\(674\) 0 0
\(675\) −1.95699 18.1577i −0.0753247 0.698892i
\(676\) 0 0
\(677\) 8.76618i 0.336912i 0.985709 + 0.168456i \(0.0538781\pi\)
−0.985709 + 0.168456i \(0.946122\pi\)
\(678\) 0 0
\(679\) −0.246015 −0.00944118
\(680\) 0 0
\(681\) −14.3083 −0.548297
\(682\) 0 0
\(683\) 49.2320i 1.88381i −0.335877 0.941906i \(-0.609033\pi\)
0.335877 0.941906i \(-0.390967\pi\)
\(684\) 0 0
\(685\) 0.888837 + 16.5417i 0.0339607 + 0.632026i
\(686\) 0 0
\(687\) 1.83775i 0.0701146i
\(688\) 0 0
\(689\) −40.1427 −1.52931
\(690\) 0 0
\(691\) 18.1483 0.690395 0.345198 0.938530i \(-0.387812\pi\)
0.345198 + 0.938530i \(0.387812\pi\)
\(692\) 0 0
\(693\) 1.06861i 0.0405932i
\(694\) 0 0
\(695\) 3.77722 0.202962i 0.143278 0.00769877i
\(696\) 0 0
\(697\) 65.8059i 2.49258i
\(698\) 0 0
\(699\) 5.40626 0.204483
\(700\) 0 0
\(701\) 22.6587 0.855808 0.427904 0.903824i \(-0.359252\pi\)
0.427904 + 0.903824i \(0.359252\pi\)
\(702\) 0 0
\(703\) 46.6497i 1.75943i
\(704\) 0 0
\(705\) −8.22869 + 0.442153i −0.309911 + 0.0166525i
\(706\) 0 0
\(707\) 1.92229i 0.0722952i
\(708\) 0 0
\(709\) 36.7366 1.37967 0.689836 0.723966i \(-0.257683\pi\)
0.689836 + 0.723966i \(0.257683\pi\)
\(710\) 0 0
\(711\) −28.9589 −1.08604
\(712\) 0 0
\(713\) 57.6015i 2.15719i
\(714\) 0 0
\(715\) 0.479911 + 8.93139i 0.0179477 + 0.334015i
\(716\) 0 0
\(717\) 7.38923i 0.275956i
\(718\) 0 0
\(719\) 8.74738 0.326222 0.163111 0.986608i \(-0.447847\pi\)
0.163111 + 0.986608i \(0.447847\pi\)
\(720\) 0 0
\(721\) 3.42745 0.127645
\(722\) 0 0
\(723\) 14.6799i 0.545952i
\(724\) 0 0
\(725\) −4.45280 + 0.479911i −0.165373 + 0.0178235i
\(726\) 0 0
\(727\) 2.20887i 0.0819226i 0.999161 + 0.0409613i \(0.0130420\pi\)
−0.999161 + 0.0409613i \(0.986958\pi\)
\(728\) 0 0
\(729\) 6.47301 0.239741
\(730\) 0 0
\(731\) −31.1982 −1.15391
\(732\) 0 0
\(733\) 3.58552i 0.132434i −0.997805 0.0662171i \(-0.978907\pi\)
0.997805 0.0662171i \(-0.0210930\pi\)
\(734\) 0 0
\(735\) 0.537135 + 9.99636i 0.0198125 + 0.368721i
\(736\) 0 0
\(737\) 10.6914i 0.393824i
\(738\) 0 0
\(739\) −24.9314 −0.917116 −0.458558 0.888665i \(-0.651634\pi\)
−0.458558 + 0.888665i \(0.651634\pi\)
\(740\) 0 0
\(741\) 13.6505 0.501463
\(742\) 0 0
\(743\) 21.4257i 0.786032i 0.919532 + 0.393016i \(0.128568\pi\)
−0.919532 + 0.393016i \(0.871432\pi\)
\(744\) 0 0
\(745\) 8.37183 0.449844i 0.306720 0.0164810i
\(746\) 0 0
\(747\) 41.7439i 1.52733i
\(748\) 0 0
\(749\) 7.32645 0.267703
\(750\) 0 0
\(751\) −28.1582 −1.02751 −0.513754 0.857938i \(-0.671746\pi\)
−0.513754 + 0.857938i \(0.671746\pi\)
\(752\) 0 0
\(753\) 2.51986i 0.0918288i
\(754\) 0 0
\(755\) −33.8052 + 1.81646i −1.23030 + 0.0661077i
\(756\) 0 0
\(757\) 10.7513i 0.390761i −0.980728 0.195381i \(-0.937406\pi\)
0.980728 0.195381i \(-0.0625942\pi\)
\(758\) 0 0
\(759\) 5.60565 0.203472
\(760\) 0 0
\(761\) −38.0429 −1.37905 −0.689527 0.724260i \(-0.742182\pi\)
−0.689527 + 0.724260i \(0.742182\pi\)
\(762\) 0 0
\(763\) 1.52319i 0.0551433i
\(764\) 0 0
\(765\) −2.00901 37.3888i −0.0726361 1.35179i
\(766\) 0 0
\(767\) 6.53632i 0.236013i
\(768\) 0 0
\(769\) −26.2280 −0.945805 −0.472903 0.881115i \(-0.656794\pi\)
−0.472903 + 0.881115i \(0.656794\pi\)
\(770\) 0 0
\(771\) −6.96619 −0.250881
\(772\) 0 0
\(773\) 8.94499i 0.321729i 0.986977 + 0.160864i \(0.0514282\pi\)
−0.986977 + 0.160864i \(0.948572\pi\)
\(774\) 0 0
\(775\) 33.4978 3.61031i 1.20328 0.129686i
\(776\) 0 0
\(777\) 2.44424i 0.0876867i
\(778\) 0 0
\(779\) 52.5598 1.88315
\(780\) 0 0
\(781\) −6.19302 −0.221604
\(782\) 0 0
\(783\) 3.27168i 0.116920i
\(784\) 0 0
\(785\) 1.39020 + 25.8723i 0.0496184 + 0.923423i
\(786\) 0 0
\(787\) 29.9716i 1.06837i 0.845367 + 0.534185i \(0.179382\pi\)
−0.845367 + 0.534185i \(0.820618\pi\)
\(788\) 0 0
\(789\) −3.79867 −0.135236
\(790\) 0 0
\(791\) −4.77332 −0.169720
\(792\) 0 0
\(793\) 28.4171i 1.00912i
\(794\) 0 0
\(795\) −14.6944 + 0.789575i −0.521156 + 0.0280033i
\(796\) 0