Properties

Label 1008.2.bt.b.17.2
Level $1008$
Weight $2$
Character 1008.17
Analytic conductor $8.049$
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] = [1008,2,Mod(17,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.bt (of order \(6\), degree \(2\), 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: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 17.2
Root \(-1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 1008.17
Dual form 1008.2.bt.b.593.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.22474 + 2.12132i) q^{5} +(0.500000 - 2.59808i) q^{7} +O(q^{10})\) \(q+(1.22474 + 2.12132i) q^{5} +(0.500000 - 2.59808i) q^{7} +(-1.22474 - 0.707107i) q^{11} -5.19615i q^{13} +(2.44949 - 4.24264i) q^{17} +(-1.50000 + 0.866025i) q^{19} +(4.89898 - 2.82843i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.82843i q^{29} +(-1.50000 - 0.866025i) q^{31} +(6.12372 - 2.12132i) q^{35} +(0.500000 + 0.866025i) q^{37} +7.34847 q^{41} +1.00000 q^{43} +(6.12372 + 10.6066i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(-2.44949 - 1.41421i) q^{53} -3.46410i q^{55} +(-2.44949 + 4.24264i) q^{59} +(-3.00000 + 1.73205i) q^{61} +(11.0227 - 6.36396i) q^{65} +(5.50000 - 9.52628i) q^{67} -7.07107i q^{71} +(1.50000 + 0.866025i) q^{73} +(-2.44949 + 2.82843i) q^{77} +(2.50000 + 4.33013i) q^{79} +7.34847 q^{83} +12.0000 q^{85} +(-2.44949 - 4.24264i) q^{89} +(-13.5000 - 2.59808i) q^{91} +(-3.67423 - 2.12132i) q^{95} -10.3923i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{7} - 6 q^{19} - 2 q^{25} - 6 q^{31} + 2 q^{37} + 4 q^{43} - 26 q^{49} - 12 q^{61} + 22 q^{67} + 6 q^{73} + 10 q^{79} + 48 q^{85} - 54 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

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 0
\(4\) 0 0
\(5\) 1.22474 + 2.12132i 0.547723 + 0.948683i 0.998430 + 0.0560116i \(0.0178384\pi\)
−0.450708 + 0.892672i \(0.648828\pi\)
\(6\) 0 0
\(7\) 0.500000 2.59808i 0.188982 0.981981i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.22474 0.707107i −0.369274 0.213201i 0.303867 0.952714i \(-0.401722\pi\)
−0.673141 + 0.739514i \(0.735055\pi\)
\(12\) 0 0
\(13\) 5.19615i 1.44115i −0.693375 0.720577i \(-0.743877\pi\)
0.693375 0.720577i \(-0.256123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.44949 4.24264i 0.594089 1.02899i −0.399586 0.916696i \(-0.630846\pi\)
0.993675 0.112296i \(-0.0358205\pi\)
\(18\) 0 0
\(19\) −1.50000 + 0.866025i −0.344124 + 0.198680i −0.662094 0.749421i \(-0.730332\pi\)
0.317970 + 0.948101i \(0.396999\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.89898 2.82843i 1.02151 0.589768i 0.106967 0.994263i \(-0.465886\pi\)
0.914540 + 0.404495i \(0.132553\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.82843i 0.525226i 0.964901 + 0.262613i \(0.0845842\pi\)
−0.964901 + 0.262613i \(0.915416\pi\)
\(30\) 0 0
\(31\) −1.50000 0.866025i −0.269408 0.155543i 0.359211 0.933257i \(-0.383046\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 6.12372 2.12132i 1.03510 0.358569i
\(36\) 0 0
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 7.34847 1.14764 0.573819 0.818982i \(-0.305461\pi\)
0.573819 + 0.818982i \(0.305461\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.12372 + 10.6066i 0.893237 + 1.54713i 0.835971 + 0.548773i \(0.184905\pi\)
0.0572655 + 0.998359i \(0.481762\pi\)
\(48\) 0 0
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.44949 1.41421i −0.336463 0.194257i 0.322244 0.946657i \(-0.395563\pi\)
−0.658707 + 0.752400i \(0.728896\pi\)
\(54\) 0 0
\(55\) 3.46410i 0.467099i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.44949 + 4.24264i −0.318896 + 0.552345i −0.980258 0.197722i \(-0.936646\pi\)
0.661362 + 0.750067i \(0.269979\pi\)
\(60\) 0 0
\(61\) −3.00000 + 1.73205i −0.384111 + 0.221766i −0.679605 0.733578i \(-0.737849\pi\)
0.295495 + 0.955344i \(0.404516\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 11.0227 6.36396i 1.36720 0.789352i
\(66\) 0 0
\(67\) 5.50000 9.52628i 0.671932 1.16382i −0.305424 0.952217i \(-0.598798\pi\)
0.977356 0.211604i \(-0.0678686\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.07107i 0.839181i −0.907713 0.419591i \(-0.862174\pi\)
0.907713 0.419591i \(-0.137826\pi\)
\(72\) 0 0
\(73\) 1.50000 + 0.866025i 0.175562 + 0.101361i 0.585206 0.810885i \(-0.301014\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.44949 + 2.82843i −0.279145 + 0.322329i
\(78\) 0 0
\(79\) 2.50000 + 4.33013i 0.281272 + 0.487177i 0.971698 0.236225i \(-0.0759104\pi\)
−0.690426 + 0.723403i \(0.742577\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 7.34847 0.806599 0.403300 0.915068i \(-0.367863\pi\)
0.403300 + 0.915068i \(0.367863\pi\)
\(84\) 0 0
\(85\) 12.0000 1.30158
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.44949 4.24264i −0.259645 0.449719i 0.706502 0.707712i \(-0.250272\pi\)
−0.966147 + 0.257993i \(0.916939\pi\)
\(90\) 0 0
\(91\) −13.5000 2.59808i −1.41518 0.272352i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.67423 2.12132i −0.376969 0.217643i
\(96\) 0 0
\(97\) 10.3923i 1.05518i −0.849500 0.527589i \(-0.823096\pi\)
0.849500 0.527589i \(-0.176904\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.57321 + 14.8492i −0.853067 + 1.47755i 0.0253604 + 0.999678i \(0.491927\pi\)
−0.878427 + 0.477876i \(0.841407\pi\)
\(102\) 0 0
\(103\) 7.50000 4.33013i 0.738997 0.426660i −0.0827075 0.996574i \(-0.526357\pi\)
0.821705 + 0.569914i \(0.193023\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.44949 + 1.41421i −0.236801 + 0.136717i −0.613706 0.789535i \(-0.710322\pi\)
0.376905 + 0.926252i \(0.376988\pi\)
\(108\) 0 0
\(109\) 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i \(-0.818083\pi\)
0.888977 + 0.457951i \(0.151417\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.41421i 0.133038i −0.997785 0.0665190i \(-0.978811\pi\)
0.997785 0.0665190i \(-0.0211893\pi\)
\(114\) 0 0
\(115\) 12.0000 + 6.92820i 1.11901 + 0.646058i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −9.79796 8.48528i −0.898177 0.777844i
\(120\) 0 0
\(121\) −4.50000 7.79423i −0.409091 0.708566i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 9.79796 0.876356
\(126\) 0 0
\(127\) −11.0000 −0.976092 −0.488046 0.872818i \(-0.662290\pi\)
−0.488046 + 0.872818i \(0.662290\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.22474 2.12132i −0.107006 0.185341i 0.807550 0.589799i \(-0.200793\pi\)
−0.914556 + 0.404459i \(0.867460\pi\)
\(132\) 0 0
\(133\) 1.50000 + 4.33013i 0.130066 + 0.375470i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −9.79796 5.65685i −0.837096 0.483298i 0.0191800 0.999816i \(-0.493894\pi\)
−0.856276 + 0.516518i \(0.827228\pi\)
\(138\) 0 0
\(139\) 5.19615i 0.440732i 0.975417 + 0.220366i \(0.0707252\pi\)
−0.975417 + 0.220366i \(0.929275\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.67423 + 6.36396i −0.307255 + 0.532181i
\(144\) 0 0
\(145\) −6.00000 + 3.46410i −0.498273 + 0.287678i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −4.89898 + 2.82843i −0.401340 + 0.231714i −0.687062 0.726599i \(-0.741100\pi\)
0.285722 + 0.958313i \(0.407767\pi\)
\(150\) 0 0
\(151\) −11.0000 + 19.0526i −0.895167 + 1.55048i −0.0615699 + 0.998103i \(0.519611\pi\)
−0.833597 + 0.552372i \(0.813723\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.24264i 0.340777i
\(156\) 0 0
\(157\) 15.0000 + 8.66025i 1.19713 + 0.691164i 0.959914 0.280293i \(-0.0904318\pi\)
0.237216 + 0.971457i \(0.423765\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.89898 14.1421i −0.386094 1.11456i
\(162\) 0 0
\(163\) −5.00000 8.66025i −0.391630 0.678323i 0.601035 0.799223i \(-0.294755\pi\)
−0.992665 + 0.120900i \(0.961422\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.34847 −0.568642 −0.284321 0.958729i \(-0.591768\pi\)
−0.284321 + 0.958729i \(0.591768\pi\)
\(168\) 0 0
\(169\) −14.0000 −1.07692
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.89898 + 8.48528i 0.372463 + 0.645124i 0.989944 0.141462i \(-0.0451802\pi\)
−0.617481 + 0.786586i \(0.711847\pi\)
\(174\) 0 0
\(175\) 2.00000 + 1.73205i 0.151186 + 0.130931i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −8.57321 4.94975i −0.640792 0.369961i 0.144127 0.989559i \(-0.453962\pi\)
−0.784920 + 0.619598i \(0.787296\pi\)
\(180\) 0 0
\(181\) 15.5885i 1.15868i 0.815086 + 0.579340i \(0.196690\pi\)
−0.815086 + 0.579340i \(0.803310\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.22474 + 2.12132i −0.0900450 + 0.155963i
\(186\) 0 0
\(187\) −6.00000 + 3.46410i −0.438763 + 0.253320i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.22474 0.707107i 0.0886194 0.0511645i −0.455035 0.890473i \(-0.650373\pi\)
0.543655 + 0.839309i \(0.317040\pi\)
\(192\) 0 0
\(193\) −5.50000 + 9.52628i −0.395899 + 0.685717i −0.993215 0.116289i \(-0.962900\pi\)
0.597317 + 0.802005i \(0.296234\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 19.7990i 1.41062i 0.708899 + 0.705310i \(0.249192\pi\)
−0.708899 + 0.705310i \(0.750808\pi\)
\(198\) 0 0
\(199\) 12.0000 + 6.92820i 0.850657 + 0.491127i 0.860873 0.508821i \(-0.169918\pi\)
−0.0102152 + 0.999948i \(0.503252\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 7.34847 + 1.41421i 0.515761 + 0.0992583i
\(204\) 0 0
\(205\) 9.00000 + 15.5885i 0.628587 + 1.08875i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.44949 0.169435
\(210\) 0 0
\(211\) 22.0000 1.51454 0.757271 0.653101i \(-0.226532\pi\)
0.757271 + 0.653101i \(0.226532\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.22474 + 2.12132i 0.0835269 + 0.144673i
\(216\) 0 0
\(217\) −3.00000 + 3.46410i −0.203653 + 0.235159i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −22.0454 12.7279i −1.48293 0.856173i
\(222\) 0 0
\(223\) 20.7846i 1.39184i −0.718119 0.695920i \(-0.754997\pi\)
0.718119 0.695920i \(-0.245003\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −13.4722 + 23.3345i −0.894181 + 1.54877i −0.0593658 + 0.998236i \(0.518908\pi\)
−0.834815 + 0.550530i \(0.814425\pi\)
\(228\) 0 0
\(229\) 19.5000 11.2583i 1.28860 0.743971i 0.310192 0.950674i \(-0.399607\pi\)
0.978404 + 0.206702i \(0.0662732\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −8.57321 + 4.94975i −0.561650 + 0.324269i −0.753807 0.657095i \(-0.771785\pi\)
0.192158 + 0.981364i \(0.438452\pi\)
\(234\) 0 0
\(235\) −15.0000 + 25.9808i −0.978492 + 1.69480i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 26.8701i 1.73808i 0.494742 + 0.869040i \(0.335262\pi\)
−0.494742 + 0.869040i \(0.664738\pi\)
\(240\) 0 0
\(241\) −12.0000 6.92820i −0.772988 0.446285i 0.0609515 0.998141i \(-0.480586\pi\)
−0.833939 + 0.551856i \(0.813920\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2.44949 16.9706i −0.156492 1.08421i
\(246\) 0 0
\(247\) 4.50000 + 7.79423i 0.286328 + 0.495935i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −8.00000 −0.502956
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.22474 + 2.12132i 0.0763975 + 0.132324i 0.901693 0.432377i \(-0.142325\pi\)
−0.825296 + 0.564701i \(0.808992\pi\)
\(258\) 0 0
\(259\) 2.50000 0.866025i 0.155342 0.0538122i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −12.2474 7.07107i −0.755210 0.436021i 0.0723633 0.997378i \(-0.476946\pi\)
−0.827573 + 0.561358i \(0.810279\pi\)
\(264\) 0 0
\(265\) 6.92820i 0.425596i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −8.57321 + 14.8492i −0.522718 + 0.905374i 0.476932 + 0.878940i \(0.341749\pi\)
−0.999651 + 0.0264343i \(0.991585\pi\)
\(270\) 0 0
\(271\) 12.0000 6.92820i 0.728948 0.420858i −0.0890891 0.996024i \(-0.528396\pi\)
0.818037 + 0.575165i \(0.195062\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.22474 0.707107i 0.0738549 0.0426401i
\(276\) 0 0
\(277\) −11.5000 + 19.9186i −0.690968 + 1.19679i 0.280553 + 0.959839i \(0.409482\pi\)
−0.971521 + 0.236953i \(0.923851\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 22.6274i 1.34984i −0.737892 0.674919i \(-0.764178\pi\)
0.737892 0.674919i \(-0.235822\pi\)
\(282\) 0 0
\(283\) −1.50000 0.866025i −0.0891657 0.0514799i 0.454754 0.890617i \(-0.349727\pi\)
−0.543920 + 0.839137i \(0.683060\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.67423 19.0919i 0.216883 1.12696i
\(288\) 0 0
\(289\) −3.50000 6.06218i −0.205882 0.356599i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −14.6969 −0.858604 −0.429302 0.903161i \(-0.641240\pi\)
−0.429302 + 0.903161i \(0.641240\pi\)
\(294\) 0 0
\(295\) −12.0000 −0.698667
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −14.6969 25.4558i −0.849946 1.47215i
\(300\) 0 0
\(301\) 0.500000 2.59808i 0.0288195 0.149751i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −7.34847 4.24264i −0.420772 0.242933i
\(306\) 0 0
\(307\) 15.5885i 0.889680i 0.895610 + 0.444840i \(0.146740\pi\)
−0.895610 + 0.444840i \(0.853260\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 8.57321 14.8492i 0.486142 0.842023i −0.513731 0.857951i \(-0.671737\pi\)
0.999873 + 0.0159282i \(0.00507031\pi\)
\(312\) 0 0
\(313\) 10.5000 6.06218i 0.593495 0.342655i −0.172983 0.984925i \(-0.555341\pi\)
0.766478 + 0.642270i \(0.222007\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −12.2474 + 7.07107i −0.687885 + 0.397151i −0.802819 0.596222i \(-0.796668\pi\)
0.114934 + 0.993373i \(0.463334\pi\)
\(318\) 0 0
\(319\) 2.00000 3.46410i 0.111979 0.193952i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.48528i 0.472134i
\(324\) 0 0
\(325\) 4.50000 + 2.59808i 0.249615 + 0.144115i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 30.6186 10.6066i 1.68806 0.584761i
\(330\) 0 0
\(331\) −15.5000 26.8468i −0.851957 1.47563i −0.879440 0.476011i \(-0.842082\pi\)
0.0274825 0.999622i \(-0.491251\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 26.9444 1.47213
\(336\) 0 0
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.22474 + 2.12132i 0.0663237 + 0.114876i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −26.9444 15.5563i −1.44645 0.835109i −0.448183 0.893942i \(-0.647929\pi\)
−0.998268 + 0.0588334i \(0.981262\pi\)
\(348\) 0 0
\(349\) 10.3923i 0.556287i −0.960539 0.278144i \(-0.910281\pi\)
0.960539 0.278144i \(-0.0897191\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −8.57321 + 14.8492i −0.456306 + 0.790345i −0.998762 0.0497387i \(-0.984161\pi\)
0.542456 + 0.840084i \(0.317494\pi\)
\(354\) 0 0
\(355\) 15.0000 8.66025i 0.796117 0.459639i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −24.4949 + 14.1421i −1.29279 + 0.746393i −0.979148 0.203148i \(-0.934883\pi\)
−0.313643 + 0.949541i \(0.601550\pi\)
\(360\) 0 0
\(361\) −8.00000 + 13.8564i −0.421053 + 0.729285i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.24264i 0.222070i
\(366\) 0 0
\(367\) −1.50000 0.866025i −0.0782994 0.0452062i 0.460339 0.887743i \(-0.347728\pi\)
−0.538639 + 0.842537i \(0.681061\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4.89898 + 5.65685i −0.254342 + 0.293689i
\(372\) 0 0
\(373\) −14.5000 25.1147i −0.750782 1.30039i −0.947444 0.319921i \(-0.896344\pi\)
0.196663 0.980471i \(-0.436990\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 14.6969 0.756931
\(378\) 0 0
\(379\) 7.00000 0.359566 0.179783 0.983706i \(-0.442460\pi\)
0.179783 + 0.983706i \(0.442460\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9.79796 + 16.9706i 0.500652 + 0.867155i 1.00000 0.000753393i \(0.000239813\pi\)
−0.499347 + 0.866402i \(0.666427\pi\)
\(384\) 0 0
\(385\) −9.00000 1.73205i −0.458682 0.0882735i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 23.2702 + 13.4350i 1.17984 + 0.681183i 0.955978 0.293437i \(-0.0947991\pi\)
0.223865 + 0.974620i \(0.428132\pi\)
\(390\) 0 0
\(391\) 27.7128i 1.40150i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6.12372 + 10.6066i −0.308118 + 0.533676i
\(396\) 0 0
\(397\) 1.50000 0.866025i 0.0752828 0.0434646i −0.461886 0.886939i \(-0.652827\pi\)
0.537169 + 0.843475i \(0.319494\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 17.1464 9.89949i 0.856252 0.494357i −0.00650355 0.999979i \(-0.502070\pi\)
0.862755 + 0.505622i \(0.168737\pi\)
\(402\) 0 0
\(403\) −4.50000 + 7.79423i −0.224161 + 0.388258i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.41421i 0.0701000i
\(408\) 0 0
\(409\) 28.5000 + 16.4545i 1.40923 + 0.813622i 0.995314 0.0966915i \(-0.0308260\pi\)
0.413920 + 0.910313i \(0.364159\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 9.79796 + 8.48528i 0.482126 + 0.417533i
\(414\) 0 0
\(415\) 9.00000 + 15.5885i 0.441793 + 0.765207i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 36.7423 1.79498 0.897491 0.441034i \(-0.145388\pi\)
0.897491 + 0.441034i \(0.145388\pi\)
\(420\) 0 0
\(421\) −1.00000 −0.0487370 −0.0243685 0.999703i \(-0.507758\pi\)
−0.0243685 + 0.999703i \(0.507758\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.44949 + 4.24264i 0.118818 + 0.205798i
\(426\) 0 0
\(427\) 3.00000 + 8.66025i 0.145180 + 0.419099i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 13.4722 + 7.77817i 0.648933 + 0.374661i 0.788047 0.615615i \(-0.211092\pi\)
−0.139114 + 0.990276i \(0.544426\pi\)
\(432\) 0 0
\(433\) 15.5885i 0.749133i 0.927200 + 0.374567i \(0.122209\pi\)
−0.927200 + 0.374567i \(0.877791\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.89898 + 8.48528i −0.234350 + 0.405906i
\(438\) 0 0
\(439\) −24.0000 + 13.8564i −1.14546 + 0.661330i −0.947776 0.318936i \(-0.896674\pi\)
−0.197681 + 0.980266i \(0.563341\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 34.2929 19.7990i 1.62930 0.940678i 0.645002 0.764181i \(-0.276857\pi\)
0.984301 0.176497i \(-0.0564767\pi\)
\(444\) 0 0
\(445\) 6.00000 10.3923i 0.284427 0.492642i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 7.07107i 0.333704i 0.985982 + 0.166852i \(0.0533603\pi\)
−0.985982 + 0.166852i \(0.946640\pi\)
\(450\) 0 0
\(451\) −9.00000 5.19615i −0.423793 0.244677i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −11.0227 31.8198i −0.516752 1.49174i
\(456\) 0 0
\(457\) −2.50000 4.33013i −0.116945 0.202555i 0.801611 0.597847i \(-0.203977\pi\)
−0.918556 + 0.395292i \(0.870643\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 14.6969 0.684505 0.342252 0.939608i \(-0.388810\pi\)
0.342252 + 0.939608i \(0.388810\pi\)
\(462\) 0 0
\(463\) 13.0000 0.604161 0.302081 0.953282i \(-0.402319\pi\)
0.302081 + 0.953282i \(0.402319\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 13.4722 + 23.3345i 0.623419 + 1.07979i 0.988844 + 0.148952i \(0.0475901\pi\)
−0.365426 + 0.930841i \(0.619077\pi\)
\(468\) 0 0
\(469\) −22.0000 19.0526i −1.01587 0.879765i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.22474 0.707107i −0.0563138 0.0325128i
\(474\) 0 0
\(475\) 1.73205i 0.0794719i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −2.44949 + 4.24264i −0.111920 + 0.193851i −0.916544 0.399933i \(-0.869033\pi\)
0.804624 + 0.593784i \(0.202367\pi\)
\(480\) 0 0
\(481\) 4.50000 2.59808i 0.205182 0.118462i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 22.0454 12.7279i 1.00103 0.577945i
\(486\) 0 0
\(487\) 8.50000 14.7224i 0.385172 0.667137i −0.606621 0.794991i \(-0.707476\pi\)
0.991793 + 0.127854i \(0.0408089\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 11.3137i 0.510581i −0.966864 0.255290i \(-0.917829\pi\)
0.966864 0.255290i \(-0.0821710\pi\)
\(492\) 0 0
\(493\) 12.0000 + 6.92820i 0.540453 + 0.312031i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −18.3712 3.53553i −0.824060 0.158590i
\(498\) 0 0
\(499\) −12.5000 21.6506i −0.559577 0.969216i −0.997532 0.0702185i \(-0.977630\pi\)
0.437955 0.898997i \(-0.355703\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 22.0454 0.982956 0.491478 0.870890i \(-0.336457\pi\)
0.491478 + 0.870890i \(0.336457\pi\)
\(504\) 0 0
\(505\) −42.0000 −1.86898
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.22474 + 2.12132i 0.0542859 + 0.0940259i 0.891891 0.452250i \(-0.149378\pi\)
−0.837605 + 0.546276i \(0.816045\pi\)
\(510\) 0 0
\(511\) 3.00000 3.46410i 0.132712 0.153243i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 18.3712 + 10.6066i 0.809531 + 0.467383i
\(516\) 0 0
\(517\) 17.3205i 0.761755i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 2.44949 4.24264i 0.107314 0.185873i −0.807367 0.590049i \(-0.799108\pi\)
0.914681 + 0.404176i \(0.132442\pi\)
\(522\) 0 0
\(523\) −1.50000 + 0.866025i −0.0655904 + 0.0378686i −0.532437 0.846470i \(-0.678724\pi\)
0.466846 + 0.884339i \(0.345390\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −7.34847 + 4.24264i −0.320104 + 0.184812i
\(528\) 0 0
\(529\) 4.50000 7.79423i 0.195652 0.338880i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 38.1838i 1.65392i
\(534\) 0 0
\(535\) −6.00000 3.46410i −0.259403 0.149766i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 6.12372 + 7.77817i 0.263767 + 0.335030i
\(540\) 0 0
\(541\) −8.50000 14.7224i −0.365444 0.632967i 0.623404 0.781900i \(-0.285749\pi\)
−0.988847 + 0.148933i \(0.952416\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.44949 0.104925
\(546\) 0 0
\(547\) 10.0000 0.427569 0.213785 0.976881i \(-0.431421\pi\)
0.213785 + 0.976881i \(0.431421\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.44949 4.24264i −0.104352 0.180743i
\(552\) 0 0
\(553\) 12.5000 4.33013i 0.531554 0.184136i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −13.4722 7.77817i −0.570835 0.329572i 0.186648 0.982427i \(-0.440238\pi\)
−0.757483 + 0.652855i \(0.773571\pi\)
\(558\) 0 0
\(559\) 5.19615i 0.219774i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −13.4722 + 23.3345i −0.567785 + 0.983433i 0.428999 + 0.903305i \(0.358866\pi\)
−0.996785 + 0.0801281i \(0.974467\pi\)
\(564\) 0 0
\(565\) 3.00000 1.73205i 0.126211 0.0728679i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.22474 + 0.707107i −0.0513440 + 0.0296435i −0.525452 0.850823i \(-0.676104\pi\)
0.474108 + 0.880467i \(0.342771\pi\)
\(570\) 0 0
\(571\) 5.50000 9.52628i 0.230168 0.398662i −0.727690 0.685907i \(-0.759406\pi\)
0.957857 + 0.287244i \(0.0927391\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 5.65685i 0.235907i
\(576\) 0 0
\(577\) 1.50000 + 0.866025i 0.0624458 + 0.0360531i 0.530898 0.847436i \(-0.321855\pi\)
−0.468452 + 0.883489i \(0.655188\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.67423 19.0919i 0.152433 0.792065i
\(582\) 0 0
\(583\) 2.00000 + 3.46410i 0.0828315 + 0.143468i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −14.6969 −0.606608 −0.303304 0.952894i \(-0.598090\pi\)
−0.303304 + 0.952894i \(0.598090\pi\)
\(588\) 0 0
\(589\) 3.00000 0.123613
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8.57321 + 14.8492i 0.352060 + 0.609785i 0.986610 0.163096i \(-0.0521481\pi\)
−0.634550 + 0.772881i \(0.718815\pi\)
\(594\) 0 0
\(595\) 6.00000 31.1769i 0.245976 1.27813i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −4.89898 2.82843i −0.200167 0.115566i 0.396566 0.918006i \(-0.370202\pi\)
−0.596733 + 0.802440i \(0.703535\pi\)
\(600\) 0 0
\(601\) 25.9808i 1.05978i −0.848067 0.529889i \(-0.822234\pi\)
0.848067 0.529889i \(-0.177766\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 11.0227 19.0919i 0.448137 0.776195i
\(606\) 0 0
\(607\) 34.5000 19.9186i 1.40031 0.808470i 0.405887 0.913923i \(-0.366962\pi\)
0.994424 + 0.105453i \(0.0336291\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 55.1135 31.8198i 2.22965 1.28729i
\(612\) 0 0
\(613\) −4.00000 + 6.92820i −0.161558 + 0.279827i −0.935428 0.353518i \(-0.884985\pi\)
0.773869 + 0.633345i \(0.218319\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 24.0416i 0.967880i 0.875101 + 0.483940i \(0.160795\pi\)
−0.875101 + 0.483940i \(0.839205\pi\)
\(618\) 0 0
\(619\) 25.5000 + 14.7224i 1.02493 + 0.591744i 0.915529 0.402253i \(-0.131773\pi\)
0.109403 + 0.993997i \(0.465106\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −12.2474 + 4.24264i −0.490684 + 0.169978i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 4.89898 0.195335
\(630\) 0 0
\(631\) −38.0000 −1.51276 −0.756378 0.654135i \(-0.773033\pi\)
−0.756378 + 0.654135i \(0.773033\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −13.4722 23.3345i −0.534628 0.926002i
\(636\) 0 0
\(637\) −13.5000 + 33.7750i −0.534889 + 1.33821i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 12.2474 + 7.07107i 0.483745 + 0.279290i 0.721976 0.691918i \(-0.243234\pi\)
−0.238231 + 0.971209i \(0.576567\pi\)
\(642\) 0 0
\(643\) 25.9808i 1.02458i −0.858812 0.512291i \(-0.828797\pi\)
0.858812 0.512291i \(-0.171203\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.57321 14.8492i 0.337048 0.583784i −0.646828 0.762636i \(-0.723905\pi\)
0.983876 + 0.178852i \(0.0572383\pi\)
\(648\) 0 0
\(649\) 6.00000 3.46410i 0.235521 0.135978i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 6.12372 3.53553i 0.239640 0.138356i −0.375371 0.926875i \(-0.622485\pi\)
0.615011 + 0.788518i \(0.289151\pi\)
\(654\) 0 0
\(655\) 3.00000 5.19615i 0.117220 0.203030i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 22.6274i 0.881439i 0.897645 + 0.440720i \(0.145277\pi\)
−0.897645 + 0.440720i \(0.854723\pi\)
\(660\) 0 0
\(661\) −25.5000 14.7224i −0.991835 0.572636i −0.0860127 0.996294i \(-0.527413\pi\)
−0.905822 + 0.423658i \(0.860746\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −7.34847 + 8.48528i −0.284961 + 0.329045i
\(666\) 0 0
\(667\) 8.00000 + 13.8564i 0.309761 + 0.536522i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4.89898 0.189123
\(672\) 0 0
\(673\) 35.0000 1.34915 0.674575 0.738206i \(-0.264327\pi\)
0.674575 + 0.738206i \(0.264327\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.89898 + 8.48528i 0.188283 + 0.326116i 0.944678 0.327999i \(-0.106374\pi\)
−0.756395 + 0.654115i \(0.773041\pi\)
\(678\) 0 0
\(679\) −27.0000 5.19615i −1.03616 0.199410i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −41.6413 24.0416i −1.59336 0.919927i −0.992725 0.120405i \(-0.961581\pi\)
−0.600636 0.799522i \(-0.705086\pi\)
\(684\) 0 0
\(685\) 27.7128i 1.05885i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −7.34847 + 12.7279i −0.279954 + 0.484895i
\(690\) 0 0
\(691\) −37.5000 + 21.6506i −1.42657 + 0.823629i −0.996848 0.0793336i \(-0.974721\pi\)
−0.429719 + 0.902963i \(0.641387\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −11.0227 + 6.36396i −0.418115 + 0.241399i
\(696\) 0 0
\(697\) 18.0000 31.1769i 0.681799 1.18091i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 5.65685i 0.213656i −0.994277 0.106828i \(-0.965931\pi\)
0.994277 0.106828i \(-0.0340695\pi\)
\(702\) 0 0
\(703\) −1.50000 0.866025i −0.0565736 0.0326628i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 34.2929 + 29.6985i 1.28972 + 1.11693i
\(708\) 0 0
\(709\) 20.0000 + 34.6410i 0.751116 + 1.30097i 0.947282 + 0.320400i \(0.103817\pi\)
−0.196167 + 0.980571i \(0.562849\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −9.79796 −0.366936
\(714\) 0 0
\(715\) −18.0000 −0.673162
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 13.4722 + 23.3345i 0.502428 + 0.870231i 0.999996 + 0.00280593i \(0.000893157\pi\)
−0.497568 + 0.867425i \(0.665774\pi\)
\(720\) 0 0
\(721\) −7.50000 21.6506i −0.279315 0.806312i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.44949 1.41421i −0.0909718 0.0525226i
\(726\) 0 0
\(727\) 25.9808i 0.963573i 0.876289 + 0.481787i \(0.160012\pi\)
−0.876289 + 0.481787i \(0.839988\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 2.44949 4.24264i 0.0905977 0.156920i
\(732\) 0 0
\(733\) −34.5000 + 19.9186i −1.27429 + 0.735710i −0.975792 0.218702i \(-0.929818\pi\)
−0.298495 + 0.954411i \(0.596485\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −13.4722 + 7.77817i −0.496255 + 0.286513i
\(738\) 0 0
\(739\) −0.500000 + 0.866025i −0.0183928 + 0.0318573i −0.875075 0.483987i \(-0.839188\pi\)
0.856683 + 0.515844i \(0.172522\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0416i 0.882002i −0.897507 0.441001i \(-0.854624\pi\)
0.897507 0.441001i \(-0.145376\pi\)
\(744\) 0 0
\(745\) −12.0000 6.92820i −0.439646 0.253830i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.44949 + 7.07107i 0.0895024 + 0.258371i
\(750\) 0 0
\(751\) 14.5000 + 25.1147i 0.529113 + 0.916450i 0.999424 + 0.0339490i \(0.0108084\pi\)
−0.470311 + 0.882501i \(0.655858\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −53.8888 −1.96121
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 12.2474 + 21.2132i 0.443970 + 0.768978i 0.997980 0.0635319i \(-0.0202365\pi\)
−0.554010 + 0.832510i \(0.686903\pi\)
\(762\) 0 0
\(763\) −2.00000 1.73205i −0.0724049 0.0627044i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 22.0454 + 12.7279i 0.796014 + 0.459579i
\(768\) 0 0
\(769\) 25.9808i 0.936890i 0.883493 + 0.468445i \(0.155186\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 13.4722 23.3345i 0.484561 0.839284i −0.515282 0.857021i \(-0.672313\pi\)
0.999843 + 0.0177365i \(0.00564599\pi\)
\(774\) 0 0
\(775\) 1.50000 0.866025i 0.0538816 0.0311086i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −11.0227 + 6.36396i −0.394929 + 0.228013i
\(780\) 0 0
\(781\) −5.00000 + 8.66025i −0.178914 + 0.309888i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 42.4264i 1.51426i
\(786\) 0 0
\(787\) 39.0000 + 22.5167i 1.39020 + 0.802632i 0.993337 0.115246i \(-0.0367655\pi\)
0.396863 + 0.917878i \(0.370099\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3.67423 0.707107i −0.130641 0.0251418i
\(792\) 0 0
\(793\) 9.00000 + 15.5885i 0.319599 + 0.553562i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 29.3939 1.04118 0.520592 0.853805i \(-0.325711\pi\)