Properties

Label 676.2.l.c.427.1
Level $676$
Weight $2$
Character 676.427
Analytic conductor $5.398$
Analytic rank $0$
Dimension $4$
CM discriminant -4
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [676,2,Mod(19,676)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(676, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("676.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 676 = 2^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 676.l (of order \(12\), degree \(4\), 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: \(5.39788717664\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 52)
Sato-Tate group: $\mathrm{U}(1)[D_{12}]$

Embedding invariants

Embedding label 427.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 676.427
Dual form 676.2.l.c.19.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(2.36603 + 2.36603i) q^{5} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(2.36603 + 2.36603i) q^{5} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(4.09808 - 2.36603i) q^{10} +(2.00000 + 3.46410i) q^{16} +(5.13397 + 2.96410i) q^{17} +(3.00000 + 3.00000i) q^{18} +(-1.73205 - 6.46410i) q^{20} +6.19615i q^{25} +(5.33013 + 9.23205i) q^{29} +(5.46410 - 1.46410i) q^{32} +(5.92820 - 5.92820i) q^{34} +(5.19615 - 3.00000i) q^{36} +(-4.86603 - 1.30385i) q^{37} -9.46410 q^{40} +(3.03590 - 11.3301i) q^{41} +(-9.69615 + 2.59808i) q^{45} +(-6.06218 + 3.50000i) q^{49} +(8.46410 + 2.26795i) q^{50} +3.53590 q^{53} +(14.5622 - 3.90192i) q^{58} +(7.69615 - 13.3301i) q^{61} -8.00000i q^{64} +(-5.92820 - 10.2679i) q^{68} +(-2.19615 - 8.19615i) q^{72} +(1.16987 - 1.16987i) q^{73} +(-3.56218 + 6.16987i) q^{74} +(-3.46410 + 12.9282i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-14.3660 - 8.29423i) q^{82} +(5.13397 + 19.1603i) q^{85} +(-4.09808 - 1.09808i) q^{89} +14.1962i q^{90} +(-6.83013 + 1.83013i) q^{97} +(2.56218 + 9.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 6 q^{5} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 6 q^{5} - 8 q^{8} - 6 q^{9} + 6 q^{10} + 8 q^{16} + 24 q^{17} + 12 q^{18} + 4 q^{29} + 8 q^{32} - 4 q^{34} - 16 q^{37} - 24 q^{40} + 26 q^{41} - 18 q^{45} + 20 q^{50} + 28 q^{53} + 34 q^{58} + 10 q^{61} + 4 q^{68} + 12 q^{72} + 22 q^{73} + 10 q^{74} - 18 q^{81} - 54 q^{82} + 24 q^{85} - 6 q^{89} - 10 q^{97} - 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/676\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(509\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.366025 1.36603i 0.258819 0.965926i
\(3\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(4\) −1.73205 1.00000i −0.866025 0.500000i
\(5\) 2.36603 + 2.36603i 1.05812 + 1.05812i 0.998203 + 0.0599153i \(0.0190830\pi\)
0.0599153 + 0.998203i \(0.480917\pi\)
\(6\) 0 0
\(7\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(8\) −2.00000 + 2.00000i −0.707107 + 0.707107i
\(9\) −1.50000 + 2.59808i −0.500000 + 0.866025i
\(10\) 4.09808 2.36603i 1.29593 0.748203i
\(11\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) 0 0
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 5.13397 + 2.96410i 1.24517 + 0.718900i 0.970143 0.242536i \(-0.0779791\pi\)
0.275029 + 0.961436i \(0.411312\pi\)
\(18\) 3.00000 + 3.00000i 0.707107 + 0.707107i
\(19\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(20\) −1.73205 6.46410i −0.387298 1.44542i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0 0
\(25\) 6.19615i 1.23923i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.33013 + 9.23205i 0.989780 + 1.71435i 0.618389 + 0.785872i \(0.287786\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(32\) 5.46410 1.46410i 0.965926 0.258819i
\(33\) 0 0
\(34\) 5.92820 5.92820i 1.01668 1.01668i
\(35\) 0 0
\(36\) 5.19615 3.00000i 0.866025 0.500000i
\(37\) −4.86603 1.30385i −0.799970 0.214351i −0.164399 0.986394i \(-0.552568\pi\)
−0.635571 + 0.772043i \(0.719235\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −9.46410 −1.49641
\(41\) 3.03590 11.3301i 0.474128 1.76947i −0.150567 0.988600i \(-0.548110\pi\)
0.624695 0.780869i \(-0.285223\pi\)
\(42\) 0 0
\(43\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(44\) 0 0
\(45\) −9.69615 + 2.59808i −1.44542 + 0.387298i
\(46\) 0 0
\(47\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(48\) 0 0
\(49\) −6.06218 + 3.50000i −0.866025 + 0.500000i
\(50\) 8.46410 + 2.26795i 1.19700 + 0.320736i
\(51\) 0 0
\(52\) 0 0
\(53\) 3.53590 0.485693 0.242846 0.970065i \(-0.421919\pi\)
0.242846 + 0.970065i \(0.421919\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 14.5622 3.90192i 1.91211 0.512348i
\(59\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(60\) 0 0
\(61\) 7.69615 13.3301i 0.985391 1.70675i 0.345207 0.938527i \(-0.387809\pi\)
0.640184 0.768221i \(-0.278858\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(68\) −5.92820 10.2679i −0.718900 1.24517i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(72\) −2.19615 8.19615i −0.258819 0.965926i
\(73\) 1.16987 1.16987i 0.136923 0.136923i −0.635323 0.772246i \(-0.719133\pi\)
0.772246 + 0.635323i \(0.219133\pi\)
\(74\) −3.56218 + 6.16987i −0.414095 + 0.717233i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −3.46410 + 12.9282i −0.387298 + 1.44542i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −14.3660 8.29423i −1.58646 0.915944i
\(83\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(84\) 0 0
\(85\) 5.13397 + 19.1603i 0.556858 + 2.07822i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.09808 1.09808i −0.434395 0.116396i 0.0349934 0.999388i \(-0.488859\pi\)
−0.469389 + 0.882992i \(0.655526\pi\)
\(90\) 14.1962i 1.49641i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −6.83013 + 1.83013i −0.693494 + 0.185821i −0.588315 0.808632i \(-0.700208\pi\)
−0.105180 + 0.994453i \(0.533542\pi\)
\(98\) 2.56218 + 9.56218i 0.258819 + 0.965926i
\(99\) 0 0
\(100\) 6.19615 10.7321i 0.619615 1.07321i
\(101\) −7.16025 + 4.13397i −0.712472 + 0.411346i −0.811976 0.583691i \(-0.801608\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 1.29423 4.83013i 0.125707 0.469143i
\(107\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(108\) 0 0
\(109\) −7.00000 7.00000i −0.670478 0.670478i 0.287348 0.957826i \(-0.407226\pi\)
−0.957826 + 0.287348i \(0.907226\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −10.0622 + 17.4282i −0.946570 + 1.63951i −0.193993 + 0.981003i \(0.562144\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 21.3205i 1.97956i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 9.52628 + 5.50000i 0.866025 + 0.500000i
\(122\) −15.3923 15.3923i −1.39355 1.39355i
\(123\) 0 0
\(124\) 0 0
\(125\) −2.83013 + 2.83013i −0.253134 + 0.253134i
\(126\) 0 0
\(127\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(128\) −10.9282 2.92820i −0.965926 0.258819i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −16.1962 + 4.33975i −1.38881 + 0.372130i
\(137\) −3.47372 12.9641i −0.296780 1.10760i −0.939793 0.341743i \(-0.888983\pi\)
0.643013 0.765855i \(-0.277684\pi\)
\(138\) 0 0
\(139\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −12.0000 −1.00000
\(145\) −9.23205 + 34.4545i −0.766680 + 2.86129i
\(146\) −1.16987 2.02628i −0.0968194 0.167696i
\(147\) 0 0
\(148\) 7.12436 + 7.12436i 0.585618 + 0.585618i
\(149\) 8.06218 2.16025i 0.660479 0.176975i 0.0870170 0.996207i \(-0.472267\pi\)
0.573462 + 0.819232i \(0.305600\pi\)
\(150\) 0 0
\(151\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(152\) 0 0
\(153\) −15.4019 + 8.89230i −1.24517 + 0.718900i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 13.0526 1.04171 0.520854 0.853646i \(-0.325614\pi\)
0.520854 + 0.853646i \(0.325614\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 16.3923 + 9.46410i 1.29593 + 0.748203i
\(161\) 0 0
\(162\) −12.2942 + 3.29423i −0.965926 + 0.258819i
\(163\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(164\) −16.5885 + 16.5885i −1.29534 + 1.29534i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 28.0526 2.15153
\(171\) 0 0
\(172\) 0 0
\(173\) −3.46410 2.00000i −0.263371 0.152057i 0.362500 0.931984i \(-0.381923\pi\)
−0.625871 + 0.779926i \(0.715256\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) 19.3923 + 5.19615i 1.44542 + 0.387298i
\(181\) 8.32051i 0.618458i −0.950988 0.309229i \(-0.899929\pi\)
0.950988 0.309229i \(-0.100071\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −8.42820 14.5981i −0.619654 1.07327i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(192\) 0 0
\(193\) 25.8923 + 6.93782i 1.86377 + 0.499395i 0.999990 0.00447566i \(-0.00142465\pi\)
0.863779 + 0.503871i \(0.168091\pi\)
\(194\) 10.0000i 0.717958i
\(195\) 0 0
\(196\) 14.0000 1.00000
\(197\) 5.49038 20.4904i 0.391173 1.45988i −0.437028 0.899448i \(-0.643969\pi\)
0.828201 0.560431i \(-0.189365\pi\)
\(198\) 0 0
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) −12.3923 12.3923i −0.876268 0.876268i
\(201\) 0 0
\(202\) 3.02628 + 11.2942i 0.212928 + 0.794659i
\(203\) 0 0
\(204\) 0 0
\(205\) 33.9904 19.6244i 2.37399 1.37062i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) −6.12436 3.53590i −0.420622 0.242846i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −12.1244 + 7.00000i −0.821165 + 0.474100i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(224\) 0 0
\(225\) −16.0981 9.29423i −1.07321 0.619615i
\(226\) 20.1244 + 20.1244i 1.33865 + 1.33865i
\(227\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(228\) 0 0
\(229\) −17.0000 + 17.0000i −1.12339 + 1.12339i −0.132164 + 0.991228i \(0.542192\pi\)
−0.991228 + 0.132164i \(0.957808\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −29.1244 7.80385i −1.91211 0.512348i
\(233\) 16.0000i 1.04819i −0.851658 0.524097i \(-0.824403\pi\)
0.851658 0.524097i \(-0.175597\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(240\) 0 0
\(241\) 0.00961894 + 0.0358984i 0.000619611 + 0.00231242i 0.966235 0.257663i \(-0.0829523\pi\)
−0.965615 + 0.259975i \(0.916286\pi\)
\(242\) 11.0000 11.0000i 0.707107 0.707107i
\(243\) 0 0
\(244\) −26.6603 + 15.3923i −1.70675 + 0.985391i
\(245\) −22.6244 6.06218i −1.44542 0.387298i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 2.83013 + 4.90192i 0.178993 + 0.310025i
\(251\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 15.3564 8.86603i 0.957906 0.553047i 0.0623783 0.998053i \(-0.480131\pi\)
0.895528 + 0.445005i \(0.146798\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −31.9808 −1.97956
\(262\) 0 0
\(263\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) 0 0
\(265\) 8.36603 + 8.36603i 0.513921 + 0.513921i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 10.0000 17.3205i 0.609711 1.05605i −0.381577 0.924337i \(-0.624619\pi\)
0.991288 0.131713i \(-0.0420477\pi\)
\(270\) 0 0
\(271\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(272\) 23.7128i 1.43780i
\(273\) 0 0
\(274\) −18.9808 −1.14667
\(275\) 0 0
\(276\) 0 0
\(277\) −25.6244 14.7942i −1.53962 0.888899i −0.998861 0.0477206i \(-0.984804\pi\)
−0.540758 0.841178i \(-0.681862\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 23.6865 23.6865i 1.41302 1.41302i 0.677466 0.735554i \(-0.263078\pi\)
0.735554 0.677466i \(-0.236922\pi\)
\(282\) 0 0
\(283\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −4.39230 + 16.3923i −0.258819 + 0.965926i
\(289\) 9.07180 + 15.7128i 0.533635 + 0.924283i
\(290\) 43.6865 + 25.2224i 2.56536 + 1.48111i
\(291\) 0 0
\(292\) −3.19615 + 0.856406i −0.187041 + 0.0501174i
\(293\) −8.23205 30.7224i −0.480922 1.79482i −0.597763 0.801673i \(-0.703944\pi\)
0.116841 0.993151i \(-0.462723\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 12.3397 7.12436i 0.717233 0.414095i
\(297\) 0 0
\(298\) 11.8038i 0.683779i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 49.7487 13.3301i 2.84860 0.763281i
\(306\) 6.50962 + 24.2942i 0.372130 + 1.38881i
\(307\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −24.0000 −1.35656 −0.678280 0.734803i \(-0.737274\pi\)
−0.678280 + 0.734803i \(0.737274\pi\)
\(314\) 4.77757 17.8301i 0.269614 1.00621i
\(315\) 0 0
\(316\) 0 0
\(317\) −20.1506 20.1506i −1.13177 1.13177i −0.989882 0.141890i \(-0.954682\pi\)
−0.141890 0.989882i \(-0.545318\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 18.9282 18.9282i 1.05812 1.05812i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 18.0000i 1.00000i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 16.5885 + 28.7321i 0.915944 + 1.58646i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(332\) 0 0
\(333\) 10.6865 10.6865i 0.585618 0.585618i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 36.7128i 1.99987i 0.0112091 + 0.999937i \(0.496432\pi\)
−0.0112091 + 0.999937i \(0.503568\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 10.2679 38.3205i 0.556858 2.07822i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −4.00000 + 4.00000i −0.215041 + 0.215041i
\(347\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(348\) 0 0
\(349\) 31.4186 + 8.41858i 1.68180 + 0.450636i 0.968253 0.249973i \(-0.0804216\pi\)
0.713545 + 0.700609i \(0.247088\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.72243 + 6.42820i −0.0916758 + 0.342139i −0.996495 0.0836583i \(-0.973340\pi\)
0.904819 + 0.425797i \(0.140006\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.00000 + 6.00000i 0.317999 + 0.317999i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(360\) 14.1962 24.5885i 0.748203 1.29593i
\(361\) 16.4545 9.50000i 0.866025 0.500000i
\(362\) −11.3660 3.04552i −0.597385 0.160069i
\(363\) 0 0
\(364\) 0 0
\(365\) 5.53590 0.289762
\(366\) 0 0
\(367\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(368\) 0 0
\(369\) 24.8827 + 24.8827i 1.29534 + 1.29534i
\(370\) −23.0263 + 6.16987i −1.19708 + 0.320756i
\(371\) 0 0
\(372\) 0 0
\(373\) 2.93782 5.08846i 0.152115 0.263470i −0.779890 0.625917i \(-0.784725\pi\)
0.932005 + 0.362446i \(0.118058\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 18.9545 32.8301i 0.964758 1.67101i
\(387\) 0 0
\(388\) 13.6603 + 3.66025i 0.693494 + 0.185821i
\(389\) 34.3205i 1.74012i −0.492947 0.870059i \(-0.664080\pi\)
0.492947 0.870059i \(-0.335920\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 5.12436 19.1244i 0.258819 0.965926i
\(393\) 0 0
\(394\) −25.9808 15.0000i −1.30889 0.755689i
\(395\) 0 0
\(396\) 0 0
\(397\) −9.15064 34.1506i −0.459257 1.71397i −0.675261 0.737579i \(-0.735969\pi\)
0.216004 0.976392i \(-0.430698\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −21.4641 + 12.3923i −1.07321 + 0.619615i
\(401\) 8.13397 + 2.17949i 0.406191 + 0.108839i 0.456129 0.889914i \(-0.349236\pi\)
−0.0499376 + 0.998752i \(0.515902\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 16.5359 0.822692
\(405\) 7.79423 29.0885i 0.387298 1.44542i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 38.8205 10.4019i 1.91955 0.514342i 0.930614 0.366002i \(-0.119274\pi\)
0.988936 0.148340i \(-0.0473931\pi\)
\(410\) −14.3660 53.6147i −0.709487 2.64784i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(420\) 0 0
\(421\) 15.3660 + 15.3660i 0.748894 + 0.748894i 0.974272 0.225377i \(-0.0723615\pi\)
−0.225377 + 0.974272i \(0.572361\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −7.07180 + 7.07180i −0.343437 + 0.343437i
\(425\) −18.3660 + 31.8109i −0.890883 + 1.54305i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(432\) 0 0
\(433\) 35.8923 + 20.7224i 1.72487 + 0.995857i 0.907906 + 0.419173i \(0.137680\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 5.12436 + 19.1244i 0.245412 + 0.915891i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) 21.0000i 1.00000i
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) −7.09808 12.2942i −0.336481 0.582802i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 9.88269 + 36.8827i 0.466393 + 1.74060i 0.652230 + 0.758021i \(0.273834\pi\)
−0.185837 + 0.982581i \(0.559500\pi\)
\(450\) −18.5885 + 18.5885i −0.876268 + 0.876268i
\(451\) 0 0
\(452\) 34.8564 20.1244i 1.63951 0.946570i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −9.96410 + 37.1865i −0.466101 + 1.73951i 0.187112 + 0.982339i \(0.440087\pi\)
−0.653213 + 0.757174i \(0.726579\pi\)
\(458\) 17.0000 + 29.4449i 0.794358 + 1.37587i
\(459\) 0 0
\(460\) 0 0
\(461\) −40.4545 + 10.8397i −1.88415 + 0.504857i −0.884918 + 0.465746i \(0.845786\pi\)
−0.999235 + 0.0391109i \(0.987547\pi\)
\(462\) 0 0
\(463\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(464\) −21.3205 + 36.9282i −0.989780 + 1.71435i
\(465\) 0 0
\(466\) −21.8564 5.85641i −1.01248 0.271293i
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −5.30385 + 9.18653i −0.242846 + 0.420622i
\(478\) 0 0
\(479\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.0525589 0.00239399
\(483\) 0 0
\(484\) −11.0000 19.0526i −0.500000 0.866025i
\(485\) −20.4904 11.8301i −0.930420 0.537178i
\(486\) 0 0
\(487\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(488\) 11.2679 + 42.0526i 0.510076 + 1.90363i
\(489\) 0 0
\(490\) −16.5622 + 28.6865i −0.748203 + 1.29593i
\(491\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) 0 0
\(493\) 63.1962i 2.84621i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(500\) 7.73205 2.07180i 0.345788 0.0926536i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(504\) 0 0
\(505\) −26.7224 7.16025i −1.18913 0.318627i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −0.447441 + 1.66987i −0.0198325 + 0.0740158i −0.975133 0.221621i \(-0.928865\pi\)
0.955300 + 0.295637i \(0.0955319\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) 0 0
\(514\) −6.49038 24.2224i −0.286278 1.06841i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 39.0526 1.71092 0.855462 0.517866i \(-0.173273\pi\)
0.855462 + 0.517866i \(0.173273\pi\)
\(522\) −11.7058 + 43.6865i −0.512348 + 1.91211i
\(523\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 14.4904 8.36603i 0.629422 0.363397i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −20.0000 20.0000i −0.862261 0.862261i
\(539\) 0 0
\(540\) 0 0
\(541\) −21.3468 + 21.3468i −0.917770 + 0.917770i −0.996867 0.0790969i \(-0.974796\pi\)
0.0790969 + 0.996867i \(0.474796\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 32.3923 + 8.67949i 1.38881 + 0.372130i
\(545\) 33.1244i 1.41889i
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) −6.94744 + 25.9282i −0.296780 + 1.10760i
\(549\) 23.0885 + 39.9904i 0.985391 + 1.70675i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −29.5885 + 29.5885i −1.25709 + 1.25709i
\(555\) 0 0
\(556\) 0 0
\(557\) −35.6244 9.54552i −1.50945 0.404457i −0.593199 0.805056i \(-0.702135\pi\)
−0.916253 + 0.400599i \(0.868802\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −23.6865 41.0263i −0.999156 1.73059i
\(563\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 0 0
\(565\) −65.0429 + 17.4282i −2.73638 + 0.733210i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −34.6410 + 20.0000i −1.45223 + 0.838444i −0.998608 0.0527519i \(-0.983201\pi\)
−0.453619 + 0.891196i \(0.649867\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 20.7846 + 12.0000i 0.866025 + 0.500000i
\(577\) −33.1506 33.1506i −1.38008 1.38008i −0.844459 0.535620i \(-0.820078\pi\)
−0.535620 0.844459i \(-0.679922\pi\)
\(578\) 24.7846 6.64102i 1.03090 0.276230i
\(579\) 0 0
\(580\) 50.4449 50.4449i 2.09461 2.09461i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 4.67949i 0.193639i
\(585\) 0 0
\(586\) −44.9808 −1.85814
\(587\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −5.21539 19.4641i −0.214351 0.799970i
\(593\) −34.3468 + 34.3468i −1.41045 + 1.41045i −0.653698 + 0.756756i \(0.726783\pi\)
−0.756756 + 0.653698i \(0.773217\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −16.1244 4.32051i −0.660479 0.176975i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −7.66987 13.2846i −0.312861 0.541891i 0.666120 0.745845i \(-0.267954\pi\)
−0.978980 + 0.203954i \(0.934621\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 9.52628 + 35.5526i 0.387298 + 1.44542i
\(606\) 0 0
\(607\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 72.8372i 2.94909i
\(611\) 0 0
\(612\) 35.5692 1.43780
\(613\) 11.2776 42.0885i 0.455497 1.69994i −0.231127 0.972924i \(-0.574241\pi\)
0.686624 0.727013i \(-0.259092\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −27.4545 + 7.35641i −1.10528 + 0.296158i −0.764911 0.644136i \(-0.777217\pi\)
−0.340365 + 0.940294i \(0.610551\pi\)
\(618\) 0 0
\(619\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 17.5885 0.703538
\(626\) −8.78461 + 32.7846i −0.351104 + 1.31034i
\(627\) 0 0
\(628\) −22.6077 13.0526i −0.902145 0.520854i
\(629\) −21.1173 21.1173i −0.842002 0.842002i
\(630\) 0 0
\(631\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −34.9019 + 20.1506i −1.38613 + 0.800284i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −18.9282 32.7846i −0.748203 1.29593i
\(641\) 27.6506 + 15.9641i 1.09213 + 0.630544i 0.934144 0.356897i \(-0.116165\pi\)
0.157991 + 0.987441i \(0.449498\pi\)
\(642\) 0 0
\(643\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) 24.5885 + 6.58846i 0.965926 + 0.258819i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −22.0000 38.1051i −0.860927 1.49117i −0.871036 0.491220i \(-0.836551\pi\)
0.0101092 0.999949i \(-0.496782\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 45.3205 12.1436i 1.76947 0.474128i
\(657\) 1.28461 + 4.79423i 0.0501174 + 0.187041i
\(658\) 0 0
\(659\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(660\) 0 0
\(661\) 43.6506 + 11.6962i 1.69781 + 0.454928i 0.972387 0.233373i \(-0.0749763\pi\)
0.725426 + 0.688301i \(0.241643\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −10.6865 18.5096i −0.414095 0.717233i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −37.9186 + 21.8923i −1.46165 + 0.843886i −0.999088 0.0426985i \(-0.986405\pi\)
−0.462566 + 0.886585i \(0.653071\pi\)
\(674\) 50.1506 + 13.4378i 1.93173 + 0.517606i
\(675\) 0 0
\(676\) 0 0
\(677\) 2.00000 0.0768662 0.0384331 0.999261i \(-0.487763\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −48.5885 28.0526i −1.86328 1.07577i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(684\) 0 0
\(685\) 22.4545 38.8923i 0.857942 1.48600i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(692\) 4.00000 + 6.92820i 0.152057 + 0.263371i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 49.1699 49.1699i 1.86244 1.86244i
\(698\) 23.0000 39.8372i 0.870563 1.50786i
\(699\) 0 0
\(700\) 0 0
\(701\) 10.0000i 0.377695i 0.982006 + 0.188847i \(0.0604752\pi\)
−0.982006 + 0.188847i \(0.939525\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 8.15064 + 4.70577i 0.306753 + 0.177104i
\(707\) 0 0
\(708\) 0 0
\(709\) 13.0096 + 48.5526i 0.488586 + 1.82343i 0.563337 + 0.826227i \(0.309517\pi\)
−0.0747503 + 0.997202i \(0.523816\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 10.3923 6.00000i 0.389468 0.224860i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) −28.3923 28.3923i −1.05812 1.05812i
\(721\) 0 0
\(722\) −6.95448 25.9545i −0.258819 0.965926i
\(723\) 0 0
\(724\) −8.32051 + 14.4115i −0.309229 + 0.535601i
\(725\) −57.2032 + 33.0263i −2.12447 + 1.22657i
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 2.02628 7.56218i 0.0749960 0.279889i
\(731\) 0 0
\(732\) 0 0
\(733\) −7.15064 7.15064i −0.264115 0.264115i 0.562609 0.826723i \(-0.309798\pi\)
−0.826723 + 0.562609i \(0.809798\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 43.0981 24.8827i 1.58646 0.915944i
\(739\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(740\) 33.7128i 1.23931i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(744\) 0 0
\(745\) 24.1865 + 13.9641i 0.886126 + 0.511605i
\(746\) −5.87564 5.87564i −0.215123 0.215123i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −9.00000 15.5885i −0.327111 0.566572i 0.654827 0.755779i \(-0.272742\pi\)
−0.981937 + 0.189207i \(0.939408\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.366025 + 1.36603i 0.0132684 + 0.0495184i 0.972243 0.233975i \(-0.0751733\pi\)
−0.958974 + 0.283493i \(0.908507\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −57.4808 15.4019i −2.07822 0.556858i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −13.5429 + 50.5429i −0.488371 + 1.82263i 0.0760054 + 0.997107i \(0.475783\pi\)
−0.564376 + 0.825518i \(0.690883\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −37.9090 37.9090i −1.36437 1.36437i
\(773\) −6.83013 + 1.83013i −0.245663 + 0.0658251i −0.379549 0.925172i \(-0.623921\pi\)
0.133887 + 0.990997i \(0.457254\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 10.0000 17.3205i 0.358979 0.621770i
\(777\) 0 0
\(778\) −46.8827 12.5622i −1.68083 0.450376i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −24.2487 14.0000i −0.866025 0.500000i
\(785\) 30.8827 + 30.8827i 1.10225 + 1.10225i
\(786\) 0 0
\(787\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(788\) −30.0000 + 30.0000i −1.06871 + 1.06871i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −50.0000 −1.77443
\(795\) 0 0
\(796\)