Properties

Label 52.2.l.a.11.1
Level $52$
Weight $2$
Character 52.11
Analytic conductor $0.415$
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] = [52,2,Mod(7,52)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(52, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("52.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 52 = 2^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 52.l (of order \(12\), degree \(4\), 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: \(0.415222090511\)
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: yes
Sato-Tate group: $\mathrm{U}(1)[D_{12}]$

Embedding invariants

Embedding label 11.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 52.11
Dual form 52.2.l.a.19.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(0.633975 + 0.633975i) q^{5} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.366025 - 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(0.633975 + 0.633975i) q^{5} +(-2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(1.09808 - 0.633975i) q^{10} +(3.59808 + 0.232051i) q^{13} +(2.00000 + 3.46410i) q^{16} +(-6.86603 - 3.96410i) q^{17} +(3.00000 + 3.00000i) q^{18} +(-0.464102 - 1.73205i) q^{20} -4.19615i q^{25} +(1.63397 - 4.83013i) q^{26} +(-3.33013 - 5.76795i) q^{29} +(5.46410 - 1.46410i) q^{32} +(-7.92820 + 7.92820i) q^{34} +(5.19615 - 3.00000i) q^{36} +(11.6962 + 3.13397i) q^{37} -2.53590 q^{40} +(-2.66987 + 9.96410i) q^{41} +(-2.59808 + 0.696152i) q^{45} +(-6.06218 + 3.50000i) q^{49} +(-5.73205 - 1.53590i) q^{50} +(-6.00000 - 4.00000i) q^{52} +10.4641 q^{53} +(-9.09808 + 2.43782i) q^{58} +(-2.69615 + 4.66987i) q^{61} -8.00000i q^{64} +(2.13397 + 2.42820i) q^{65} +(7.92820 + 13.7321i) q^{68} +(-2.19615 - 8.19615i) q^{72} +(9.83013 - 9.83013i) q^{73} +(8.56218 - 14.8301i) q^{74} +(-0.928203 + 3.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(12.6340 + 7.29423i) q^{82} +(-1.83975 - 6.86603i) q^{85} +(-4.09808 - 1.09808i) q^{89} +3.80385i q^{90} +(-6.83013 + 1.83013i) q^{97} +(2.56218 + 9.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 6 q^{5} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 6 q^{5} - 8 q^{8} - 6 q^{9} - 6 q^{10} + 4 q^{13} + 8 q^{16} - 24 q^{17} + 12 q^{18} + 12 q^{20} + 10 q^{26} + 4 q^{29} + 8 q^{32} - 4 q^{34} + 26 q^{37} - 24 q^{40} - 28 q^{41} - 16 q^{50} - 24 q^{52} + 28 q^{53} - 26 q^{58} + 10 q^{61} + 12 q^{65} + 4 q^{68} + 12 q^{72} + 22 q^{73} + 10 q^{74} + 24 q^{80} - 18 q^{81} + 54 q^{82} - 42 q^{85} - 6 q^{89} - 10 q^{97} - 14 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/52\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{12}\right)\)

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
\(5\) 0.633975 + 0.633975i 0.283522 + 0.283522i 0.834512 0.550990i \(-0.185750\pi\)
−0.550990 + 0.834512i \(0.685750\pi\)
\(6\) 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
\(10\) 1.09808 0.633975i 0.347242 0.200480i
\(11\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(12\) 0 0
\(13\) 3.59808 + 0.232051i 0.997927 + 0.0643593i
\(14\) 0 0
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −6.86603 3.96410i −1.66526 0.961436i −0.970143 0.242536i \(-0.922021\pi\)
−0.695113 0.718900i \(-0.744646\pi\)
\(18\) 3.00000 + 3.00000i 0.707107 + 0.707107i
\(19\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(20\) −0.464102 1.73205i −0.103776 0.387298i
\(21\) 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
\(25\) 4.19615i 0.839230i
\(26\) 1.63397 4.83013i 0.320449 0.947266i
\(27\) 0 0
\(28\) 0 0
\(29\) −3.33013 5.76795i −0.618389 1.07108i −0.989780 0.142605i \(-0.954452\pi\)
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
\(34\) −7.92820 + 7.92820i −1.35968 + 1.35968i
\(35\) 0 0
\(36\) 5.19615 3.00000i 0.866025 0.500000i
\(37\) 11.6962 + 3.13397i 1.92284 + 0.515222i 0.986394 + 0.164399i \(0.0525685\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −2.53590 −0.400961
\(41\) −2.66987 + 9.96410i −0.416964 + 1.55613i 0.363905 + 0.931436i \(0.381443\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(44\) 0 0
\(45\) −2.59808 + 0.696152i −0.387298 + 0.103776i
\(46\) 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
\(50\) −5.73205 1.53590i −0.810634 0.217209i
\(51\) 0 0
\(52\) −6.00000 4.00000i −0.832050 0.554700i
\(53\) 10.4641 1.43735 0.718677 0.695344i \(-0.244748\pi\)
0.718677 + 0.695344i \(0.244748\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −9.09808 + 2.43782i −1.19464 + 0.320102i
\(59\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(60\) 0 0
\(61\) −2.69615 + 4.66987i −0.345207 + 0.597916i −0.985391 0.170305i \(-0.945525\pi\)
0.640184 + 0.768221i \(0.278858\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 2.13397 + 2.42820i 0.264687 + 0.301182i
\(66\) 0 0
\(67\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(68\) 7.92820 + 13.7321i 0.961436 + 1.66526i
\(69\) 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
\(73\) 9.83013 9.83013i 1.15053 1.15053i 0.164083 0.986447i \(-0.447534\pi\)
0.986447 0.164083i \(-0.0524664\pi\)
\(74\) 8.56218 14.8301i 0.995333 1.72397i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −0.928203 + 3.46410i −0.103776 + 0.387298i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 12.6340 + 7.29423i 1.39519 + 0.805513i
\(83\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(84\) 0 0
\(85\) −1.83975 6.86603i −0.199548 0.744725i
\(86\) 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 \(0.655526\pi\)
\(90\) 3.80385i 0.400961i
\(91\) 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
\(100\) −4.19615 + 7.26795i −0.419615 + 0.726795i
\(101\) −10.1603 + 5.86603i −1.01098 + 0.583691i −0.911479 0.411346i \(-0.865059\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) −7.66025 + 6.73205i −0.751150 + 0.660132i
\(105\) 0 0
\(106\) 3.83013 14.2942i 0.372015 1.38838i
\(107\) 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
\(113\) 2.06218 3.57180i 0.193993 0.336006i −0.752577 0.658505i \(-0.771189\pi\)
0.946570 + 0.322498i \(0.104523\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 13.3205i 1.23678i
\(117\) −6.00000 + 9.00000i −0.554700 + 0.832050i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 9.52628 + 5.50000i 0.866025 + 0.500000i
\(122\) 5.39230 + 5.39230i 0.488196 + 0.488196i
\(123\) 0 0
\(124\) 0 0
\(125\) 5.83013 5.83013i 0.521462 0.521462i
\(126\) 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
\(130\) 4.09808 2.02628i 0.359425 0.177716i
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 21.6603 5.80385i 1.85735 0.497676i
\(137\) 6.03590 + 22.5263i 0.515682 + 1.92455i 0.341743 + 0.939793i \(0.388983\pi\)
0.173939 + 0.984757i \(0.444351\pi\)
\(138\) 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
\(145\) 1.54552 5.76795i 0.128348 0.479002i
\(146\) −9.83013 17.0263i −0.813547 1.40910i
\(147\) 0 0
\(148\) −17.1244 17.1244i −1.40761 1.40761i
\(149\) 15.1603 4.06218i 1.24198 0.332787i 0.422744 0.906249i \(-0.361067\pi\)
0.819232 + 0.573462i \(0.194400\pi\)
\(150\) 0 0
\(151\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(152\) 0 0
\(153\) 20.5981 11.8923i 1.66526 0.961436i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −25.0526 −1.99941 −0.999706 0.0242497i \(-0.992280\pi\)
−0.999706 + 0.0242497i \(0.992280\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 4.39230 + 2.53590i 0.347242 + 0.200480i
\(161\) 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 \(0.416667\pi\)
\(164\) 14.5885 14.5885i 1.13917 1.13917i
\(165\) 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
\(169\) 12.8923 + 1.66987i 0.991716 + 0.128452i
\(170\) −10.0526 −0.770996
\(171\) 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 \(0.833333\pi\)
\(180\) 5.19615 + 1.39230i 0.387298 + 0.103776i
\(181\) 26.3205i 1.95639i 0.207693 + 0.978194i \(0.433404\pi\)
−0.207693 + 0.978194i \(0.566596\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.42820 + 9.40192i 0.399089 + 0.691243i
\(186\) 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
\(193\) −19.0622 5.10770i −1.37213 0.367660i −0.503871 0.863779i \(-0.668091\pi\)
−0.868255 + 0.496119i \(0.834758\pi\)
\(194\) 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 \(0.166667\pi\)
\(200\) 8.39230 + 8.39230i 0.593426 + 0.593426i
\(201\) 0 0
\(202\) 4.29423 + 16.0263i 0.302141 + 1.12761i
\(203\) 0 0
\(204\) 0 0
\(205\) −8.00962 + 4.62436i −0.559416 + 0.322979i
\(206\) 0 0
\(207\) 0 0
\(208\) 6.39230 + 12.9282i 0.443227 + 0.896410i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(212\) −18.1244 10.4641i −1.24479 0.718677i
\(213\) 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
\(221\) −23.7846 15.8564i −1.59993 1.06662i
\(222\) 0 0
\(223\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(224\) 0 0
\(225\) 10.9019 + 6.29423i 0.726795 + 0.419615i
\(226\) −4.12436 4.12436i −0.274348 0.274348i
\(227\) 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
\(232\) 18.1962 + 4.87564i 1.19464 + 0.320102i
\(233\) 16.0000i 1.04819i −0.851658 0.524097i \(-0.824403\pi\)
0.851658 0.524097i \(-0.175597\pi\)
\(234\) 10.0981 + 11.4904i 0.660132 + 0.751150i
\(235\) 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
\(241\) −6.96410 25.9904i −0.448597 1.67419i −0.706260 0.707953i \(-0.749619\pi\)
0.257663 0.966235i \(-0.417048\pi\)
\(242\) 11.0000 11.0000i 0.707107 0.707107i
\(243\) 0 0
\(244\) 9.33975 5.39230i 0.597916 0.345207i
\(245\) −6.06218 1.62436i −0.387298 0.103776i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −5.83013 10.0981i −0.368730 0.638658i
\(251\) 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
\(257\) 12.3564 7.13397i 0.770771 0.445005i −0.0623783 0.998053i \(-0.519869\pi\)
0.833150 + 0.553047i \(0.186535\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1.26795 6.33975i −0.0786349 0.393174i
\(261\) 19.9808 1.23678
\(262\) 0 0
\(263\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) 0 0
\(265\) 6.63397 + 6.63397i 0.407522 + 0.407522i
\(266\) 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 \(0.0833333\pi\)
\(272\) 31.7128i 1.92287i
\(273\) 0 0
\(274\) 32.9808 1.99244
\(275\) 0 0
\(276\) 0 0
\(277\) 1.37564 + 0.794229i 0.0826545 + 0.0477206i 0.540758 0.841178i \(-0.318138\pi\)
−0.458103 + 0.888899i \(0.651471\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −12.6865 + 12.6865i −0.756815 + 0.756815i −0.975741 0.218926i \(-0.929745\pi\)
0.218926 + 0.975741i \(0.429745\pi\)
\(282\) 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
\(289\) 22.9282 + 39.7128i 1.34872 + 2.33605i
\(290\) −7.31347 4.22243i −0.429462 0.247950i
\(291\) 0 0
\(292\) −26.8564 + 7.19615i −1.57165 + 0.421123i
\(293\) 1.27757 + 4.76795i 0.0746363 + 0.278547i 0.993151 0.116841i \(-0.0372769\pi\)
−0.918514 + 0.395388i \(0.870610\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −29.6603 + 17.1244i −1.72397 + 0.995333i
\(297\) 0 0
\(298\) 22.1962i 1.28579i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.66987 + 1.25129i −0.267396 + 0.0716486i
\(306\) −8.70577 32.4904i −0.497676 1.85735i
\(307\) 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 \(0.737274\pi\)
\(314\) −9.16987 + 34.2224i −0.517486 + 1.93128i
\(315\) 0 0
\(316\) 0 0
\(317\) 23.1506 + 23.1506i 1.30027 + 1.30027i 0.928208 + 0.372061i \(0.121349\pi\)
0.372061 + 0.928208i \(0.378651\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 5.07180 5.07180i 0.283522 0.283522i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 18.0000i 1.00000i
\(325\) 0.973721 15.0981i 0.0540123 0.837491i
\(326\) 0 0
\(327\) 0 0
\(328\) −14.5885 25.2679i −0.805513 1.39519i
\(329\) 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
\(333\) −25.6865 + 25.6865i −1.40761 + 1.40761i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 18.7128i 1.01935i −0.860366 0.509676i \(-0.829765\pi\)
0.860366 0.509676i \(-0.170235\pi\)
\(338\) 7.00000 17.0000i 0.380750 0.924678i
\(339\) 0 0
\(340\) −3.67949 + 13.7321i −0.199548 + 0.744725i
\(341\) 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
\(353\) −7.42820 + 27.7224i −0.395363 + 1.47552i 0.425797 + 0.904819i \(0.359994\pi\)
−0.821160 + 0.570697i \(0.806673\pi\)
\(354\) 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 \(0.750000\pi\)
\(360\) 3.80385 6.58846i 0.200480 0.347242i
\(361\) 16.4545 9.50000i 0.866025 0.500000i
\(362\) 35.9545 + 9.63397i 1.88973 + 0.506350i
\(363\) 0 0
\(364\) 0 0
\(365\) 12.4641 0.652401
\(366\) 0 0
\(367\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(368\) 0 0
\(369\) −21.8827 21.8827i −1.13917 1.13917i
\(370\) 14.8301 3.97372i 0.770982 0.206584i
\(371\) 0 0
\(372\) 0 0
\(373\) 15.0622 26.0885i 0.779890 1.35081i −0.152115 0.988363i \(-0.548608\pi\)
0.932005 0.362446i \(-0.118058\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −10.6436 21.5263i −0.548173 1.10866i
\(378\) 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
\(386\) −13.9545 + 24.1699i −0.710264 + 1.23021i
\(387\) 0 0
\(388\) 13.6603 + 3.66025i 0.693494 + 0.185821i
\(389\) 0.320508i 0.0162504i 0.999967 + 0.00812520i \(0.00258636\pi\)
−0.999967 + 0.00812520i \(0.997414\pi\)
\(390\) 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
\(400\) 14.5359 8.39230i 0.726795 0.419615i
\(401\) −36.8205 9.86603i −1.83873 0.492686i −0.839976 0.542623i \(-0.817431\pi\)
−0.998752 + 0.0499376i \(0.984098\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 23.4641 1.16738
\(405\) 2.08846 7.79423i 0.103776 0.387298i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −15.5981 + 4.17949i −0.771275 + 0.206663i −0.622935 0.782274i \(-0.714060\pi\)
−0.148340 + 0.988936i \(0.547393\pi\)
\(410\) 3.38526 + 12.6340i 0.167186 + 0.623948i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 20.0000 4.00000i 0.980581 0.196116i
\(417\) 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
\(421\) 13.6340 + 13.6340i 0.664479 + 0.664479i 0.956433 0.291953i \(-0.0943052\pi\)
−0.291953 + 0.956433i \(0.594305\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −20.9282 + 20.9282i −1.01636 + 1.01636i
\(425\) −16.6340 + 28.8109i −0.806866 + 1.39753i
\(426\) 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
\(433\) −15.1077 8.72243i −0.726029 0.419173i 0.0909384 0.995857i \(-0.471013\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 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
\(442\) −30.3660 + 26.6865i −1.44436 + 1.26935i
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) −1.90192 3.29423i −0.0901598 0.156161i
\(446\) 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 \(0.559500\pi\)
\(450\) 12.5885 12.5885i 0.593426 0.593426i
\(451\) 0 0
\(452\) −7.14359 + 4.12436i −0.336006 + 0.193993i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.813467 3.03590i 0.0380524 0.142013i −0.944286 0.329125i \(-0.893246\pi\)
0.982339 + 0.187112i \(0.0599128\pi\)
\(458\) 17.0000 + 29.4449i 0.794358 + 1.37587i
\(459\) 0 0
\(460\) 0 0
\(461\) 28.1603 7.54552i 1.31155 0.351430i 0.465746 0.884918i \(-0.345786\pi\)
0.845807 + 0.533488i \(0.179119\pi\)
\(462\) 0 0
\(463\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(464\) 13.3205 23.0718i 0.618389 1.07108i
\(465\) 0 0
\(466\) −21.8564 5.85641i −1.01248 0.271293i
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 19.3923 9.58846i 0.896410 0.443227i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −15.6962 + 27.1865i −0.718677 + 1.24479i
\(478\) 0 0
\(479\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(480\) 0 0
\(481\) 41.3564 + 13.9904i 1.88569 + 0.637906i
\(482\) −38.0526 −1.73325
\(483\) 0 0
\(484\) −11.0000 19.0526i −0.500000 0.866025i
\(485\) −5.49038 3.16987i −0.249305 0.143937i
\(486\) 0 0
\(487\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(488\) −3.94744 14.7321i −0.178692 0.666889i
\(489\) 0 0
\(490\) −4.43782 + 7.68653i −0.200480 + 0.347242i
\(491\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) 0 0
\(493\) 52.8038i 2.37817i
\(494\) 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 \(0.250000\pi\)
\(500\) −15.9282 + 4.26795i −0.712331 + 0.190868i
\(501\) 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
\(505\) −10.1603 2.72243i −0.452125 0.121147i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 10.3301 38.5526i 0.457875 1.70881i −0.221621 0.975133i \(-0.571135\pi\)
0.679496 0.733679i \(-0.262199\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) 0 0
\(514\) −5.22243 19.4904i −0.230352 0.859684i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −9.12436 0.588457i −0.400129 0.0258056i
\(521\) 0.947441 0.0415081 0.0207541 0.999785i \(-0.493393\pi\)
0.0207541 + 0.999785i \(0.493393\pi\)
\(522\) 7.31347 27.2942i 0.320102 1.19464i
\(523\) 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
\(530\) 11.4904 6.63397i 0.499110 0.288161i
\(531\) 0 0
\(532\) 0 0
\(533\) −11.9186 + 35.2321i −0.516251 + 1.52607i
\(534\) 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
\(541\) 32.3468 32.3468i 1.39070 1.39070i 0.566933 0.823764i \(-0.308130\pi\)
0.823764 0.566933i \(-0.191870\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −43.3205 11.6077i −1.85735 0.497676i
\(545\) 8.87564i 0.380191i
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 12.0718 45.0526i 0.515682 1.92455i
\(549\) −8.08846 14.0096i −0.345207 0.597916i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 1.58846 1.58846i 0.0674871 0.0674871i
\(555\) 0 0
\(556\) 0 0
\(557\) 42.4545 + 11.3756i 1.79885 + 0.482002i 0.993798 0.111198i \(-0.0354686\pi\)
0.805056 + 0.593199i \(0.202135\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 12.6865 + 21.9737i 0.535149 + 0.926905i
\(563\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 0 0
\(565\) 3.57180 0.957060i 0.150267 0.0402638i
\(566\) 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
\(577\) 10.1506 + 10.1506i 0.422576 + 0.422576i 0.886090 0.463513i \(-0.153411\pi\)
−0.463513 + 0.886090i \(0.653411\pi\)
\(578\) 62.6410 16.7846i 2.60552 0.698148i
\(579\) 0 0
\(580\) −8.44486 + 8.44486i −0.350654 + 0.350654i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 39.3205i 1.62709i
\(585\) −9.50962 + 1.90192i −0.393174 + 0.0786349i
\(586\) 6.98076 0.288373
\(587\) 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
\(592\) 12.5359 + 46.7846i 0.515222 + 1.92284i
\(593\) 19.3468 19.3468i 0.794477 0.794477i −0.187741 0.982219i \(-0.560117\pi\)
0.982219 + 0.187741i \(0.0601166\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −30.3205 8.12436i −1.24198 0.332787i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) −16.3301 28.2846i −0.666120 1.15375i −0.978980 0.203954i \(-0.934621\pi\)
0.312861 0.949799i \(-0.398713\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.55256 + 9.52628i 0.103776 + 0.387298i
\(606\) 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
\(610\) 6.83717i 0.276829i
\(611\) 0 0
\(612\) −47.5692 −1.92287
\(613\) −10.9115 + 40.7224i −0.440713 + 1.64476i 0.286300 + 0.958140i \(0.407575\pi\)
−0.727013 + 0.686624i \(0.759092\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −20.3564 + 5.45448i −0.819518 + 0.219589i −0.644136 0.764911i \(-0.722783\pi\)
−0.175382 + 0.984500i \(0.556116\pi\)
\(618\) 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
\(625\) −13.5885 −0.543538
\(626\) −8.78461 + 32.7846i −0.351104 + 1.31034i
\(627\) 0 0
\(628\) 43.3923 + 25.0526i 1.73154 + 0.999706i
\(629\) −67.8827 67.8827i −2.70666 2.70666i
\(630\) 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
\(634\) 40.0981 23.1506i 1.59250 0.919429i
\(635\) 0 0
\(636\) 0 0
\(637\) −22.6244 + 11.1865i −0.896410 + 0.443227i
\(638\) 0 0
\(639\) 0 0
\(640\) −5.07180 8.78461i −0.200480 0.347242i
\(641\) 15.6506 + 9.03590i 0.618163 + 0.356897i 0.776153 0.630544i \(-0.217168\pi\)
−0.157991 + 0.987441i \(0.550502\pi\)
\(642\) 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
\(650\) −20.2679 6.85641i −0.794974 0.268930i
\(651\) 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
\(656\) −39.8564 + 10.6795i −1.55613 + 0.416964i
\(657\) 10.7942 + 40.2846i 0.421123 + 1.57165i
\(658\) 0 0
\(659\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(660\) 0 0
\(661\) −1.30385 0.349365i −0.0507138 0.0135887i 0.233373 0.972387i \(-0.425024\pi\)
−0.284087 + 0.958799i \(0.591690\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 25.6865 + 44.4904i 0.995333 + 1.72397i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.91858 + 1.10770i −0.0739560 + 0.0426985i −0.536522 0.843886i \(-0.680262\pi\)
0.462566 + 0.886585i \(0.346929\pi\)
\(674\) −25.5622 6.84936i −0.984618 0.263828i
\(675\) 0 0
\(676\) −20.6603 15.7846i −0.794625 0.607100i
\(677\) 2.00000 0.0768662 0.0384331 0.999261i \(-0.487763\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 17.4115 + 10.0526i 0.667702 + 0.385498i
\(681\) 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
\(685\) −10.4545 + 18.1077i −0.399445 + 0.691859i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 37.6506 + 2.42820i 1.43437 + 0.0925072i
\(690\) 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
\(697\) 57.8301 57.8301i 2.19047 2.19047i
\(698\) 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
\(706\) 35.1506 + 20.2942i 1.32291 + 0.763783i
\(707\) 0 0
\(708\) 0 0
\(709\) −10.4474 38.9904i −0.392362 1.46431i −0.826227 0.563337i \(-0.809517\pi\)
0.433865 0.900978i \(-0.357149\pi\)
\(710\) 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 \(0.166667\pi\)
\(720\) −7.60770 7.60770i −0.283522 0.283522i
\(721\) 0 0
\(722\) −6.95448 25.9545i −0.258819 0.965926i
\(723\) 0 0
\(724\) 26.3205 45.5885i 0.978194 1.69428i
\(725\) −24.2032 + 13.9737i −0.898884 + 0.518971i
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 4.56218 17.0263i 0.168854 0.630171i
\(731\) 0 0
\(732\) 0 0
\(733\) 36.1506 + 36.1506i 1.33525 + 1.33525i 0.900595 + 0.434659i \(0.143131\pi\)
0.434659 + 0.900595i \(0.356869\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) −37.9019 + 21.8827i −1.39519 + 0.805513i
\(739\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(740\) 21.7128i 0.798179i
\(741\) 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
\(745\) 12.1865 + 7.03590i 0.446480 + 0.257775i
\(746\) −30.1244 30.1244i −1.10293 1.10293i
\(747\) 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
\(754\) −33.3013 + 6.66025i −1.21276 + 0.242552i
\(755\) 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
\(765\) 20.5981 + 5.51924i 0.744725 + 0.199548i
\(766\) 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
\(772\) 27.9090 + 27.9090i 1.00447 + 1.00447i
\(773\) −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
\(778\) 0.437822 + 0.117314i 0.0156967 + 0.00420591i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −24.2487 14.0000i −0.866025 0.500000i
\(785\) −15.8827 15.8827i −0.566877 0.566877i
\(786\) 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
\(793\) −10.7846 + 16.1769i −0.382973 + 0.574459i
\(794\) −50.0000 −1.77443