Properties

Label 52.2.l.a.15.1
Level $52$
Weight $2$
Character 52.15
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 15.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 52.15
Dual form 52.2.l.a.7.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(2.36603 - 2.36603i) q^{5} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(2.36603 - 2.36603i) q^{5} +(-2.00000 - 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(-4.09808 + 2.36603i) q^{10} +(-1.59808 + 3.23205i) q^{13} +(2.00000 + 3.46410i) q^{16} +(-5.13397 - 2.96410i) q^{17} +(3.00000 - 3.00000i) q^{18} +(6.46410 - 1.73205i) q^{20} -6.19615i q^{25} +(3.36603 - 3.83013i) q^{26} +(5.33013 + 9.23205i) q^{29} +(-1.46410 - 5.46410i) q^{32} +(5.92820 + 5.92820i) q^{34} +(-5.19615 + 3.00000i) q^{36} +(1.30385 - 4.86603i) q^{37} -9.46410 q^{40} +(-11.3301 - 3.03590i) q^{41} +(2.59808 + 9.69615i) q^{45} +(6.06218 - 3.50000i) q^{49} +(-2.26795 + 8.46410i) q^{50} +(-6.00000 + 4.00000i) q^{52} +3.53590 q^{53} +(-3.90192 - 14.5622i) q^{58} +(7.69615 - 13.3301i) q^{61} +8.00000i q^{64} +(3.86603 + 11.4282i) q^{65} +(-5.92820 - 10.2679i) q^{68} +(8.19615 - 2.19615i) q^{72} +(1.16987 + 1.16987i) q^{73} +(-3.56218 + 6.16987i) q^{74} +(12.9282 + 3.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(14.3660 + 8.29423i) q^{82} +(-19.1603 + 5.13397i) q^{85} +(1.09808 - 4.09808i) q^{89} -14.1962i q^{90} +(1.83013 + 6.83013i) q^{97} +(-9.56218 + 2.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 6 q^{5} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/52\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 0.366025i −0.965926 0.258819i
\(3\) 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 0.0599153 0.998203i \(-0.480917\pi\)
0.998203 0.0599153i \(-0.0190830\pi\)
\(6\) 0 0
\(7\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(8\) −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 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(12\) 0 0
\(13\) −1.59808 + 3.23205i −0.443227 + 0.896410i
\(14\) 0 0
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −5.13397 2.96410i −1.24517 0.718900i −0.275029 0.961436i \(-0.588688\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 3.00000 3.00000i 0.707107 0.707107i
\(19\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(20\) 6.46410 1.73205i 1.44542 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
\(25\) 6.19615i 1.23923i
\(26\) 3.36603 3.83013i 0.660132 0.751150i
\(27\) 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 \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(32\) −1.46410 5.46410i −0.258819 0.965926i
\(33\) 0 0
\(34\) 5.92820 + 5.92820i 1.01668 + 1.01668i
\(35\) 0 0
\(36\) −5.19615 + 3.00000i −0.866025 + 0.500000i
\(37\) 1.30385 4.86603i 0.214351 0.799970i −0.772043 0.635571i \(-0.780765\pi\)
0.986394 0.164399i \(-0.0525685\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −9.46410 −1.49641
\(41\) −11.3301 3.03590i −1.76947 0.474128i −0.780869 0.624695i \(-0.785223\pi\)
−0.988600 + 0.150567i \(0.951890\pi\)
\(42\) 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 + 9.69615i 0.387298 + 1.44542i
\(46\) 0 0
\(47\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(48\) 0 0
\(49\) 6.06218 3.50000i 0.866025 0.500000i
\(50\) −2.26795 + 8.46410i −0.320736 + 1.19700i
\(51\) 0 0
\(52\) −6.00000 + 4.00000i −0.832050 + 0.554700i
\(53\) 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
\(58\) −3.90192 14.5622i −0.512348 1.91211i
\(59\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(60\) 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
\(65\) 3.86603 + 11.4282i 0.479521 + 1.41749i
\(66\) 0 0
\(67\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(68\) −5.92820 10.2679i −0.718900 1.24517i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(72\) 8.19615 2.19615i 0.965926 0.258819i
\(73\) 1.16987 + 1.16987i 0.136923 + 0.136923i 0.772246 0.635323i \(-0.219133\pi\)
−0.635323 + 0.772246i \(0.719133\pi\)
\(74\) −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 \(\pi\)
\(80\) 12.9282 + 3.46410i 1.44542 + 0.387298i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 14.3660 + 8.29423i 1.58646 + 0.915944i
\(83\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(84\) 0 0
\(85\) −19.1603 + 5.13397i −2.07822 + 0.556858i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.09808 4.09808i 0.116396 0.434395i −0.882992 0.469389i \(-0.844474\pi\)
0.999388 + 0.0349934i \(0.0111410\pi\)
\(90\) 14.1962i 1.49641i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1.83013 + 6.83013i 0.185821 + 0.693494i 0.994453 + 0.105180i \(0.0335417\pi\)
−0.808632 + 0.588315i \(0.799792\pi\)
\(98\) −9.56218 + 2.56218i −0.965926 + 0.258819i
\(99\) 0 0
\(100\) 6.19615 10.7321i 0.619615 1.07321i
\(101\) 7.16025 4.13397i 0.712472 0.411346i −0.0995037 0.995037i \(-0.531726\pi\)
0.811976 + 0.583691i \(0.198392\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 9.66025 3.26795i 0.947266 0.320449i
\(105\) 0 0
\(106\) −4.83013 1.29423i −0.469143 0.125707i
\(107\) 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 −0.957826 0.287348i \(-0.907226\pi\)
0.287348 + 0.957826i \(0.407226\pi\)
\(110\) 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
\(117\) −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
\(122\) −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 \(0.833333\pi\)
\(128\) 2.92820 10.9282i 0.258819 0.965926i
\(129\) 0 0
\(130\) −1.09808 17.0263i −0.0963077 1.49330i
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 4.33975 + 16.1962i 0.372130 + 1.38881i
\(137\) 12.9641 3.47372i 1.10760 0.296780i 0.341743 0.939793i \(-0.388983\pi\)
0.765855 + 0.643013i \(0.222316\pi\)
\(138\) 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
\(145\) 34.4545 + 9.23205i 2.86129 + 0.766680i
\(146\) −1.16987 2.02628i −0.0968194 0.167696i
\(147\) 0 0
\(148\) 7.12436 7.12436i 0.585618 0.585618i
\(149\) −2.16025 8.06218i −0.176975 0.660479i −0.996207 0.0870170i \(-0.972267\pi\)
0.819232 0.573462i \(-0.194400\pi\)
\(150\) 0 0
\(151\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(152\) 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
\(162\) 3.29423 + 12.2942i 0.258819 + 0.965926i
\(163\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(164\) −16.5885 16.5885i −1.29534 1.29534i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(168\) 0 0
\(169\) −7.89230 10.3301i −0.607100 0.794625i
\(170\) 28.0526 2.15153
\(171\) 0 0
\(172\) 0 0
\(173\) 3.46410 + 2.00000i 0.263371 + 0.152057i 0.625871 0.779926i \(-0.284744\pi\)
−0.362500 + 0.931984i \(0.618077\pi\)
\(174\) 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 + 19.3923i −0.387298 + 1.44542i
\(181\) 8.32051i 0.618458i 0.950988 + 0.309229i \(0.100071\pi\)
−0.950988 + 0.309229i \(0.899929\pi\)
\(182\) 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
\(193\) −6.93782 + 25.8923i −0.499395 + 1.86377i 0.00447566 + 0.999990i \(0.498575\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) 10.0000i 0.717958i
\(195\) 0 0
\(196\) 14.0000 1.00000
\(197\) −20.4904 5.49038i −1.45988 0.391173i −0.560431 0.828201i \(-0.689365\pi\)
−0.899448 + 0.437028i \(0.856031\pi\)
\(198\) 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
\(202\) −11.2942 + 3.02628i −0.794659 + 0.212928i
\(203\) 0 0
\(204\) 0 0
\(205\) −33.9904 + 19.6244i −2.37399 + 1.37062i
\(206\) 0 0
\(207\) 0 0
\(208\) −14.3923 + 0.928203i −0.997927 + 0.0643593i
\(209\) 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
\(221\) 17.7846 11.8564i 1.19632 0.797548i
\(222\) 0 0
\(223\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(224\) 0 0
\(225\) 16.0981 + 9.29423i 1.07321 + 0.619615i
\(226\) 20.1244 20.1244i 1.33865 1.33865i
\(227\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(228\) 0 0
\(229\) −17.0000 17.0000i −1.12339 1.12339i −0.991228 0.132164i \(-0.957808\pi\)
−0.132164 0.991228i \(-0.542192\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 7.80385 29.1244i 0.512348 1.91211i
\(233\) 16.0000i 1.04819i 0.851658 + 0.524097i \(0.175597\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 4.90192 + 14.4904i 0.320449 + 0.947266i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(240\) 0 0
\(241\) −0.0358984 + 0.00961894i −0.00231242 + 0.000619611i −0.259975 0.965615i \(-0.583714\pi\)
0.257663 + 0.966235i \(0.417048\pi\)
\(242\) 11.0000 + 11.0000i 0.707107 + 0.707107i
\(243\) 0 0
\(244\) 26.6603 15.3923i 1.70675 0.985391i
\(245\) 6.06218 22.6244i 0.387298 1.44542i
\(246\) 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 −0.895528 0.445005i \(-0.853202\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −4.73205 + 23.6603i −0.293469 + 1.46735i
\(261\) −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 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(272\) 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 \(0.0151957\pi\)
0.540758 + 0.841178i \(0.318138\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 23.6865 + 23.6865i 1.41302 + 1.41302i 0.735554 + 0.677466i \(0.236922\pi\)
0.677466 + 0.735554i \(0.263078\pi\)
\(282\) 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
\(288\) 16.3923 + 4.39230i 0.965926 + 0.258819i
\(289\) 9.07180 + 15.7128i 0.533635 + 0.924283i
\(290\) −43.6865 25.2224i −2.56536 1.48111i
\(291\) 0 0
\(292\) 0.856406 + 3.19615i 0.0501174 + 0.187041i
\(293\) 30.7224 8.23205i 1.79482 0.480922i 0.801673 0.597763i \(-0.203944\pi\)
0.993151 + 0.116841i \(0.0372769\pi\)
\(294\) 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
\(305\) −13.3301 49.7487i −0.763281 2.84860i
\(306\) −24.2942 + 6.50962i −1.38881 + 0.372130i
\(307\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(308\) 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 \(0.737274\pi\)
\(314\) −17.8301 4.77757i −1.00621 0.269614i
\(315\) 0 0
\(316\) 0 0
\(317\) −20.1506 + 20.1506i −1.13177 + 1.13177i −0.141890 + 0.989882i \(0.545318\pi\)
−0.989882 + 0.141890i \(0.954682\pi\)
\(318\) 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
\(325\) 20.0263 + 9.90192i 1.11086 + 0.549260i
\(326\) 0 0
\(327\) 0 0
\(328\) 16.5885 + 28.7321i 0.915944 + 1.58646i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(332\) 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 \(-0.503568\pi\)
0.0112091 0.999937i \(-0.496432\pi\)
\(338\) 7.00000 + 17.0000i 0.380750 + 0.924678i
\(339\) 0 0
\(340\) −38.3205 10.2679i −2.07822 0.556858i
\(341\) 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
\(349\) −8.41858 + 31.4186i −0.450636 + 1.68180i 0.249973 + 0.968253i \(0.419578\pi\)
−0.700609 + 0.713545i \(0.747088\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 6.42820 + 1.72243i 0.342139 + 0.0916758i 0.425797 0.904819i \(-0.359994\pi\)
−0.0836583 + 0.996495i \(0.526660\pi\)
\(354\) 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 \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(360\) 14.1962 24.5885i 0.748203 1.29593i
\(361\) −16.4545 + 9.50000i −0.866025 + 0.500000i
\(362\) 3.04552 11.3660i 0.160069 0.597385i
\(363\) 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
\(370\) 6.16987 + 23.0263i 0.320756 + 1.19708i
\(371\) 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
\(377\) −38.3564 + 2.47372i −1.97546 + 0.127403i
\(378\) 0 0
\(379\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 18.9545 32.8301i 0.964758 1.67101i
\(387\) 0 0
\(388\) −3.66025 + 13.6603i −0.185821 + 0.693494i
\(389\) 34.3205i 1.74012i 0.492947 + 0.870059i \(0.335920\pi\)
−0.492947 + 0.870059i \(0.664080\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −19.1244 5.12436i −0.965926 0.258819i
\(393\) 0 0
\(394\) 25.9808 + 15.0000i 1.30889 + 0.755689i
\(395\) 0 0
\(396\) 0 0
\(397\) 34.1506 9.15064i 1.71397 0.459257i 0.737579 0.675261i \(-0.235969\pi\)
0.976392 + 0.216004i \(0.0693024\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 21.4641 12.3923i 1.07321 0.619615i
\(401\) −2.17949 + 8.13397i −0.108839 + 0.406191i −0.998752 0.0499376i \(-0.984098\pi\)
0.889914 + 0.456129i \(0.150764\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 16.5359 0.822692
\(405\) −29.0885 7.79423i −1.44542 0.387298i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −10.4019 38.8205i −0.514342 1.91955i −0.366002 0.930614i \(-0.619274\pi\)
−0.148340 0.988936i \(-0.547393\pi\)
\(410\) 53.6147 14.3660i 2.64784 0.709487i
\(411\) 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
\(421\) 15.3660 15.3660i 0.748894 0.748894i −0.225377 0.974272i \(-0.572361\pi\)
0.974272 + 0.225377i \(0.0723615\pi\)
\(422\) 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 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(432\) 0 0
\(433\) −35.8923 20.7224i −1.72487 0.995857i −0.907906 0.419173i \(-0.862320\pi\)
−0.816968 0.576683i \(-0.804347\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −19.1244 + 5.12436i −0.915891 + 0.245412i
\(437\) 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
\(442\) −28.6340 + 9.68653i −1.36198 + 0.460741i
\(443\) 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
\(449\) −36.8827 + 9.88269i −1.74060 + 0.466393i −0.982581 0.185837i \(-0.940500\pi\)
−0.758021 + 0.652230i \(0.773834\pi\)
\(450\) −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
\(457\) 37.1865 + 9.96410i 1.73951 + 0.466101i 0.982339 0.187112i \(-0.0599128\pi\)
0.757174 + 0.653213i \(0.226579\pi\)
\(458\) 17.0000 + 29.4449i 0.794358 + 1.37587i
\(459\) 0 0
\(460\) 0 0
\(461\) 10.8397 + 40.4545i 0.504857 + 1.88415i 0.465746 + 0.884918i \(0.345786\pi\)
0.0391109 + 0.999235i \(0.487547\pi\)
\(462\) 0 0
\(463\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(464\) −21.3205 + 36.9282i −0.989780 + 1.71435i
\(465\) 0 0
\(466\) 5.85641 21.8564i 0.271293 1.01248i
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) −1.39230 21.5885i −0.0643593 0.997927i
\(469\) 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 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(480\) 0 0
\(481\) 13.6436 + 11.9904i 0.622094 + 0.546714i
\(482\) 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 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(488\) −42.0526 + 11.2679i −1.90363 + 0.510076i
\(489\) 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 \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(500\) −2.07180 7.73205i −0.0926536 0.345788i
\(501\) 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
\(505\) 7.16025 26.7224i 0.318627 1.18913i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.66987 + 0.447441i 0.0740158 + 0.0198325i 0.295637 0.955300i \(-0.404468\pi\)
−0.221621 + 0.975133i \(0.571135\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) 0 0
\(514\) 24.2224 6.49038i 1.06841 0.286278i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 15.1244 30.5885i 0.663247 1.34139i
\(521\) 39.0526 1.71092 0.855462 0.517866i \(-0.173273\pi\)
0.855462 + 0.517866i \(0.173273\pi\)
\(522\) 43.6865 + 11.7058i 1.91211 + 0.512348i
\(523\) 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
\(533\) 27.9186 31.7679i 1.20929 1.37602i
\(534\) 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 0.0790969 0.996867i \(-0.474796\pi\)
−0.996867 + 0.0790969i \(0.974796\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −8.67949 + 32.3923i −0.372130 + 1.38881i
\(545\) 33.1244i 1.41889i
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 25.9282 + 6.94744i 1.10760 + 0.296780i
\(549\) 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
\(557\) 9.54552 35.6244i 0.404457 1.50945i −0.400599 0.916253i \(-0.631198\pi\)
0.805056 0.593199i \(-0.202135\pi\)
\(558\) 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
\(565\) 17.4282 + 65.0429i 0.733210 + 2.73638i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 34.6410 20.0000i 1.45223 0.838444i 0.453619 0.891196i \(-0.350133\pi\)
0.998608 + 0.0527519i \(0.0167993\pi\)
\(570\) 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 −0.535620 + 0.844459i \(0.679922\pi\)
−0.844459 + 0.535620i \(0.820078\pi\)
\(578\) −6.64102 24.7846i −0.276230 1.03090i
\(579\) 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
\(585\) −35.4904 7.09808i −1.46735 0.293469i
\(586\) −44.9808 −1.85814
\(587\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 19.4641 5.21539i 0.799970 0.214351i
\(593\) −34.3468 34.3468i −1.41045 1.41045i −0.756756 0.653698i \(-0.773217\pi\)
−0.653698 0.756756i \(-0.726783\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4.32051 16.1244i 0.176975 0.660479i
\(597\) 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
\(605\) −35.5526 + 9.52628i −1.44542 + 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
\(610\) 72.8372i 2.94909i
\(611\) 0 0
\(612\) 35.5692 1.43780
\(613\) −42.0885 11.2776i −1.69994 0.455497i −0.727013 0.686624i \(-0.759092\pi\)
−0.972924 + 0.231127i \(0.925759\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7.35641 + 27.4545i 0.296158 + 1.10528i 0.940294 + 0.340365i \(0.110551\pi\)
−0.644136 + 0.764911i \(0.722783\pi\)
\(618\) 0 0
\(619\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 17.5885 0.703538
\(626\) 32.7846 + 8.78461i 1.31034 + 0.351104i
\(627\) 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 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 34.9019 20.1506i 1.38613 0.800284i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.62436 + 25.1865i 0.0643593 + 0.997927i
\(638\) 0 0
\(639\) 0 0
\(640\) −18.9282 32.7846i −0.748203 1.29593i
\(641\) −27.6506 15.9641i −1.09213 0.630544i −0.157991 0.987441i \(-0.550502\pi\)
−0.934144 + 0.356897i \(0.883835\pi\)
\(642\) 0 0
\(643\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) −6.58846 + 24.5885i −0.258819 + 0.965926i
\(649\) 0 0
\(650\) −23.7321 20.8564i −0.930848 0.818056i
\(651\) 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
\(656\) −12.1436 45.3205i −0.474128 1.76947i
\(657\) −4.79423 + 1.28461i −0.187041 + 0.0501174i
\(658\) 0 0
\(659\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(660\) 0 0
\(661\) −11.6962 + 43.6506i −0.454928 + 1.69781i 0.233373 + 0.972387i \(0.425024\pi\)
−0.688301 + 0.725426i \(0.741643\pi\)
\(662\) 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 0.462566 0.886585i \(-0.346929\pi\)
0.999088 + 0.0426985i \(0.0135955\pi\)
\(674\) −13.4378 + 50.1506i −0.517606 + 1.93173i
\(675\) 0 0
\(676\) −3.33975 25.7846i −0.128452 0.991716i
\(677\) 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 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(684\) 0 0
\(685\) 22.4545 38.8923i 0.857942 1.48600i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −5.65064 + 11.4282i −0.215272 + 0.435380i
\(690\) 0 0
\(691\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(692\) 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 \(-0.939525\pi\)
0.982006 0.188847i \(-0.0604752\pi\)
\(702\) 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
\(709\) −48.5526 + 13.0096i −1.82343 + 0.488586i −0.997202 0.0747503i \(-0.976184\pi\)
−0.826227 + 0.563337i \(0.809517\pi\)
\(710\) 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
\(722\) 25.9545 6.95448i 0.965926 0.258819i
\(723\) 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
\(730\) −7.56218 2.02628i −0.279889 0.0749960i
\(731\) 0 0
\(732\) 0 0
\(733\) −7.15064 + 7.15064i −0.264115 + 0.264115i −0.826723 0.562609i \(-0.809798\pi\)
0.562609 + 0.826723i \(0.309798\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) −43.0981 + 24.8827i −1.58646 + 0.915944i
\(739\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(740\) 33.7128i 1.23931i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(744\) 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
\(754\) 53.3013 + 10.6603i 1.94112 + 0.388224i
\(755\) 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
\(761\) −1.36603 + 0.366025i −0.0495184 + 0.0132684i −0.283493 0.958974i \(-0.591493\pi\)
0.233975 + 0.972243i \(0.424827\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 15.4019 57.4808i 0.556858 2.07822i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 50.5429 + 13.5429i 1.82263 + 0.488371i 0.997107 0.0760054i \(-0.0242166\pi\)
0.825518 + 0.564376i \(0.190883\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −37.9090 + 37.9090i −1.36437 + 1.36437i
\(773\) 1.83013 + 6.83013i 0.0658251 + 0.245663i 0.990997 0.133887i \(-0.0427458\pi\)
−0.925172 + 0.379549i \(0.876079\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 10.0000 17.3205i 0.358979 0.621770i
\(777\) 0 0
\(778\) 12.5622 46.8827i 0.450376 1.68083i
\(779\) 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 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(788\) −30.0000 30.0000i −1.06871 1.06871i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 30.7846 + 46.1769i 1.09319 + 1.63979i
\(794\) −50.0000 −1.77443