Properties

Label 1078.2.e.p.177.2
Level $1078$
Weight $2$
Character 1078.177
Analytic conductor $8.608$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1078.177
Dual form 1078.2.e.p.67.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.707107 + 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.12132 - 3.67423i) q^{5} -1.41421 q^{6} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.707107 + 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.12132 - 3.67423i) q^{5} -1.41421 q^{6} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(2.12132 + 3.67423i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.707107 - 1.22474i) q^{12} +6.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.82843 - 4.89898i) q^{17} +(0.500000 + 0.866025i) q^{18} -4.24264 q^{20} -1.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(0.707107 + 1.22474i) q^{24} +(-6.50000 - 11.2583i) q^{25} +5.65685 q^{27} +2.00000 q^{29} +(-3.00000 + 5.19615i) q^{30} +(-0.707107 - 1.22474i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.707107 + 1.22474i) q^{33} +5.65685 q^{34} -1.00000 q^{36} +(5.00000 - 8.66025i) q^{37} +(2.12132 - 3.67423i) q^{40} +11.3137 q^{41} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-2.12132 - 3.67423i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(2.12132 - 3.67423i) q^{47} -1.41421 q^{48} +13.0000 q^{50} +(4.00000 - 6.92820i) q^{51} +(-4.00000 - 6.92820i) q^{53} +(-2.82843 + 4.89898i) q^{54} +4.24264 q^{55} +(-1.00000 + 1.73205i) q^{58} +(0.707107 + 1.22474i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(-1.41421 + 2.44949i) q^{61} +1.41421 q^{62} +1.00000 q^{64} +(-0.707107 - 1.22474i) q^{66} +(-1.00000 - 1.73205i) q^{67} +(-2.82843 + 4.89898i) q^{68} -8.48528 q^{69} -2.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(4.24264 + 7.34847i) q^{73} +(5.00000 + 8.66025i) q^{74} +(9.19239 - 15.9217i) q^{75} +(-8.00000 + 13.8564i) q^{79} +(2.12132 + 3.67423i) q^{80} +(2.50000 + 4.33013i) q^{81} +(-5.65685 + 9.79796i) q^{82} +16.9706 q^{83} -24.0000 q^{85} +(4.00000 - 6.92820i) q^{86} +(1.41421 + 2.44949i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-3.53553 + 6.12372i) q^{89} +4.24264 q^{90} +6.00000 q^{92} +(1.00000 - 1.73205i) q^{93} +(2.12132 + 3.67423i) q^{94} +(0.707107 - 1.22474i) q^{96} +9.89949 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{9} + 2 q^{11} + 24 q^{15} - 2 q^{16} + 2 q^{18} - 4 q^{22} - 12 q^{23} - 26 q^{25} + 8 q^{29} - 12 q^{30} - 2 q^{32} - 4 q^{36} + 20 q^{37} - 32 q^{43} + 2 q^{44} - 12 q^{46} + 52 q^{50} + 16 q^{51} - 16 q^{53} - 4 q^{58} - 12 q^{60} + 4 q^{64} - 4 q^{67} - 8 q^{71} + 2 q^{72} + 20 q^{74} - 32 q^{79} + 10 q^{81} - 96 q^{85} + 16 q^{86} + 2 q^{88} + 24 q^{92} + 4 q^{93} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.707107 + 1.22474i 0.408248 + 0.707107i 0.994694 0.102882i \(-0.0328064\pi\)
−0.586445 + 0.809989i \(0.699473\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.12132 3.67423i 0.948683 1.64317i 0.200480 0.979698i \(-0.435750\pi\)
0.748203 0.663470i \(-0.230917\pi\)
\(6\) −1.41421 −0.577350
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 2.12132 + 3.67423i 0.670820 + 1.16190i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) 0.707107 1.22474i 0.204124 0.353553i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 6.00000 1.54919
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.82843 4.89898i −0.685994 1.18818i −0.973123 0.230285i \(-0.926034\pi\)
0.287129 0.957892i \(-0.407299\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(20\) −4.24264 −0.948683
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 0.707107 + 1.22474i 0.144338 + 0.250000i
\(25\) −6.50000 11.2583i −1.30000 2.25167i
\(26\) 0 0
\(27\) 5.65685 1.08866
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) −3.00000 + 5.19615i −0.547723 + 0.948683i
\(31\) −0.707107 1.22474i −0.127000 0.219971i 0.795513 0.605937i \(-0.207202\pi\)
−0.922513 + 0.385966i \(0.873868\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.707107 + 1.22474i −0.123091 + 0.213201i
\(34\) 5.65685 0.970143
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 5.00000 8.66025i 0.821995 1.42374i −0.0821995 0.996616i \(-0.526194\pi\)
0.904194 0.427121i \(-0.140472\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 2.12132 3.67423i 0.335410 0.580948i
\(41\) 11.3137 1.76690 0.883452 0.468521i \(-0.155213\pi\)
0.883452 + 0.468521i \(0.155213\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) −2.12132 3.67423i −0.316228 0.547723i
\(46\) −3.00000 5.19615i −0.442326 0.766131i
\(47\) 2.12132 3.67423i 0.309426 0.535942i −0.668811 0.743433i \(-0.733196\pi\)
0.978237 + 0.207491i \(0.0665296\pi\)
\(48\) −1.41421 −0.204124
\(49\) 0 0
\(50\) 13.0000 1.83848
\(51\) 4.00000 6.92820i 0.560112 0.970143i
\(52\) 0 0
\(53\) −4.00000 6.92820i −0.549442 0.951662i −0.998313 0.0580651i \(-0.981507\pi\)
0.448871 0.893597i \(-0.351826\pi\)
\(54\) −2.82843 + 4.89898i −0.384900 + 0.666667i
\(55\) 4.24264 0.572078
\(56\) 0 0
\(57\) 0 0
\(58\) −1.00000 + 1.73205i −0.131306 + 0.227429i
\(59\) 0.707107 + 1.22474i 0.0920575 + 0.159448i 0.908377 0.418153i \(-0.137322\pi\)
−0.816319 + 0.577601i \(0.803989\pi\)
\(60\) −3.00000 5.19615i −0.387298 0.670820i
\(61\) −1.41421 + 2.44949i −0.181071 + 0.313625i −0.942246 0.334922i \(-0.891290\pi\)
0.761174 + 0.648547i \(0.224623\pi\)
\(62\) 1.41421 0.179605
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −0.707107 1.22474i −0.0870388 0.150756i
\(67\) −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) −2.82843 + 4.89898i −0.342997 + 0.594089i
\(69\) −8.48528 −1.02151
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 4.24264 + 7.34847i 0.496564 + 0.860073i 0.999992 0.00396356i \(-0.00126164\pi\)
−0.503429 + 0.864037i \(0.667928\pi\)
\(74\) 5.00000 + 8.66025i 0.581238 + 1.00673i
\(75\) 9.19239 15.9217i 1.06145 1.83848i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −8.00000 + 13.8564i −0.900070 + 1.55897i −0.0726692 + 0.997356i \(0.523152\pi\)
−0.827401 + 0.561611i \(0.810182\pi\)
\(80\) 2.12132 + 3.67423i 0.237171 + 0.410792i
\(81\) 2.50000 + 4.33013i 0.277778 + 0.481125i
\(82\) −5.65685 + 9.79796i −0.624695 + 1.08200i
\(83\) 16.9706 1.86276 0.931381 0.364047i \(-0.118605\pi\)
0.931381 + 0.364047i \(0.118605\pi\)
\(84\) 0 0
\(85\) −24.0000 −2.60317
\(86\) 4.00000 6.92820i 0.431331 0.747087i
\(87\) 1.41421 + 2.44949i 0.151620 + 0.262613i
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) −3.53553 + 6.12372i −0.374766 + 0.649113i −0.990292 0.139003i \(-0.955610\pi\)
0.615526 + 0.788116i \(0.288944\pi\)
\(90\) 4.24264 0.447214
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 1.00000 1.73205i 0.103695 0.179605i
\(94\) 2.12132 + 3.67423i 0.218797 + 0.378968i
\(95\) 0 0
\(96\) 0.707107 1.22474i 0.0721688 0.125000i
\(97\) 9.89949 1.00514 0.502571 0.864536i \(-0.332388\pi\)
0.502571 + 0.864536i \(0.332388\pi\)
\(98\) 0 0
\(99\) 1.00000 0.100504
\(100\) −6.50000 + 11.2583i −0.650000 + 1.12583i
\(101\) 2.82843 + 4.89898i 0.281439 + 0.487467i 0.971739 0.236056i \(-0.0758550\pi\)
−0.690300 + 0.723523i \(0.742522\pi\)
\(102\) 4.00000 + 6.92820i 0.396059 + 0.685994i
\(103\) 9.19239 15.9217i 0.905753 1.56881i 0.0858496 0.996308i \(-0.472640\pi\)
0.819903 0.572502i \(-0.194027\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 8.00000 0.777029
\(107\) −8.00000 + 13.8564i −0.773389 + 1.33955i 0.162306 + 0.986740i \(0.448107\pi\)
−0.935695 + 0.352809i \(0.885227\pi\)
\(108\) −2.82843 4.89898i −0.272166 0.471405i
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) −2.12132 + 3.67423i −0.202260 + 0.350325i
\(111\) 14.1421 1.34231
\(112\) 0 0
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 0 0
\(115\) 12.7279 + 22.0454i 1.18688 + 2.05574i
\(116\) −1.00000 1.73205i −0.0928477 0.160817i
\(117\) 0 0
\(118\) −1.41421 −0.130189
\(119\) 0 0
\(120\) 6.00000 0.547723
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −1.41421 2.44949i −0.128037 0.221766i
\(123\) 8.00000 + 13.8564i 0.721336 + 1.24939i
\(124\) −0.707107 + 1.22474i −0.0635001 + 0.109985i
\(125\) −33.9411 −3.03579
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −5.65685 9.79796i −0.498058 0.862662i
\(130\) 0 0
\(131\) −9.89949 + 17.1464i −0.864923 + 1.49809i 0.00220084 + 0.999998i \(0.499299\pi\)
−0.867124 + 0.498093i \(0.834034\pi\)
\(132\) 1.41421 0.123091
\(133\) 0 0
\(134\) 2.00000 0.172774
\(135\) 12.0000 20.7846i 1.03280 1.78885i
\(136\) −2.82843 4.89898i −0.242536 0.420084i
\(137\) 9.00000 + 15.5885i 0.768922 + 1.33181i 0.938148 + 0.346235i \(0.112540\pi\)
−0.169226 + 0.985577i \(0.554127\pi\)
\(138\) 4.24264 7.34847i 0.361158 0.625543i
\(139\) −11.3137 −0.959616 −0.479808 0.877373i \(-0.659294\pi\)
−0.479808 + 0.877373i \(0.659294\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 1.00000 1.73205i 0.0839181 0.145350i
\(143\) 0 0
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) 4.24264 7.34847i 0.352332 0.610257i
\(146\) −8.48528 −0.702247
\(147\) 0 0
\(148\) −10.0000 −0.821995
\(149\) 5.00000 8.66025i 0.409616 0.709476i −0.585231 0.810867i \(-0.698996\pi\)
0.994847 + 0.101391i \(0.0323294\pi\)
\(150\) 9.19239 + 15.9217i 0.750555 + 1.30000i
\(151\) −2.00000 3.46410i −0.162758 0.281905i 0.773099 0.634285i \(-0.218706\pi\)
−0.935857 + 0.352381i \(0.885372\pi\)
\(152\) 0 0
\(153\) −5.65685 −0.457330
\(154\) 0 0
\(155\) −6.00000 −0.481932
\(156\) 0 0
\(157\) 2.12132 + 3.67423i 0.169300 + 0.293236i 0.938174 0.346164i \(-0.112516\pi\)
−0.768874 + 0.639400i \(0.779183\pi\)
\(158\) −8.00000 13.8564i −0.636446 1.10236i
\(159\) 5.65685 9.79796i 0.448618 0.777029i
\(160\) −4.24264 −0.335410
\(161\) 0 0
\(162\) −5.00000 −0.392837
\(163\) 5.00000 8.66025i 0.391630 0.678323i −0.601035 0.799223i \(-0.705245\pi\)
0.992665 + 0.120900i \(0.0385779\pi\)
\(164\) −5.65685 9.79796i −0.441726 0.765092i
\(165\) 3.00000 + 5.19615i 0.233550 + 0.404520i
\(166\) −8.48528 + 14.6969i −0.658586 + 1.14070i
\(167\) −5.65685 −0.437741 −0.218870 0.975754i \(-0.570237\pi\)
−0.218870 + 0.975754i \(0.570237\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 12.0000 20.7846i 0.920358 1.59411i
\(171\) 0 0
\(172\) 4.00000 + 6.92820i 0.304997 + 0.528271i
\(173\) −5.65685 + 9.79796i −0.430083 + 0.744925i −0.996880 0.0789322i \(-0.974849\pi\)
0.566797 + 0.823857i \(0.308182\pi\)
\(174\) −2.82843 −0.214423
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) −1.00000 + 1.73205i −0.0751646 + 0.130189i
\(178\) −3.53553 6.12372i −0.264999 0.458993i
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) −2.12132 + 3.67423i −0.158114 + 0.273861i
\(181\) 7.07107 0.525588 0.262794 0.964852i \(-0.415356\pi\)
0.262794 + 0.964852i \(0.415356\pi\)
\(182\) 0 0
\(183\) −4.00000 −0.295689
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) −21.2132 36.7423i −1.55963 2.70135i
\(186\) 1.00000 + 1.73205i 0.0733236 + 0.127000i
\(187\) 2.82843 4.89898i 0.206835 0.358249i
\(188\) −4.24264 −0.309426
\(189\) 0 0
\(190\) 0 0
\(191\) −8.00000 + 13.8564i −0.578860 + 1.00261i 0.416751 + 0.909021i \(0.363169\pi\)
−0.995610 + 0.0935936i \(0.970165\pi\)
\(192\) 0.707107 + 1.22474i 0.0510310 + 0.0883883i
\(193\) 3.00000 + 5.19615i 0.215945 + 0.374027i 0.953564 0.301189i \(-0.0973836\pi\)
−0.737620 + 0.675216i \(0.764050\pi\)
\(194\) −4.94975 + 8.57321i −0.355371 + 0.615521i
\(195\) 0 0
\(196\) 0 0
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) −0.500000 + 0.866025i −0.0355335 + 0.0615457i
\(199\) −0.707107 1.22474i −0.0501255 0.0868199i 0.839874 0.542781i \(-0.182629\pi\)
−0.889999 + 0.455962i \(0.849295\pi\)
\(200\) −6.50000 11.2583i −0.459619 0.796084i
\(201\) 1.41421 2.44949i 0.0997509 0.172774i
\(202\) −5.65685 −0.398015
\(203\) 0 0
\(204\) −8.00000 −0.560112
\(205\) 24.0000 41.5692i 1.67623 2.90332i
\(206\) 9.19239 + 15.9217i 0.640464 + 1.10932i
\(207\) 3.00000 + 5.19615i 0.208514 + 0.361158i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) −4.00000 + 6.92820i −0.274721 + 0.475831i
\(213\) −1.41421 2.44949i −0.0969003 0.167836i
\(214\) −8.00000 13.8564i −0.546869 0.947204i
\(215\) −16.9706 + 29.3939i −1.15738 + 2.00465i
\(216\) 5.65685 0.384900
\(217\) 0 0
\(218\) −2.00000 −0.135457
\(219\) −6.00000 + 10.3923i −0.405442 + 0.702247i
\(220\) −2.12132 3.67423i −0.143019 0.247717i
\(221\) 0 0
\(222\) −7.07107 + 12.2474i −0.474579 + 0.821995i
\(223\) 21.2132 1.42054 0.710271 0.703929i \(-0.248573\pi\)
0.710271 + 0.703929i \(0.248573\pi\)
\(224\) 0 0
\(225\) −13.0000 −0.866667
\(226\) 1.00000 1.73205i 0.0665190 0.115214i
\(227\) −7.07107 12.2474i −0.469323 0.812892i 0.530062 0.847959i \(-0.322169\pi\)
−0.999385 + 0.0350674i \(0.988835\pi\)
\(228\) 0 0
\(229\) 4.94975 8.57321i 0.327089 0.566534i −0.654844 0.755764i \(-0.727266\pi\)
0.981933 + 0.189230i \(0.0605991\pi\)
\(230\) −25.4558 −1.67851
\(231\) 0 0
\(232\) 2.00000 0.131306
\(233\) −7.00000 + 12.1244i −0.458585 + 0.794293i −0.998886 0.0471787i \(-0.984977\pi\)
0.540301 + 0.841472i \(0.318310\pi\)
\(234\) 0 0
\(235\) −9.00000 15.5885i −0.587095 1.01688i
\(236\) 0.707107 1.22474i 0.0460287 0.0797241i
\(237\) −22.6274 −1.46981
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) −3.00000 + 5.19615i −0.193649 + 0.335410i
\(241\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) 4.94975 8.57321i 0.317526 0.549972i
\(244\) 2.82843 0.181071
\(245\) 0 0
\(246\) −16.0000 −1.02012
\(247\) 0 0
\(248\) −0.707107 1.22474i −0.0449013 0.0777714i
\(249\) 12.0000 + 20.7846i 0.760469 + 1.31717i
\(250\) 16.9706 29.3939i 1.07331 1.85903i
\(251\) −18.3848 −1.16044 −0.580218 0.814461i \(-0.697033\pi\)
−0.580218 + 0.814461i \(0.697033\pi\)
\(252\) 0 0
\(253\) −6.00000 −0.377217
\(254\) −8.00000 + 13.8564i −0.501965 + 0.869428i
\(255\) −16.9706 29.3939i −1.06274 1.84072i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 0.707107 1.22474i 0.0441081 0.0763975i −0.843129 0.537712i \(-0.819289\pi\)
0.887237 + 0.461315i \(0.152622\pi\)
\(258\) 11.3137 0.704361
\(259\) 0 0
\(260\) 0 0
\(261\) 1.00000 1.73205i 0.0618984 0.107211i
\(262\) −9.89949 17.1464i −0.611593 1.05931i
\(263\) 4.00000 + 6.92820i 0.246651 + 0.427211i 0.962594 0.270947i \(-0.0873367\pi\)
−0.715944 + 0.698158i \(0.754003\pi\)
\(264\) −0.707107 + 1.22474i −0.0435194 + 0.0753778i
\(265\) −33.9411 −2.08499
\(266\) 0 0
\(267\) −10.0000 −0.611990
\(268\) −1.00000 + 1.73205i −0.0610847 + 0.105802i
\(269\) 9.19239 + 15.9217i 0.560470 + 0.970762i 0.997455 + 0.0712937i \(0.0227127\pi\)
−0.436986 + 0.899469i \(0.643954\pi\)
\(270\) 12.0000 + 20.7846i 0.730297 + 1.26491i
\(271\) −4.24264 + 7.34847i −0.257722 + 0.446388i −0.965631 0.259916i \(-0.916305\pi\)
0.707909 + 0.706303i \(0.249639\pi\)
\(272\) 5.65685 0.342997
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) 6.50000 11.2583i 0.391965 0.678903i
\(276\) 4.24264 + 7.34847i 0.255377 + 0.442326i
\(277\) 1.00000 + 1.73205i 0.0600842 + 0.104069i 0.894503 0.447062i \(-0.147530\pi\)
−0.834419 + 0.551131i \(0.814196\pi\)
\(278\) 5.65685 9.79796i 0.339276 0.587643i
\(279\) −1.41421 −0.0846668
\(280\) 0 0
\(281\) −14.0000 −0.835170 −0.417585 0.908638i \(-0.637123\pi\)
−0.417585 + 0.908638i \(0.637123\pi\)
\(282\) −3.00000 + 5.19615i −0.178647 + 0.309426i
\(283\) −9.89949 17.1464i −0.588464 1.01925i −0.994434 0.105363i \(-0.966400\pi\)
0.405970 0.913886i \(-0.366934\pi\)
\(284\) 1.00000 + 1.73205i 0.0593391 + 0.102778i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) −7.50000 + 12.9904i −0.441176 + 0.764140i
\(290\) 4.24264 + 7.34847i 0.249136 + 0.431517i
\(291\) 7.00000 + 12.1244i 0.410347 + 0.710742i
\(292\) 4.24264 7.34847i 0.248282 0.430037i
\(293\) 8.48528 0.495715 0.247858 0.968796i \(-0.420273\pi\)
0.247858 + 0.968796i \(0.420273\pi\)
\(294\) 0 0
\(295\) 6.00000 0.349334
\(296\) 5.00000 8.66025i 0.290619 0.503367i
\(297\) 2.82843 + 4.89898i 0.164122 + 0.284268i
\(298\) 5.00000 + 8.66025i 0.289642 + 0.501675i
\(299\) 0 0
\(300\) −18.3848 −1.06145
\(301\) 0 0
\(302\) 4.00000 0.230174
\(303\) −4.00000 + 6.92820i −0.229794 + 0.398015i
\(304\) 0 0
\(305\) 6.00000 + 10.3923i 0.343559 + 0.595062i
\(306\) 2.82843 4.89898i 0.161690 0.280056i
\(307\) 25.4558 1.45284 0.726421 0.687250i \(-0.241182\pi\)
0.726421 + 0.687250i \(0.241182\pi\)
\(308\) 0 0
\(309\) 26.0000 1.47909
\(310\) 3.00000 5.19615i 0.170389 0.295122i
\(311\) 9.19239 + 15.9217i 0.521253 + 0.902836i 0.999694 + 0.0247167i \(0.00786836\pi\)
−0.478442 + 0.878119i \(0.658798\pi\)
\(312\) 0 0
\(313\) −6.36396 + 11.0227i −0.359712 + 0.623040i −0.987913 0.155012i \(-0.950459\pi\)
0.628200 + 0.778052i \(0.283792\pi\)
\(314\) −4.24264 −0.239426
\(315\) 0 0
\(316\) 16.0000 0.900070
\(317\) −15.0000 + 25.9808i −0.842484 + 1.45922i 0.0453045 + 0.998973i \(0.485574\pi\)
−0.887788 + 0.460252i \(0.847759\pi\)
\(318\) 5.65685 + 9.79796i 0.317221 + 0.549442i
\(319\) 1.00000 + 1.73205i 0.0559893 + 0.0969762i
\(320\) 2.12132 3.67423i 0.118585 0.205396i
\(321\) −22.6274 −1.26294
\(322\) 0 0
\(323\) 0 0
\(324\) 2.50000 4.33013i 0.138889 0.240563i
\(325\) 0 0
\(326\) 5.00000 + 8.66025i 0.276924 + 0.479647i
\(327\) −1.41421 + 2.44949i −0.0782062 + 0.135457i
\(328\) 11.3137 0.624695
\(329\) 0 0
\(330\) −6.00000 −0.330289
\(331\) −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i \(0.351905\pi\)
−0.998298 + 0.0583130i \(0.981428\pi\)
\(332\) −8.48528 14.6969i −0.465690 0.806599i
\(333\) −5.00000 8.66025i −0.273998 0.474579i
\(334\) 2.82843 4.89898i 0.154765 0.268060i
\(335\) −8.48528 −0.463600
\(336\) 0 0
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 6.50000 11.2583i 0.353553 0.612372i
\(339\) −1.41421 2.44949i −0.0768095 0.133038i
\(340\) 12.0000 + 20.7846i 0.650791 + 1.12720i
\(341\) 0.707107 1.22474i 0.0382920 0.0663237i
\(342\) 0 0
\(343\) 0 0
\(344\) −8.00000 −0.431331
\(345\) −18.0000 + 31.1769i −0.969087 + 1.67851i
\(346\) −5.65685 9.79796i −0.304114 0.526742i
\(347\) −10.0000 17.3205i −0.536828 0.929814i −0.999072 0.0430610i \(-0.986289\pi\)
0.462244 0.886753i \(-0.347044\pi\)
\(348\) 1.41421 2.44949i 0.0758098 0.131306i
\(349\) −14.1421 −0.757011 −0.378506 0.925599i \(-0.623562\pi\)
−0.378506 + 0.925599i \(0.623562\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) 0.707107 + 1.22474i 0.0376355 + 0.0651866i 0.884230 0.467052i \(-0.154684\pi\)
−0.846594 + 0.532239i \(0.821351\pi\)
\(354\) −1.00000 1.73205i −0.0531494 0.0920575i
\(355\) −4.24264 + 7.34847i −0.225176 + 0.390016i
\(356\) 7.07107 0.374766
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) 6.00000 10.3923i 0.316668 0.548485i −0.663123 0.748511i \(-0.730769\pi\)
0.979791 + 0.200026i \(0.0641026\pi\)
\(360\) −2.12132 3.67423i −0.111803 0.193649i
\(361\) 9.50000 + 16.4545i 0.500000 + 0.866025i
\(362\) −3.53553 + 6.12372i −0.185824 + 0.321856i
\(363\) −1.41421 −0.0742270
\(364\) 0 0
\(365\) 36.0000 1.88433
\(366\) 2.00000 3.46410i 0.104542 0.181071i
\(367\) −10.6066 18.3712i −0.553660 0.958967i −0.998006 0.0631123i \(-0.979897\pi\)
0.444346 0.895855i \(-0.353436\pi\)
\(368\) −3.00000 5.19615i −0.156386 0.270868i
\(369\) 5.65685 9.79796i 0.294484 0.510061i
\(370\) 42.4264 2.20564
\(371\) 0 0
\(372\) −2.00000 −0.103695
\(373\) 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) 2.82843 + 4.89898i 0.146254 + 0.253320i
\(375\) −24.0000 41.5692i −1.23935 2.14663i
\(376\) 2.12132 3.67423i 0.109399 0.189484i
\(377\) 0 0
\(378\) 0 0
\(379\) −6.00000 −0.308199 −0.154100 0.988055i \(-0.549248\pi\)
−0.154100 + 0.988055i \(0.549248\pi\)
\(380\) 0 0
\(381\) 11.3137 + 19.5959i 0.579619 + 1.00393i
\(382\) −8.00000 13.8564i −0.409316 0.708955i
\(383\) 7.77817 13.4722i 0.397446 0.688397i −0.595964 0.803011i \(-0.703230\pi\)
0.993410 + 0.114614i \(0.0365632\pi\)
\(384\) −1.41421 −0.0721688
\(385\) 0 0
\(386\) −6.00000 −0.305392
\(387\) −4.00000 + 6.92820i −0.203331 + 0.352180i
\(388\) −4.94975 8.57321i −0.251285 0.435239i
\(389\) 12.0000 + 20.7846i 0.608424 + 1.05382i 0.991500 + 0.130105i \(0.0415314\pi\)
−0.383076 + 0.923717i \(0.625135\pi\)
\(390\) 0 0
\(391\) 33.9411 1.71648
\(392\) 0 0
\(393\) −28.0000 −1.41241
\(394\) −11.0000 + 19.0526i −0.554172 + 0.959854i
\(395\) 33.9411 + 58.7878i 1.70776 + 2.95793i
\(396\) −0.500000 0.866025i −0.0251259 0.0435194i
\(397\) 6.36396 11.0227i 0.319398 0.553214i −0.660965 0.750417i \(-0.729853\pi\)
0.980363 + 0.197203i \(0.0631860\pi\)
\(398\) 1.41421 0.0708881
\(399\) 0 0
\(400\) 13.0000 0.650000
\(401\) −6.00000 + 10.3923i −0.299626 + 0.518967i −0.976050 0.217545i \(-0.930195\pi\)
0.676425 + 0.736512i \(0.263528\pi\)
\(402\) 1.41421 + 2.44949i 0.0705346 + 0.122169i
\(403\) 0 0
\(404\) 2.82843 4.89898i 0.140720 0.243733i
\(405\) 21.2132 1.05409
\(406\) 0 0
\(407\) 10.0000 0.495682
\(408\) 4.00000 6.92820i 0.198030 0.342997i
\(409\) −1.41421 2.44949i −0.0699284 0.121119i 0.828941 0.559336i \(-0.188944\pi\)
−0.898870 + 0.438216i \(0.855610\pi\)
\(410\) 24.0000 + 41.5692i 1.18528 + 2.05296i
\(411\) −12.7279 + 22.0454i −0.627822 + 1.08742i
\(412\) −18.3848 −0.905753
\(413\) 0 0
\(414\) −6.00000 −0.294884
\(415\) 36.0000 62.3538i 1.76717 3.06083i
\(416\) 0 0
\(417\) −8.00000 13.8564i −0.391762 0.678551i
\(418\) 0 0
\(419\) −24.0416 −1.17451 −0.587255 0.809402i \(-0.699792\pi\)
−0.587255 + 0.809402i \(0.699792\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) −4.00000 + 6.92820i −0.194717 + 0.337260i
\(423\) −2.12132 3.67423i −0.103142 0.178647i
\(424\) −4.00000 6.92820i −0.194257 0.336463i
\(425\) −36.7696 + 63.6867i −1.78359 + 3.08926i
\(426\) 2.82843 0.137038
\(427\) 0 0
\(428\) 16.0000 0.773389
\(429\) 0 0
\(430\) −16.9706 29.3939i −0.818393 1.41750i
\(431\) −16.0000 27.7128i −0.770693 1.33488i −0.937184 0.348836i \(-0.886577\pi\)
0.166491 0.986043i \(-0.446756\pi\)
\(432\) −2.82843 + 4.89898i −0.136083 + 0.235702i
\(433\) 12.7279 0.611665 0.305832 0.952085i \(-0.401065\pi\)
0.305832 + 0.952085i \(0.401065\pi\)
\(434\) 0 0
\(435\) 12.0000 0.575356
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) 0 0
\(438\) −6.00000 10.3923i −0.286691 0.496564i
\(439\) −12.7279 + 22.0454i −0.607471 + 1.05217i 0.384185 + 0.923256i \(0.374482\pi\)
−0.991656 + 0.128914i \(0.958851\pi\)
\(440\) 4.24264 0.202260
\(441\) 0 0
\(442\) 0 0
\(443\) −18.0000 + 31.1769i −0.855206 + 1.48126i 0.0212481 + 0.999774i \(0.493236\pi\)
−0.876454 + 0.481486i \(0.840097\pi\)
\(444\) −7.07107 12.2474i −0.335578 0.581238i
\(445\) 15.0000 + 25.9808i 0.711068 + 1.23161i
\(446\) −10.6066 + 18.3712i −0.502237 + 0.869900i
\(447\) 14.1421 0.668900
\(448\) 0 0
\(449\) −20.0000 −0.943858 −0.471929 0.881636i \(-0.656442\pi\)
−0.471929 + 0.881636i \(0.656442\pi\)
\(450\) 6.50000 11.2583i 0.306413 0.530723i
\(451\) 5.65685 + 9.79796i 0.266371 + 0.461368i
\(452\) 1.00000 + 1.73205i 0.0470360 + 0.0814688i
\(453\) 2.82843 4.89898i 0.132891 0.230174i
\(454\) 14.1421 0.663723
\(455\) 0 0
\(456\) 0 0
\(457\) −7.00000 + 12.1244i −0.327446 + 0.567153i −0.982004 0.188858i \(-0.939521\pi\)
0.654558 + 0.756012i \(0.272855\pi\)
\(458\) 4.94975 + 8.57321i 0.231287 + 0.400600i
\(459\) −16.0000 27.7128i −0.746816 1.29352i
\(460\) 12.7279 22.0454i 0.593442 1.02787i
\(461\) −2.82843 −0.131733 −0.0658665 0.997828i \(-0.520981\pi\)
−0.0658665 + 0.997828i \(0.520981\pi\)
\(462\) 0 0
\(463\) 26.0000 1.20832 0.604161 0.796862i \(-0.293508\pi\)
0.604161 + 0.796862i \(0.293508\pi\)
\(464\) −1.00000 + 1.73205i −0.0464238 + 0.0804084i
\(465\) −4.24264 7.34847i −0.196748 0.340777i
\(466\) −7.00000 12.1244i −0.324269 0.561650i
\(467\) −2.12132 + 3.67423i −0.0981630 + 0.170023i −0.910924 0.412574i \(-0.864630\pi\)
0.812761 + 0.582597i \(0.197963\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 18.0000 0.830278
\(471\) −3.00000 + 5.19615i −0.138233 + 0.239426i
\(472\) 0.707107 + 1.22474i 0.0325472 + 0.0563735i
\(473\) −4.00000 6.92820i −0.183920 0.318559i
\(474\) 11.3137 19.5959i 0.519656 0.900070i
\(475\) 0 0
\(476\) 0 0
\(477\) −8.00000 −0.366295
\(478\) 6.00000 10.3923i 0.274434 0.475333i
\(479\) 1.41421 + 2.44949i 0.0646171 + 0.111920i 0.896524 0.442995i \(-0.146084\pi\)
−0.831907 + 0.554915i \(0.812751\pi\)
\(480\) −3.00000 5.19615i −0.136931 0.237171i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 21.0000 36.3731i 0.953561 1.65162i
\(486\) 4.94975 + 8.57321i 0.224525 + 0.388889i
\(487\) −1.00000 1.73205i −0.0453143 0.0784867i 0.842479 0.538730i \(-0.181096\pi\)
−0.887793 + 0.460243i \(0.847762\pi\)
\(488\) −1.41421 + 2.44949i −0.0640184 + 0.110883i
\(489\) 14.1421 0.639529
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 8.00000 13.8564i 0.360668 0.624695i
\(493\) −5.65685 9.79796i −0.254772 0.441278i
\(494\) 0 0
\(495\) 2.12132 3.67423i 0.0953463 0.165145i
\(496\) 1.41421 0.0635001
\(497\) 0 0
\(498\) −24.0000 −1.07547
\(499\) −3.00000 + 5.19615i −0.134298 + 0.232612i −0.925329 0.379165i \(-0.876211\pi\)
0.791031 + 0.611776i \(0.209545\pi\)
\(500\) 16.9706 + 29.3939i 0.758947 + 1.31453i
\(501\) −4.00000 6.92820i −0.178707 0.309529i
\(502\) 9.19239 15.9217i 0.410276 0.710620i
\(503\) −31.1127 −1.38725 −0.693623 0.720338i \(-0.743987\pi\)
−0.693623 + 0.720338i \(0.743987\pi\)
\(504\) 0 0
\(505\) 24.0000 1.06799
\(506\) 3.00000 5.19615i 0.133366 0.230997i
\(507\) −9.19239 15.9217i −0.408248 0.707107i
\(508\) −8.00000 13.8564i −0.354943 0.614779i
\(509\) 6.36396 11.0227i 0.282078 0.488573i −0.689819 0.723982i \(-0.742310\pi\)
0.971896 + 0.235409i \(0.0756431\pi\)
\(510\) 33.9411 1.50294
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 0.707107 + 1.22474i 0.0311891 + 0.0540212i
\(515\) −39.0000 67.5500i −1.71855 2.97661i
\(516\) −5.65685 + 9.79796i −0.249029 + 0.431331i
\(517\) 4.24264 0.186591
\(518\) 0 0
\(519\) −16.0000 −0.702322
\(520\) 0 0
\(521\) 0.707107 + 1.22474i 0.0309789 + 0.0536570i 0.881099 0.472931i \(-0.156804\pi\)
−0.850120 + 0.526589i \(0.823471\pi\)
\(522\) 1.00000 + 1.73205i 0.0437688 + 0.0758098i
\(523\) 4.24264 7.34847i 0.185518 0.321326i −0.758233 0.651984i \(-0.773937\pi\)
0.943751 + 0.330657i \(0.107270\pi\)
\(524\) 19.7990 0.864923
\(525\) 0 0
\(526\) −8.00000 −0.348817
\(527\) −4.00000 + 6.92820i −0.174243 + 0.301797i
\(528\) −0.707107 1.22474i −0.0307729 0.0533002i
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 16.9706 29.3939i 0.737154 1.27679i
\(531\) 1.41421 0.0613716
\(532\) 0 0
\(533\) 0 0
\(534\) 5.00000 8.66025i 0.216371 0.374766i
\(535\) 33.9411 + 58.7878i 1.46740 + 2.54162i
\(536\) −1.00000 1.73205i −0.0431934 0.0748132i
\(537\) 8.48528 14.6969i 0.366167 0.634220i
\(538\) −18.3848 −0.792624
\(539\) 0 0
\(540\) −24.0000 −1.03280
\(541\) 15.0000 25.9808i 0.644900 1.11700i −0.339424 0.940633i \(-0.610232\pi\)
0.984325 0.176367i \(-0.0564345\pi\)
\(542\) −4.24264 7.34847i −0.182237 0.315644i
\(543\) 5.00000 + 8.66025i 0.214571 + 0.371647i
\(544\) −2.82843 + 4.89898i −0.121268 + 0.210042i
\(545\) 8.48528 0.363470
\(546\) 0 0
\(547\) 44.0000 1.88130 0.940652 0.339372i \(-0.110215\pi\)
0.940652 + 0.339372i \(0.110215\pi\)
\(548\) 9.00000 15.5885i 0.384461 0.665906i
\(549\) 1.41421 + 2.44949i 0.0603572 + 0.104542i
\(550\) 6.50000 + 11.2583i 0.277161 + 0.480057i
\(551\) 0 0
\(552\) −8.48528 −0.361158
\(553\) 0 0
\(554\) −2.00000 −0.0849719
\(555\) 30.0000 51.9615i 1.27343 2.20564i
\(556\) 5.65685 + 9.79796i 0.239904 + 0.415526i
\(557\) 15.0000 + 25.9808i 0.635570 + 1.10084i 0.986394 + 0.164399i \(0.0525683\pi\)
−0.350824 + 0.936442i \(0.614098\pi\)
\(558\) 0.707107 1.22474i 0.0299342 0.0518476i
\(559\) 0 0
\(560\) 0 0
\(561\) 8.00000 0.337760
\(562\) 7.00000 12.1244i 0.295277 0.511435i
\(563\) 11.3137 + 19.5959i 0.476816 + 0.825869i 0.999647 0.0265668i \(-0.00845748\pi\)
−0.522831 + 0.852436i \(0.675124\pi\)
\(564\) −3.00000 5.19615i −0.126323 0.218797i
\(565\) −4.24264 + 7.34847i −0.178489 + 0.309152i
\(566\) 19.7990 0.832214
\(567\) 0 0
\(568\) −2.00000 −0.0839181
\(569\) −15.0000 + 25.9808i −0.628833 + 1.08917i 0.358954 + 0.933355i \(0.383134\pi\)
−0.987786 + 0.155815i \(0.950200\pi\)
\(570\) 0 0
\(571\) −4.00000 6.92820i −0.167395 0.289936i 0.770108 0.637913i \(-0.220202\pi\)
−0.937503 + 0.347977i \(0.886869\pi\)
\(572\) 0 0
\(573\) −22.6274 −0.945274
\(574\) 0 0
\(575\) 78.0000 3.25282
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) −3.53553 6.12372i −0.147186 0.254934i 0.783000 0.622021i \(-0.213688\pi\)
−0.930186 + 0.367087i \(0.880355\pi\)
\(578\) −7.50000 12.9904i −0.311959 0.540329i
\(579\) −4.24264 + 7.34847i −0.176318 + 0.305392i
\(580\) −8.48528 −0.352332
\(581\) 0 0
\(582\) −14.0000 −0.580319
\(583\) 4.00000 6.92820i 0.165663 0.286937i
\(584\) 4.24264 + 7.34847i 0.175562 + 0.304082i
\(585\) 0 0
\(586\) −4.24264 + 7.34847i −0.175262 + 0.303562i
\(587\) 26.8701 1.10905 0.554523 0.832168i \(-0.312901\pi\)
0.554523 + 0.832168i \(0.312901\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −3.00000 + 5.19615i −0.123508 + 0.213922i
\(591\) 15.5563 + 26.9444i 0.639903 + 1.10834i
\(592\) 5.00000 + 8.66025i 0.205499 + 0.355934i
\(593\) 21.2132 36.7423i 0.871122 1.50883i 0.0102845 0.999947i \(-0.496726\pi\)
0.860837 0.508880i \(-0.169940\pi\)
\(594\) −5.65685 −0.232104
\(595\) 0 0
\(596\) −10.0000 −0.409616
\(597\) 1.00000 1.73205i 0.0409273 0.0708881i
\(598\) 0 0
\(599\) 3.00000 + 5.19615i 0.122577 + 0.212309i 0.920783 0.390075i \(-0.127551\pi\)
−0.798206 + 0.602384i \(0.794218\pi\)
\(600\) 9.19239 15.9217i 0.375278 0.650000i
\(601\) −5.65685 −0.230748 −0.115374 0.993322i \(-0.536807\pi\)
−0.115374 + 0.993322i \(0.536807\pi\)
\(602\) 0 0
\(603\) −2.00000 −0.0814463
\(604\) −2.00000 + 3.46410i −0.0813788 + 0.140952i
\(605\) 2.12132 + 3.67423i 0.0862439 + 0.149379i
\(606\) −4.00000 6.92820i −0.162489 0.281439i
\(607\) 8.48528 14.6969i 0.344407 0.596530i −0.640839 0.767675i \(-0.721413\pi\)
0.985246 + 0.171145i \(0.0547467\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −12.0000 −0.485866
\(611\) 0 0
\(612\) 2.82843 + 4.89898i 0.114332 + 0.198030i
\(613\) 5.00000 + 8.66025i 0.201948 + 0.349784i 0.949156 0.314806i \(-0.101939\pi\)
−0.747208 + 0.664590i \(0.768606\pi\)
\(614\) −12.7279 + 22.0454i −0.513657 + 0.889680i
\(615\) 67.8823 2.73728
\(616\) 0 0
\(617\) 34.0000 1.36879 0.684394 0.729112i \(-0.260067\pi\)
0.684394 + 0.729112i \(0.260067\pi\)
\(618\) −13.0000 + 22.5167i −0.522937 + 0.905753i
\(619\) 4.94975 + 8.57321i 0.198947 + 0.344587i 0.948187 0.317712i \(-0.102914\pi\)
−0.749240 + 0.662298i \(0.769581\pi\)
\(620\) 3.00000 + 5.19615i 0.120483 + 0.208683i
\(621\) −16.9706 + 29.3939i −0.681005 + 1.17954i
\(622\) −18.3848 −0.737162
\(623\) 0 0
\(624\) 0 0
\(625\) −39.5000 + 68.4160i −1.58000 + 2.73664i
\(626\) −6.36396 11.0227i −0.254355 0.440556i
\(627\) 0 0
\(628\) 2.12132 3.67423i 0.0846499 0.146618i
\(629\) −56.5685 −2.25554
\(630\) 0 0
\(631\) 24.0000 0.955425 0.477712 0.878516i \(-0.341466\pi\)
0.477712 + 0.878516i \(0.341466\pi\)
\(632\) −8.00000 + 13.8564i −0.318223 + 0.551178i
\(633\) 5.65685 + 9.79796i 0.224840 + 0.389434i
\(634\) −15.0000 25.9808i −0.595726 1.03183i
\(635\) 33.9411 58.7878i 1.34691 2.33292i
\(636\) −11.3137 −0.448618
\(637\) 0 0
\(638\) −2.00000 −0.0791808
\(639\) −1.00000 + 1.73205i −0.0395594 + 0.0685189i
\(640\) 2.12132 + 3.67423i 0.0838525 + 0.145237i
\(641\) 17.0000 + 29.4449i 0.671460 + 1.16300i 0.977490 + 0.210981i \(0.0676657\pi\)
−0.306031 + 0.952022i \(0.599001\pi\)
\(642\) 11.3137 19.5959i 0.446516 0.773389i
\(643\) 38.1838 1.50582 0.752910 0.658123i \(-0.228649\pi\)
0.752910 + 0.658123i \(0.228649\pi\)
\(644\) 0 0
\(645\) −48.0000 −1.89000
\(646\) 0 0
\(647\) −7.77817 13.4722i −0.305792 0.529647i 0.671646 0.740873i \(-0.265588\pi\)
−0.977437 + 0.211226i \(0.932254\pi\)
\(648\) 2.50000 + 4.33013i 0.0982093 + 0.170103i
\(649\) −0.707107 + 1.22474i −0.0277564 + 0.0480754i
\(650\) 0 0
\(651\) 0 0
\(652\) −10.0000 −0.391630
\(653\) −6.00000 + 10.3923i −0.234798 + 0.406682i −0.959214 0.282681i \(-0.908776\pi\)
0.724416 + 0.689363i \(0.242110\pi\)
\(654\) −1.41421 2.44949i −0.0553001 0.0957826i
\(655\) 42.0000 + 72.7461i 1.64108 + 2.84243i
\(656\) −5.65685 + 9.79796i −0.220863 + 0.382546i
\(657\) 8.48528 0.331042
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 3.00000 5.19615i 0.116775 0.202260i
\(661\) 6.36396 + 11.0227i 0.247529 + 0.428733i 0.962840 0.270073i \(-0.0870480\pi\)
−0.715310 + 0.698807i \(0.753715\pi\)
\(662\) −10.0000 17.3205i −0.388661 0.673181i
\(663\) 0 0
\(664\) 16.9706 0.658586
\(665\) 0 0
\(666\) 10.0000 0.387492
\(667\) −6.00000 + 10.3923i −0.232321 + 0.402392i
\(668\) 2.82843 + 4.89898i 0.109435 + 0.189547i
\(669\) 15.0000 + 25.9808i 0.579934 + 1.00447i
\(670\) 4.24264 7.34847i 0.163908 0.283896i
\(671\) −2.82843 −0.109190
\(672\) 0 0
\(673\) −22.0000 −0.848038 −0.424019 0.905653i \(-0.639381\pi\)
−0.424019 + 0.905653i \(0.639381\pi\)
\(674\) −1.00000 + 1.73205i −0.0385186 + 0.0667161i
\(675\) −36.7696 63.6867i −1.41526 2.45130i
\(676\) 6.50000 + 11.2583i 0.250000 + 0.433013i
\(677\) −19.7990 + 34.2929i −0.760937 + 1.31798i 0.181431 + 0.983404i \(0.441927\pi\)
−0.942368 + 0.334578i \(0.891406\pi\)
\(678\) 2.82843 0.108625
\(679\) 0 0
\(680\) −24.0000 −0.920358
\(681\) 10.0000 17.3205i 0.383201 0.663723i
\(682\) 0.707107 + 1.22474i 0.0270765 + 0.0468979i
\(683\) 14.0000 + 24.2487i 0.535695 + 0.927851i 0.999129 + 0.0417198i \(0.0132837\pi\)
−0.463434 + 0.886131i \(0.653383\pi\)
\(684\) 0 0
\(685\) 76.3675 2.91785
\(686\) 0 0
\(687\) 14.0000 0.534133
\(688\) 4.00000 6.92820i 0.152499 0.264135i
\(689\) 0 0
\(690\) −18.0000 31.1769i −0.685248 1.18688i
\(691\) 7.77817 13.4722i 0.295896 0.512506i −0.679297 0.733863i \(-0.737715\pi\)
0.975193 + 0.221357i \(0.0710486\pi\)
\(692\) 11.3137 0.430083
\(693\) 0 0
\(694\) 20.0000 0.759190
\(695\) −24.0000 + 41.5692i −0.910372 + 1.57681i
\(696\) 1.41421 + 2.44949i 0.0536056 + 0.0928477i
\(697\) −32.0000 55.4256i −1.21209 2.09940i
\(698\) 7.07107 12.2474i 0.267644 0.463573i
\(699\) −19.7990 −0.748867
\(700\) 0 0
\(701\) 50.0000 1.88847 0.944237 0.329267i \(-0.106802\pi\)
0.944237 + 0.329267i \(0.106802\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 12.7279 22.0454i 0.479361 0.830278i
\(706\) −1.41421 −0.0532246
\(707\) 0 0
\(708\) 2.00000 0.0751646
\(709\) 10.0000 17.3205i 0.375558 0.650485i −0.614852 0.788642i \(-0.710784\pi\)
0.990410 + 0.138157i \(0.0441178\pi\)
\(710\) −4.24264 7.34847i −0.159223 0.275783i
\(711\) 8.00000 + 13.8564i 0.300023 + 0.519656i
\(712\) −3.53553 + 6.12372i −0.132500 + 0.229496i
\(713\) 8.48528 0.317776
\(714\) 0 0
\(715\) 0 0
\(716\) −6.00000 + 10.3923i −0.224231 + 0.388379i
\(717\) −8.48528 14.6969i −0.316889 0.548867i
\(718\) 6.00000 + 10.3923i 0.223918 + 0.387837i
\(719\) 9.19239 15.9217i 0.342818 0.593779i −0.642137 0.766590i \(-0.721952\pi\)
0.984955 + 0.172812i \(0.0552852\pi\)
\(720\) 4.24264 0.158114
\(721\) 0 0
\(722\) −19.0000 −0.707107
\(723\) 0 0
\(724\) −3.53553 6.12372i −0.131397 0.227586i
\(725\) −13.0000 22.5167i −0.482808 0.836248i
\(726\) 0.707107 1.22474i 0.0262432 0.0454545i
\(727\) −12.7279 −0.472052 −0.236026 0.971747i \(-0.575845\pi\)
−0.236026 + 0.971747i \(0.575845\pi\)
\(728\) 0 0
\(729\) 29.0000 1.07407
\(730\) −18.0000 + 31.1769i −0.666210 + 1.15391i
\(731\) 22.6274 + 39.1918i 0.836905 + 1.44956i
\(732\) 2.00000 + 3.46410i 0.0739221 + 0.128037i
\(733\) 7.07107 12.2474i 0.261176 0.452370i −0.705379 0.708831i \(-0.749223\pi\)
0.966555 + 0.256461i \(0.0825564\pi\)
\(734\) 21.2132 0.782994
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 1.00000 1.73205i 0.0368355 0.0638009i
\(738\) 5.65685 + 9.79796i 0.208232 + 0.360668i
\(739\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(740\) −21.2132 + 36.7423i −0.779813 + 1.35068i
\(741\) 0 0
\(742\) 0 0
\(743\) −44.0000 −1.61420 −0.807102 0.590412i \(-0.798965\pi\)
−0.807102 + 0.590412i \(0.798965\pi\)
\(744\) 1.00000 1.73205i 0.0366618 0.0635001i
\(745\) −21.2132 36.7423i −0.777192 1.34614i
\(746\) 5.00000 + 8.66025i 0.183063 + 0.317074i
\(747\) 8.48528 14.6969i 0.310460 0.537733i
\(748\) −5.65685 −0.206835
\(749\) 0 0
\(750\) 48.0000 1.75271
\(751\) 7.00000 12.1244i 0.255434 0.442424i −0.709580 0.704625i \(-0.751115\pi\)
0.965013 + 0.262201i \(0.0844484\pi\)
\(752\) 2.12132 + 3.67423i 0.0773566 + 0.133986i
\(753\) −13.0000 22.5167i −0.473746 0.820553i
\(754\) 0 0
\(755\) −16.9706 −0.617622
\(756\) 0 0
\(757\) −8.00000 −0.290765 −0.145382 0.989376i \(-0.546441\pi\)
−0.145382 + 0.989376i \(0.546441\pi\)
\(758\) 3.00000 5.19615i 0.108965 0.188733i
\(759\) −4.24264 7.34847i −0.153998 0.266733i
\(760\) 0 0
\(761\) −21.2132 + 36.7423i −0.768978 + 1.33191i 0.169140 + 0.985592i \(0.445901\pi\)
−0.938118 + 0.346317i \(0.887432\pi\)
\(762\) −22.6274 −0.819705
\(763\) 0 0
\(764\) 16.0000 0.578860
\(765\) −12.0000 + 20.7846i −0.433861 + 0.751469i
\(766\) 7.77817 + 13.4722i 0.281037 + 0.486770i
\(767\) 0 0
\(768\) 0.707107 1.22474i 0.0255155 0.0441942i
\(769\) −19.7990 −0.713970 −0.356985 0.934110i \(-0.616195\pi\)
−0.356985 + 0.934110i \(0.616195\pi\)
\(770\) 0 0
\(771\) 2.00000 0.0720282
\(772\) 3.00000 5.19615i 0.107972 0.187014i
\(773\) 0.707107 + 1.22474i 0.0254329 + 0.0440510i 0.878462 0.477813i \(-0.158570\pi\)
−0.853029 + 0.521864i \(0.825237\pi\)
\(774\) −4.00000 6.92820i −0.143777 0.249029i
\(775\) −9.19239 + 15.9217i −0.330200 + 0.571924i
\(776\) 9.89949 0.355371
\(777\) 0 0
\(778\) −24.0000 −0.860442
\(779\) 0 0
\(780\) 0 0
\(781\) −1.00000 1.73205i −0.0357828 0.0619777i
\(782\) −16.9706 + 29.3939i −0.606866 + 1.05112i
\(783\) 11.3137 0.404319
\(784\) 0 0
\(785\) 18.0000 0.642448
\(786\) 14.0000 24.2487i 0.499363 0.864923i