Properties

Label 1078.2.e.p.67.1
Level $1078$
Weight $2$
Character 1078.67
Analytic conductor $8.608$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 67.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1078.67
Dual form 1078.2.e.p.177.1

$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 \(-0.967194\pi\)
0.586445 + 0.809989i \(0.300527\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −2.12132 3.67423i −0.948683 1.64317i −0.748203 0.663470i \(-0.769083\pi\)
−0.200480 0.979698i \(-0.564250\pi\)
\(6\) 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 −0.287129 0.957892i \(-0.592701\pi\)
0.973123 0.230285i \(-0.0739659\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 4.24264 0.948683
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) −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 \(-0.792798\pi\)
0.922513 + 0.385966i \(0.126132\pi\)
\(32\) −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 0.904194 + 0.427121i \(0.140472\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −2.12132 3.67423i −0.335410 0.580948i
\(41\) −11.3137 −1.76690 −0.883452 0.468521i \(-0.844787\pi\)
−0.883452 + 0.468521i \(0.844787\pi\)
\(42\) 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 \(-0.266804\pi\)
−0.978237 + 0.207491i \(0.933470\pi\)
\(48\) 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 0.448871 + 0.893597i \(0.351826\pi\)
−0.998313 + 0.0580651i \(0.981507\pi\)
\(54\) 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 \(-0.862678\pi\)
0.816319 + 0.577601i \(0.196011\pi\)
\(60\) −3.00000 + 5.19615i −0.387298 + 0.670820i
\(61\) 1.41421 + 2.44949i 0.181071 + 0.313625i 0.942246 0.334922i \(-0.108710\pi\)
−0.761174 + 0.648547i \(0.775377\pi\)
\(62\) −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 −0.920623 0.390453i \(-0.872318\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(68\) 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 \(-0.998738\pi\)
0.503429 + 0.864037i \(0.332072\pi\)
\(74\) 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 −0.827401 0.561611i \(-0.810182\pi\)
−0.0726692 0.997356i \(-0.523152\pi\)
\(80\) −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 \(-0.881395\pi\)
−0.931381 + 0.364047i \(0.881395\pi\)
\(84\) 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 \(-0.0443898\pi\)
−0.615526 + 0.788116i \(0.711056\pi\)
\(90\) −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 \(-0.667612\pi\)
−0.502571 + 0.864536i \(0.667612\pi\)
\(98\) 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 \(-0.924145\pi\)
0.690300 + 0.723523i \(0.257478\pi\)
\(102\) 4.00000 6.92820i 0.396059 0.685994i
\(103\) −9.19239 15.9217i −0.905753 1.56881i −0.819903 0.572502i \(-0.805973\pi\)
−0.0858496 0.996308i \(-0.527360\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 8.00000 0.777029
\(107\) −8.00000 13.8564i −0.773389 1.33955i −0.935695 0.352809i \(-0.885227\pi\)
0.162306 0.986740i \(-0.448107\pi\)
\(108\) 2.82843 4.89898i 0.272166 0.471405i
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 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 0.867124 + 0.498093i \(0.165966\pi\)
−0.00220084 + 0.999998i \(0.500701\pi\)
\(132\) −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 −0.169226 0.985577i \(-0.554127\pi\)
0.938148 0.346235i \(-0.112540\pi\)
\(138\) −4.24264 7.34847i −0.361158 0.625543i
\(139\) 11.3137 0.959616 0.479808 0.877373i \(-0.340706\pi\)
0.479808 + 0.877373i \(0.340706\pi\)
\(140\) 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 0.994847 0.101391i \(-0.0323294\pi\)
−0.585231 + 0.810867i \(0.698996\pi\)
\(150\) −9.19239 + 15.9217i −0.750555 + 1.30000i
\(151\) −2.00000 + 3.46410i −0.162758 + 0.281905i −0.935857 0.352381i \(-0.885372\pi\)
0.773099 + 0.634285i \(0.218706\pi\)
\(152\) 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 \(-0.887484\pi\)
0.768874 + 0.639400i \(0.220817\pi\)
\(158\) −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 0.992665 0.120900i \(-0.0385779\pi\)
−0.601035 + 0.799223i \(0.705245\pi\)
\(164\) 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 \(-0.429763\pi\)
0.218870 + 0.975754i \(0.429763\pi\)
\(168\) 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 \(-0.0251511\pi\)
−0.566797 + 0.823857i \(0.691818\pi\)
\(174\) 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 −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 2.12132 + 3.67423i 0.158114 + 0.273861i
\(181\) −7.07107 −0.525588 −0.262794 0.964852i \(-0.584644\pi\)
−0.262794 + 0.964852i \(0.584644\pi\)
\(182\) 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 −0.995610 0.0935936i \(-0.970165\pi\)
0.416751 0.909021i \(-0.363169\pi\)
\(192\) −0.707107 + 1.22474i −0.0510310 + 0.0883883i
\(193\) 3.00000 5.19615i 0.215945 0.374027i −0.737620 0.675216i \(-0.764050\pi\)
0.953564 + 0.301189i \(0.0973836\pi\)
\(194\) 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 \(-0.817371\pi\)
0.889999 + 0.455962i \(0.150705\pi\)
\(200\) −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 \(-0.751427\pi\)
−0.710271 + 0.703929i \(0.751427\pi\)
\(224\) 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 \(-0.677831\pi\)
0.999385 + 0.0350674i \(0.0111646\pi\)
\(228\) 0 0
\(229\) −4.94975 8.57321i −0.327089 0.566534i 0.654844 0.755764i \(-0.272734\pi\)
−0.981933 + 0.189230i \(0.939401\pi\)
\(230\) 25.4558 1.67851
\(231\) 0 0
\(232\) 2.00000 0.131306
\(233\) −7.00000 12.1244i −0.458585 0.794293i 0.540301 0.841472i \(-0.318310\pi\)
−0.998886 + 0.0471787i \(0.984977\pi\)
\(234\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(242\) −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 \(-0.302967\pi\)
0.580218 + 0.814461i \(0.302967\pi\)
\(252\) 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 \(-0.180711\pi\)
−0.887237 + 0.461315i \(0.847378\pi\)
\(258\) −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 −0.715944 0.698158i \(-0.754003\pi\)
0.962594 + 0.270947i \(0.0873367\pi\)
\(264\) 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 0.436986 + 0.899469i \(0.356046\pi\)
−0.997455 + 0.0712937i \(0.977287\pi\)
\(270\) 12.0000 20.7846i 0.730297 1.26491i
\(271\) 4.24264 + 7.34847i 0.257722 + 0.446388i 0.965631 0.259916i \(-0.0836948\pi\)
−0.707909 + 0.706303i \(0.750361\pi\)
\(272\) −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 −0.834419 0.551131i \(-0.814196\pi\)
0.894503 + 0.447062i \(0.147530\pi\)
\(278\) −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 −0.405970 0.913886i \(-0.633066\pi\)
0.994434 0.105363i \(-0.0336004\pi\)
\(284\) 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 \(-0.579727\pi\)
−0.247858 + 0.968796i \(0.579727\pi\)
\(294\) 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 \(-0.758818\pi\)
−0.726421 + 0.687250i \(0.758818\pi\)
\(308\) 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 0.478442 + 0.878119i \(0.341202\pi\)
−0.999694 + 0.0247167i \(0.992132\pi\)
\(312\) 0 0
\(313\) 6.36396 + 11.0227i 0.359712 + 0.623040i 0.987913 0.155012i \(-0.0495415\pi\)
−0.628200 + 0.778052i \(0.716208\pi\)
\(314\) 4.24264 0.239426
\(315\) 0 0
\(316\) 16.0000 0.900070
\(317\) −15.0000 25.9808i −0.842484 1.45922i −0.887788 0.460252i \(-0.847759\pi\)
0.0453045 0.998973i \(-0.485574\pi\)
\(318\) −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 −0.998298 0.0583130i \(-0.981428\pi\)
0.448649 0.893708i \(-0.351905\pi\)
\(332\) 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 0.462244 + 0.886753i \(0.347044\pi\)
−0.999072 + 0.0430610i \(0.986289\pi\)
\(348\) −1.41421 2.44949i −0.0758098 0.131306i
\(349\) 14.1421 0.757011 0.378506 0.925599i \(-0.376438\pi\)
0.378506 + 0.925599i \(0.376438\pi\)
\(350\) 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 \(-0.845316\pi\)
0.846594 + 0.532239i \(0.178649\pi\)
\(354\) −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 0.979791 0.200026i \(-0.0641026\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(360\) 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 −0.444346 0.895855i \(-0.646564\pi\)
0.998006 0.0631123i \(-0.0201026\pi\)
\(368\) −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 0.965945 0.258748i \(-0.0833099\pi\)
−0.707055 + 0.707159i \(0.749977\pi\)
\(374\) −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 \(-0.296770\pi\)
−0.993410 + 0.114614i \(0.963437\pi\)
\(384\) 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 −0.383076 0.923717i \(-0.625135\pi\)
0.991500 0.130105i \(-0.0415314\pi\)
\(390\) 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 \(-0.270147\pi\)
−0.980363 + 0.197203i \(0.936814\pi\)
\(398\) −1.41421 −0.0708881
\(399\) 0 0
\(400\) 13.0000 0.650000
\(401\) −6.00000 10.3923i −0.299626 0.518967i 0.676425 0.736512i \(-0.263528\pi\)
−0.976050 + 0.217545i \(0.930195\pi\)
\(402\) −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 \(-0.811056\pi\)
0.898870 + 0.438216i \(0.144390\pi\)
\(410\) 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 \(-0.300208\pi\)
0.587255 + 0.809402i \(0.300208\pi\)
\(420\) 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 0.166491 + 0.986043i \(0.446756\pi\)
−0.937184 + 0.348836i \(0.886577\pi\)
\(432\) 2.82843 + 4.89898i 0.136083 + 0.235702i
\(433\) −12.7279 −0.611665 −0.305832 0.952085i \(-0.598935\pi\)
−0.305832 + 0.952085i \(0.598935\pi\)
\(434\) 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 0.991656 + 0.128914i \(0.0411491\pi\)
−0.384185 + 0.923256i \(0.625518\pi\)
\(440\) −4.24264 −0.202260
\(441\) 0 0
\(442\) 0 0
\(443\) −18.0000 31.1769i −0.855206 1.48126i −0.876454 0.481486i \(-0.840097\pi\)
0.0212481 0.999774i \(-0.493236\pi\)
\(444\) 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 0.654558 0.756012i \(-0.272855\pi\)
−0.982004 + 0.188858i \(0.939521\pi\)
\(458\) −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 \(-0.479019\pi\)
0.0658665 + 0.997828i \(0.479019\pi\)
\(462\) 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 \(-0.135370\pi\)
−0.812761 + 0.582597i \(0.802037\pi\)
\(468\) 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 \(-0.853916\pi\)
0.831907 + 0.554915i \(0.187249\pi\)
\(480\) −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 −0.887793 0.460243i \(-0.847762\pi\)
0.842479 + 0.538730i \(0.181096\pi\)
\(488\) 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 0.791031 0.611776i \(-0.209545\pi\)
−0.925329 + 0.379165i \(0.876211\pi\)
\(500\) −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 \(-0.256013\pi\)
0.693623 + 0.720338i \(0.256013\pi\)
\(504\) 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 \(-0.257690\pi\)
−0.971896 + 0.235409i \(0.924357\pi\)
\(510\) −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 \(-0.843196\pi\)
0.850120 + 0.526589i \(0.176529\pi\)
\(522\) 1.00000 1.73205i 0.0437688 0.0758098i
\(523\) −4.24264 7.34847i −0.185518 0.321326i 0.758233 0.651984i \(-0.226063\pi\)
−0.943751 + 0.330657i \(0.892730\pi\)
\(524\) −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 0.984325 + 0.176367i \(0.0564345\pi\)
−0.339424 + 0.940633i \(0.610232\pi\)
\(542\) 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 −0.350824 0.936442i \(-0.614098\pi\)
0.986394 0.164399i \(-0.0525683\pi\)
\(558\) −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 \(-0.991543\pi\)
0.522831 + 0.852436i \(0.324876\pi\)
\(564\) −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 −0.987786 0.155815i \(-0.950200\pi\)
0.358954 0.933355i \(-0.383134\pi\)
\(570\) 0 0
\(571\) −4.00000 + 6.92820i −0.167395 + 0.289936i −0.937503 0.347977i \(-0.886869\pi\)
0.770108 + 0.637913i \(0.220202\pi\)
\(572\) 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 \(-0.786312\pi\)
0.930186 + 0.367087i \(0.119645\pi\)
\(578\) −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 \(-0.687099\pi\)
−0.554523 + 0.832168i \(0.687099\pi\)
\(588\) 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 −0.860837 0.508880i \(-0.830060\pi\)
−0.0102845 0.999947i \(-0.503274\pi\)
\(594\) 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 −0.798206 0.602384i \(-0.794218\pi\)
0.920783 + 0.390075i \(0.127551\pi\)
\(600\) −9.19239 15.9217i −0.375278 0.650000i
\(601\) 5.65685 0.230748 0.115374 0.993322i \(-0.463193\pi\)
0.115374 + 0.993322i \(0.463193\pi\)
\(602\) 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 \(-0.278587\pi\)
−0.985246 + 0.171145i \(0.945253\pi\)
\(608\) 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 −0.747208 0.664590i \(-0.768606\pi\)
0.949156 + 0.314806i \(0.101939\pi\)
\(614\) 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 \(-0.897086\pi\)
0.749240 + 0.662298i \(0.230419\pi\)
\(620\) 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 −0.306031 0.952022i \(-0.599001\pi\)
0.977490 0.210981i \(-0.0676657\pi\)
\(642\) −11.3137 19.5959i −0.446516 0.773389i
\(643\) −38.1838 −1.50582 −0.752910 0.658123i \(-0.771351\pi\)
−0.752910 + 0.658123i \(0.771351\pi\)
\(644\) 0 0
\(645\) −48.0000 −1.89000
\(646\) 0 0
\(647\) 7.77817 13.4722i 0.305792 0.529647i −0.671646 0.740873i \(-0.734412\pi\)
0.977437 + 0.211226i \(0.0677456\pi\)
\(648\) 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 0.724416 0.689363i \(-0.242110\pi\)
−0.959214 + 0.282681i \(0.908776\pi\)
\(654\) 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 \(-0.912952\pi\)
0.715310 + 0.698807i \(0.246285\pi\)
\(662\) −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 0.942368 + 0.334578i \(0.108594\pi\)
−0.181431 + 0.983404i \(0.558073\pi\)
\(678\) −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 −0.463434 0.886131i \(-0.653383\pi\)
0.999129 0.0417198i \(-0.0132837\pi\)
\(684\) 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 \(-0.262285\pi\)
−0.975193 + 0.221357i \(0.928951\pi\)
\(692\) −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 0.990410 0.138157i \(-0.0441178\pi\)
−0.614852 + 0.788642i \(0.710784\pi\)
\(710\) 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 \(-0.278048\pi\)
−0.984955 + 0.172812i \(0.944715\pi\)
\(720\) −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 \(-0.424155\pi\)
0.236026 + 0.971747i \(0.424155\pi\)
\(728\) 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 \(-0.250777\pi\)
−0.966555 + 0.256461i \(0.917444\pi\)
\(734\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(740\) 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 0.965013 0.262201i \(-0.0844484\pi\)
−0.709580 + 0.704625i \(0.751115\pi\)
\(752\) −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 0.938118 + 0.346317i \(0.112568\pi\)
−0.169140 + 0.985592i \(0.554099\pi\)
\(762\) 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 \(-0.383805\pi\)
0.356985 + 0.934110i \(0.383805\pi\)
\(770\) 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 \(-0.841430\pi\)
0.853029 + 0.521864i \(0.174763\pi\)
\(774\) −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 +