Properties

Label 1078.2.e.j.177.1
Level $1078$
Weight $2$
Character 1078.177
Analytic conductor $8.608$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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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: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1078.177
Dual form 1078.2.e.j.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.00000 - 3.46410i) q^{5} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-2.00000 - 3.46410i) q^{10} +(0.500000 + 0.866025i) q^{11} +2.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(3.00000 - 5.19615i) q^{19} -4.00000 q^{20} +1.00000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(-5.50000 - 9.52628i) q^{25} +(1.00000 - 1.73205i) q^{26} -2.00000 q^{29} +(1.00000 + 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +4.00000 q^{34} -3.00000 q^{36} +(-5.00000 + 8.66025i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(-2.00000 + 3.46410i) q^{40} +4.00000 q^{41} -8.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-6.00000 - 10.3923i) q^{45} +(2.00000 + 3.46410i) q^{46} +(-1.00000 + 1.73205i) q^{47} -11.0000 q^{50} +(-1.00000 - 1.73205i) q^{52} +(-3.00000 - 5.19615i) q^{53} +4.00000 q^{55} +(-1.00000 + 1.73205i) q^{58} +(6.00000 + 10.3923i) q^{59} +(7.00000 - 12.1244i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(4.00000 - 6.92820i) q^{65} +(6.00000 + 10.3923i) q^{67} +(2.00000 - 3.46410i) q^{68} -8.00000 q^{71} +(-1.50000 + 2.59808i) q^{72} +(-2.00000 - 3.46410i) q^{73} +(5.00000 + 8.66025i) q^{74} -6.00000 q^{76} +(2.00000 + 3.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(2.00000 - 3.46410i) q^{82} -6.00000 q^{83} +16.0000 q^{85} +(-4.00000 + 6.92820i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} -12.0000 q^{90} +4.00000 q^{92} +(1.00000 + 1.73205i) q^{94} +(-12.0000 - 20.7846i) q^{95} -14.0000 q^{97} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} + 4 q^{5} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} + 4 q^{5} - 2 q^{8} + 3 q^{9} - 4 q^{10} + q^{11} + 4 q^{13} - q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 8 q^{20} + 2 q^{22} - 4 q^{23} - 11 q^{25} + 2 q^{26} - 4 q^{29} + 2 q^{31} + q^{32} + 8 q^{34} - 6 q^{36} - 10 q^{37} - 6 q^{38} - 4 q^{40} + 8 q^{41} - 16 q^{43} + q^{44} - 12 q^{45} + 4 q^{46} - 2 q^{47} - 22 q^{50} - 2 q^{52} - 6 q^{53} + 8 q^{55} - 2 q^{58} + 12 q^{59} + 14 q^{61} + 4 q^{62} + 2 q^{64} + 8 q^{65} + 12 q^{67} + 4 q^{68} - 16 q^{71} - 3 q^{72} - 4 q^{73} + 10 q^{74} - 12 q^{76} + 4 q^{80} - 9 q^{81} + 4 q^{82} - 12 q^{83} + 32 q^{85} - 8 q^{86} - q^{88} + 6 q^{89} - 24 q^{90} + 8 q^{92} + 2 q^{94} - 24 q^{95} - 28 q^{97} + 6 q^{99}+O(q^{100}) \) 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 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 2.00000 3.46410i 0.894427 1.54919i 0.0599153 0.998203i \(-0.480917\pi\)
0.834512 0.550990i \(-0.185750\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) −2.00000 3.46410i −0.632456 1.09545i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) −1.50000 2.59808i −0.353553 0.612372i
\(19\) 3.00000 5.19615i 0.688247 1.19208i −0.284157 0.958778i \(-0.591714\pi\)
0.972404 0.233301i \(-0.0749529\pi\)
\(20\) −4.00000 −0.894427
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0 0
\(25\) −5.50000 9.52628i −1.10000 1.90526i
\(26\) 1.00000 1.73205i 0.196116 0.339683i
\(27\) 0 0
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) 1.00000 + 1.73205i 0.179605 + 0.311086i 0.941745 0.336327i \(-0.109185\pi\)
−0.762140 + 0.647412i \(0.775851\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 4.00000 0.685994
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) −5.00000 + 8.66025i −0.821995 + 1.42374i 0.0821995 + 0.996616i \(0.473806\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) −3.00000 5.19615i −0.486664 0.842927i
\(39\) 0 0
\(40\) −2.00000 + 3.46410i −0.316228 + 0.547723i
\(41\) 4.00000 0.624695 0.312348 0.949968i \(-0.398885\pi\)
0.312348 + 0.949968i \(0.398885\pi\)
\(42\) 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
\(45\) −6.00000 10.3923i −0.894427 1.54919i
\(46\) 2.00000 + 3.46410i 0.294884 + 0.510754i
\(47\) −1.00000 + 1.73205i −0.145865 + 0.252646i −0.929695 0.368329i \(-0.879930\pi\)
0.783830 + 0.620975i \(0.213263\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −11.0000 −1.55563
\(51\) 0 0
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) −1.00000 + 1.73205i −0.131306 + 0.227429i
\(59\) 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 0 0
\(61\) 7.00000 12.1244i 0.896258 1.55236i 0.0640184 0.997949i \(-0.479608\pi\)
0.832240 0.554416i \(-0.187058\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 4.00000 6.92820i 0.496139 0.859338i
\(66\) 0 0
\(67\) 6.00000 + 10.3923i 0.733017 + 1.26962i 0.955588 + 0.294706i \(0.0952216\pi\)
−0.222571 + 0.974916i \(0.571445\pi\)
\(68\) 2.00000 3.46410i 0.242536 0.420084i
\(69\) 0 0
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) −1.50000 + 2.59808i −0.176777 + 0.306186i
\(73\) −2.00000 3.46410i −0.234082 0.405442i 0.724923 0.688830i \(-0.241875\pi\)
−0.959006 + 0.283387i \(0.908542\pi\)
\(74\) 5.00000 + 8.66025i 0.581238 + 1.00673i
\(75\) 0 0
\(76\) −6.00000 −0.688247
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(80\) 2.00000 + 3.46410i 0.223607 + 0.387298i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 2.00000 3.46410i 0.220863 0.382546i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 16.0000 1.73544
\(86\) −4.00000 + 6.92820i −0.431331 + 0.747087i
\(87\) 0 0
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) −12.0000 −1.26491
\(91\) 0 0
\(92\) 4.00000 0.417029
\(93\) 0 0
\(94\) 1.00000 + 1.73205i 0.103142 + 0.178647i
\(95\) −12.0000 20.7846i −1.23117 2.13246i
\(96\) 0 0
\(97\) −14.0000 −1.42148 −0.710742 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) 3.00000 0.301511
\(100\) −5.50000 + 9.52628i −0.550000 + 0.952628i
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 0 0
\(103\) −9.00000 + 15.5885i −0.886796 + 1.53598i −0.0431555 + 0.999068i \(0.513741\pi\)
−0.843641 + 0.536908i \(0.819592\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 8.00000 13.8564i 0.773389 1.33955i −0.162306 0.986740i \(-0.551893\pi\)
0.935695 0.352809i \(-0.114773\pi\)
\(108\) 0 0
\(109\) 7.00000 + 12.1244i 0.670478 + 1.16130i 0.977769 + 0.209687i \(0.0672444\pi\)
−0.307290 + 0.951616i \(0.599422\pi\)
\(110\) 2.00000 3.46410i 0.190693 0.330289i
\(111\) 0 0
\(112\) 0 0
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 0 0
\(115\) 8.00000 + 13.8564i 0.746004 + 1.29212i
\(116\) 1.00000 + 1.73205i 0.0928477 + 0.160817i
\(117\) 3.00000 5.19615i 0.277350 0.480384i
\(118\) 12.0000 1.10469
\(119\) 0 0
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −7.00000 12.1244i −0.633750 1.09769i
\(123\) 0 0
\(124\) 1.00000 1.73205i 0.0898027 0.155543i
\(125\) −24.0000 −2.14663
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −4.00000 6.92820i −0.350823 0.607644i
\(131\) −3.00000 + 5.19615i −0.262111 + 0.453990i −0.966803 0.255524i \(-0.917752\pi\)
0.704692 + 0.709514i \(0.251085\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) −2.00000 3.46410i −0.171499 0.297044i
\(137\) −3.00000 5.19615i −0.256307 0.443937i 0.708942 0.705266i \(-0.249173\pi\)
−0.965250 + 0.261329i \(0.915839\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.00000 + 6.92820i −0.335673 + 0.581402i
\(143\) 1.00000 + 1.73205i 0.0836242 + 0.144841i
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) −4.00000 + 6.92820i −0.332182 + 0.575356i
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) 10.0000 0.821995
\(149\) −1.00000 + 1.73205i −0.0819232 + 0.141895i −0.904076 0.427372i \(-0.859440\pi\)
0.822153 + 0.569267i \(0.192773\pi\)
\(150\) 0 0
\(151\) 12.0000 + 20.7846i 0.976546 + 1.69143i 0.674735 + 0.738060i \(0.264258\pi\)
0.301811 + 0.953368i \(0.402409\pi\)
\(152\) −3.00000 + 5.19615i −0.243332 + 0.421464i
\(153\) 12.0000 0.970143
\(154\) 0 0
\(155\) 8.00000 0.642575
\(156\) 0 0
\(157\) 4.00000 + 6.92820i 0.319235 + 0.552931i 0.980329 0.197372i \(-0.0632408\pi\)
−0.661094 + 0.750303i \(0.729907\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 4.00000 0.316228
\(161\) 0 0
\(162\) −9.00000 −0.707107
\(163\) −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) −2.00000 3.46410i −0.156174 0.270501i
\(165\) 0 0
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) 4.00000 0.309529 0.154765 0.987951i \(-0.450538\pi\)
0.154765 + 0.987951i \(0.450538\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 8.00000 13.8564i 0.613572 1.06274i
\(171\) −9.00000 15.5885i −0.688247 1.19208i
\(172\) 4.00000 + 6.92820i 0.304997 + 0.528271i
\(173\) 7.00000 12.1244i 0.532200 0.921798i −0.467093 0.884208i \(-0.654699\pi\)
0.999293 0.0375896i \(-0.0119679\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) −3.00000 5.19615i −0.224860 0.389468i
\(179\) −2.00000 3.46410i −0.149487 0.258919i 0.781551 0.623841i \(-0.214429\pi\)
−0.931038 + 0.364922i \(0.881096\pi\)
\(180\) −6.00000 + 10.3923i −0.447214 + 0.774597i
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 2.00000 3.46410i 0.147442 0.255377i
\(185\) 20.0000 + 34.6410i 1.47043 + 2.54686i
\(186\) 0 0
\(187\) −2.00000 + 3.46410i −0.146254 + 0.253320i
\(188\) 2.00000 0.145865
\(189\) 0 0
\(190\) −24.0000 −1.74114
\(191\) 2.00000 3.46410i 0.144715 0.250654i −0.784552 0.620063i \(-0.787107\pi\)
0.929267 + 0.369410i \(0.120440\pi\)
\(192\) 0 0
\(193\) −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i \(-0.189599\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) −7.00000 + 12.1244i −0.502571 + 0.870478i
\(195\) 0 0
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 1.50000 2.59808i 0.106600 0.184637i
\(199\) 7.00000 + 12.1244i 0.496217 + 0.859473i 0.999990 0.00436292i \(-0.00138876\pi\)
−0.503774 + 0.863836i \(0.668055\pi\)
\(200\) 5.50000 + 9.52628i 0.388909 + 0.673610i
\(201\) 0 0
\(202\) −6.00000 −0.422159
\(203\) 0 0
\(204\) 0 0
\(205\) 8.00000 13.8564i 0.558744 0.967773i
\(206\) 9.00000 + 15.5885i 0.627060 + 1.08610i
\(207\) 6.00000 + 10.3923i 0.417029 + 0.722315i
\(208\) −1.00000 + 1.73205i −0.0693375 + 0.120096i
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) 0 0
\(214\) −8.00000 13.8564i −0.546869 0.947204i
\(215\) −16.0000 + 27.7128i −1.09119 + 1.89000i
\(216\) 0 0
\(217\) 0 0
\(218\) 14.0000 0.948200
\(219\) 0 0
\(220\) −2.00000 3.46410i −0.134840 0.233550i
\(221\) 4.00000 + 6.92820i 0.269069 + 0.466041i
\(222\) 0 0
\(223\) −2.00000 −0.133930 −0.0669650 0.997755i \(-0.521332\pi\)
−0.0669650 + 0.997755i \(0.521332\pi\)
\(224\) 0 0
\(225\) −33.0000 −2.20000
\(226\) 7.00000 12.1244i 0.465633 0.806500i
\(227\) 1.00000 + 1.73205i 0.0663723 + 0.114960i 0.897302 0.441417i \(-0.145524\pi\)
−0.830930 + 0.556378i \(0.812191\pi\)
\(228\) 0 0
\(229\) −10.0000 + 17.3205i −0.660819 + 1.14457i 0.319582 + 0.947559i \(0.396457\pi\)
−0.980401 + 0.197013i \(0.936876\pi\)
\(230\) 16.0000 1.05501
\(231\) 0 0
\(232\) 2.00000 0.131306
\(233\) −15.0000 + 25.9808i −0.982683 + 1.70206i −0.330870 + 0.943676i \(0.607342\pi\)
−0.651813 + 0.758380i \(0.725991\pi\)
\(234\) −3.00000 5.19615i −0.196116 0.339683i
\(235\) 4.00000 + 6.92820i 0.260931 + 0.451946i
\(236\) 6.00000 10.3923i 0.390567 0.676481i
\(237\) 0 0
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) −6.00000 10.3923i −0.386494 0.669427i 0.605481 0.795860i \(-0.292981\pi\)
−0.991975 + 0.126432i \(0.959647\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) 0 0
\(244\) −14.0000 −0.896258
\(245\) 0 0
\(246\) 0 0
\(247\) 6.00000 10.3923i 0.381771 0.661247i
\(248\) −1.00000 1.73205i −0.0635001 0.109985i
\(249\) 0 0
\(250\) −12.0000 + 20.7846i −0.758947 + 1.31453i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) −4.00000 −0.251478
\(254\) 4.00000 6.92820i 0.250982 0.434714i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 3.00000 5.19615i 0.187135 0.324127i −0.757159 0.653231i \(-0.773413\pi\)
0.944294 + 0.329104i \(0.106747\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −8.00000 −0.496139
\(261\) −3.00000 + 5.19615i −0.185695 + 0.321634i
\(262\) 3.00000 + 5.19615i 0.185341 + 0.321019i
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 0 0
\(265\) −24.0000 −1.47431
\(266\) 0 0
\(267\) 0 0
\(268\) 6.00000 10.3923i 0.366508 0.634811i
\(269\) −6.00000 10.3923i −0.365826 0.633630i 0.623082 0.782157i \(-0.285880\pi\)
−0.988908 + 0.148527i \(0.952547\pi\)
\(270\) 0 0
\(271\) 10.0000 17.3205i 0.607457 1.05215i −0.384201 0.923249i \(-0.625523\pi\)
0.991658 0.128897i \(-0.0411435\pi\)
\(272\) −4.00000 −0.242536
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) 5.50000 9.52628i 0.331662 0.574456i
\(276\) 0 0
\(277\) 15.0000 + 25.9808i 0.901263 + 1.56103i 0.825857 + 0.563880i \(0.190692\pi\)
0.0754058 + 0.997153i \(0.475975\pi\)
\(278\) 7.00000 12.1244i 0.419832 0.727171i
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 0 0
\(283\) −3.00000 5.19615i −0.178331 0.308879i 0.762978 0.646425i \(-0.223737\pi\)
−0.941309 + 0.337546i \(0.890403\pi\)
\(284\) 4.00000 + 6.92820i 0.237356 + 0.411113i
\(285\) 0 0
\(286\) 2.00000 0.118262
\(287\) 0 0
\(288\) 3.00000 0.176777
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 4.00000 + 6.92820i 0.234888 + 0.406838i
\(291\) 0 0
\(292\) −2.00000 + 3.46410i −0.117041 + 0.202721i
\(293\) 18.0000 1.05157 0.525786 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) 0 0
\(295\) 48.0000 2.79467
\(296\) 5.00000 8.66025i 0.290619 0.503367i
\(297\) 0 0
\(298\) 1.00000 + 1.73205i 0.0579284 + 0.100335i
\(299\) −4.00000 + 6.92820i −0.231326 + 0.400668i
\(300\) 0 0
\(301\) 0 0
\(302\) 24.0000 1.38104
\(303\) 0 0
\(304\) 3.00000 + 5.19615i 0.172062 + 0.298020i
\(305\) −28.0000 48.4974i −1.60328 2.77695i
\(306\) 6.00000 10.3923i 0.342997 0.594089i
\(307\) −10.0000 −0.570730 −0.285365 0.958419i \(-0.592115\pi\)
−0.285365 + 0.958419i \(0.592115\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4.00000 6.92820i 0.227185 0.393496i
\(311\) −7.00000 12.1244i −0.396934 0.687509i 0.596412 0.802678i \(-0.296592\pi\)
−0.993346 + 0.115169i \(0.963259\pi\)
\(312\) 0 0
\(313\) 1.00000 1.73205i 0.0565233 0.0979013i −0.836379 0.548151i \(-0.815332\pi\)
0.892903 + 0.450250i \(0.148665\pi\)
\(314\) 8.00000 0.451466
\(315\) 0 0
\(316\) 0 0
\(317\) −3.00000 + 5.19615i −0.168497 + 0.291845i −0.937892 0.346929i \(-0.887225\pi\)
0.769395 + 0.638774i \(0.220558\pi\)
\(318\) 0 0
\(319\) −1.00000 1.73205i −0.0559893 0.0969762i
\(320\) 2.00000 3.46410i 0.111803 0.193649i
\(321\) 0 0
\(322\) 0 0
\(323\) 24.0000 1.33540
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) −11.0000 19.0526i −0.610170 1.05685i
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) 0 0
\(328\) −4.00000 −0.220863
\(329\) 0 0
\(330\) 0 0
\(331\) 10.0000 17.3205i 0.549650 0.952021i −0.448649 0.893708i \(-0.648095\pi\)
0.998298 0.0583130i \(-0.0185721\pi\)
\(332\) 3.00000 + 5.19615i 0.164646 + 0.285176i
\(333\) 15.0000 + 25.9808i 0.821995 + 1.42374i
\(334\) 2.00000 3.46410i 0.109435 0.189547i
\(335\) 48.0000 2.62252
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) −4.50000 + 7.79423i −0.244768 + 0.423950i
\(339\) 0 0
\(340\) −8.00000 13.8564i −0.433861 0.751469i
\(341\) −1.00000 + 1.73205i −0.0541530 + 0.0937958i
\(342\) −18.0000 −0.973329
\(343\) 0 0
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) −7.00000 12.1244i −0.376322 0.651809i
\(347\) −4.00000 6.92820i −0.214731 0.371925i 0.738458 0.674299i \(-0.235554\pi\)
−0.953189 + 0.302374i \(0.902221\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) 0 0
\(355\) −16.0000 + 27.7128i −0.849192 + 1.47084i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −4.00000 −0.211407
\(359\) 8.00000 13.8564i 0.422224 0.731313i −0.573933 0.818902i \(-0.694583\pi\)
0.996157 + 0.0875892i \(0.0279163\pi\)
\(360\) 6.00000 + 10.3923i 0.316228 + 0.547723i
\(361\) −8.50000 14.7224i −0.447368 0.774865i
\(362\) 10.0000 17.3205i 0.525588 0.910346i
\(363\) 0 0
\(364\) 0 0
\(365\) −16.0000 −0.837478
\(366\) 0 0
\(367\) −11.0000 19.0526i −0.574195 0.994535i −0.996129 0.0879086i \(-0.971982\pi\)
0.421933 0.906627i \(-0.361352\pi\)
\(368\) −2.00000 3.46410i −0.104257 0.180579i
\(369\) 6.00000 10.3923i 0.312348 0.541002i
\(370\) 40.0000 2.07950
\(371\) 0 0
\(372\) 0 0
\(373\) 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) 2.00000 + 3.46410i 0.103418 + 0.179124i
\(375\) 0 0
\(376\) 1.00000 1.73205i 0.0515711 0.0893237i
\(377\) −4.00000 −0.206010
\(378\) 0 0
\(379\) 4.00000 0.205466 0.102733 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) −12.0000 + 20.7846i −0.615587 + 1.06623i
\(381\) 0 0
\(382\) −2.00000 3.46410i −0.102329 0.177239i
\(383\) 5.00000 8.66025i 0.255488 0.442518i −0.709540 0.704665i \(-0.751097\pi\)
0.965028 + 0.262147i \(0.0844305\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −2.00000 −0.101797
\(387\) −12.0000 + 20.7846i −0.609994 + 1.05654i
\(388\) 7.00000 + 12.1244i 0.355371 + 0.615521i
\(389\) 15.0000 + 25.9808i 0.760530 + 1.31728i 0.942578 + 0.333987i \(0.108394\pi\)
−0.182047 + 0.983290i \(0.558272\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) 0 0
\(394\) 3.00000 5.19615i 0.151138 0.261778i
\(395\) 0 0
\(396\) −1.50000 2.59808i −0.0753778 0.130558i
\(397\) −12.0000 + 20.7846i −0.602263 + 1.04315i 0.390215 + 0.920724i \(0.372401\pi\)
−0.992478 + 0.122426i \(0.960933\pi\)
\(398\) 14.0000 0.701757
\(399\) 0 0
\(400\) 11.0000 0.550000
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 0 0
\(403\) 2.00000 + 3.46410i 0.0996271 + 0.172559i
\(404\) −3.00000 + 5.19615i −0.149256 + 0.258518i
\(405\) −36.0000 −1.78885
\(406\) 0 0
\(407\) −10.0000 −0.495682
\(408\) 0 0
\(409\) −8.00000 13.8564i −0.395575 0.685155i 0.597600 0.801795i \(-0.296121\pi\)
−0.993174 + 0.116639i \(0.962788\pi\)
\(410\) −8.00000 13.8564i −0.395092 0.684319i
\(411\) 0 0
\(412\) 18.0000 0.886796
\(413\) 0 0
\(414\) 12.0000 0.589768
\(415\) −12.0000 + 20.7846i −0.589057 + 1.02028i
\(416\) 1.00000 + 1.73205i 0.0490290 + 0.0849208i
\(417\) 0 0
\(418\) 3.00000 5.19615i 0.146735 0.254152i
\(419\) −32.0000 −1.56330 −0.781651 0.623716i \(-0.785622\pi\)
−0.781651 + 0.623716i \(0.785622\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) −4.00000 + 6.92820i −0.194717 + 0.337260i
\(423\) 3.00000 + 5.19615i 0.145865 + 0.252646i
\(424\) 3.00000 + 5.19615i 0.145693 + 0.252347i
\(425\) 22.0000 38.1051i 1.06716 1.84837i
\(426\) 0 0
\(427\) 0 0
\(428\) −16.0000 −0.773389
\(429\) 0 0
\(430\) 16.0000 + 27.7128i 0.771589 + 1.33643i
\(431\) −8.00000 13.8564i −0.385346 0.667440i 0.606471 0.795106i \(-0.292585\pi\)
−0.991817 + 0.127666i \(0.959251\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 7.00000 12.1244i 0.335239 0.580651i
\(437\) 12.0000 + 20.7846i 0.574038 + 0.994263i
\(438\) 0 0
\(439\) −14.0000 + 24.2487i −0.668184 + 1.15733i 0.310228 + 0.950662i \(0.399595\pi\)
−0.978412 + 0.206666i \(0.933739\pi\)
\(440\) −4.00000 −0.190693
\(441\) 0 0
\(442\) 8.00000 0.380521
\(443\) 18.0000 31.1769i 0.855206 1.48126i −0.0212481 0.999774i \(-0.506764\pi\)
0.876454 0.481486i \(-0.159903\pi\)
\(444\) 0 0
\(445\) −12.0000 20.7846i −0.568855 0.985285i
\(446\) −1.00000 + 1.73205i −0.0473514 + 0.0820150i
\(447\) 0 0
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) −16.5000 + 28.5788i −0.777817 + 1.34722i
\(451\) 2.00000 + 3.46410i 0.0941763 + 0.163118i
\(452\) −7.00000 12.1244i −0.329252 0.570282i
\(453\) 0 0
\(454\) 2.00000 0.0938647
\(455\) 0 0
\(456\) 0 0
\(457\) −1.00000 + 1.73205i −0.0467780 + 0.0810219i −0.888466 0.458942i \(-0.848229\pi\)
0.841688 + 0.539964i \(0.181562\pi\)
\(458\) 10.0000 + 17.3205i 0.467269 + 0.809334i
\(459\) 0 0
\(460\) 8.00000 13.8564i 0.373002 0.646058i
\(461\) 30.0000 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) 0 0
\(463\) −32.0000 −1.48717 −0.743583 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(464\) 1.00000 1.73205i 0.0464238 0.0804084i
\(465\) 0 0
\(466\) 15.0000 + 25.9808i 0.694862 + 1.20354i
\(467\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(468\) −6.00000 −0.277350
\(469\) 0 0
\(470\) 8.00000 0.369012
\(471\) 0 0
\(472\) −6.00000 10.3923i −0.276172 0.478345i
\(473\) −4.00000 6.92820i −0.183920 0.318559i
\(474\) 0 0
\(475\) −66.0000 −3.02829
\(476\) 0 0
\(477\) −18.0000 −0.824163
\(478\) 8.00000 13.8564i 0.365911 0.633777i
\(479\) 8.00000 + 13.8564i 0.365529 + 0.633115i 0.988861 0.148842i \(-0.0475547\pi\)
−0.623332 + 0.781958i \(0.714221\pi\)
\(480\) 0 0
\(481\) −10.0000 + 17.3205i −0.455961 + 0.789747i
\(482\) −12.0000 −0.546585
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −28.0000 + 48.4974i −1.27141 + 2.20215i
\(486\) 0 0
\(487\) 14.0000 + 24.2487i 0.634401 + 1.09881i 0.986642 + 0.162905i \(0.0520863\pi\)
−0.352241 + 0.935909i \(0.614580\pi\)
\(488\) −7.00000 + 12.1244i −0.316875 + 0.548844i
\(489\) 0 0
\(490\) 0 0
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 0 0
\(493\) −4.00000 6.92820i −0.180151 0.312031i
\(494\) −6.00000 10.3923i −0.269953 0.467572i
\(495\) 6.00000 10.3923i 0.269680 0.467099i
\(496\) −2.00000 −0.0898027
\(497\) 0 0
\(498\) 0 0
\(499\) −22.0000 + 38.1051i −0.984855 + 1.70582i −0.342277 + 0.939599i \(0.611198\pi\)
−0.642578 + 0.766220i \(0.722135\pi\)
\(500\) 12.0000 + 20.7846i 0.536656 + 0.929516i
\(501\) 0 0
\(502\) 6.00000 10.3923i 0.267793 0.463831i
\(503\) −36.0000 −1.60516 −0.802580 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 0 0
\(505\) −24.0000 −1.06799
\(506\) −2.00000 + 3.46410i −0.0889108 + 0.153998i
\(507\) 0 0
\(508\) −4.00000 6.92820i −0.177471 0.307389i
\(509\) 14.0000 24.2487i 0.620539 1.07481i −0.368846 0.929490i \(-0.620247\pi\)
0.989385 0.145315i \(-0.0464195\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −3.00000 5.19615i −0.132324 0.229192i
\(515\) 36.0000 + 62.3538i 1.58635 + 2.74764i
\(516\) 0 0
\(517\) −2.00000 −0.0879599
\(518\) 0 0
\(519\) 0 0
\(520\) −4.00000 + 6.92820i −0.175412 + 0.303822i
\(521\) −5.00000 8.66025i −0.219054 0.379413i 0.735465 0.677563i \(-0.236964\pi\)
−0.954519 + 0.298150i \(0.903630\pi\)
\(522\) 3.00000 + 5.19615i 0.131306 + 0.227429i
\(523\) 17.0000 29.4449i 0.743358 1.28753i −0.207600 0.978214i \(-0.566565\pi\)
0.950958 0.309320i \(-0.100101\pi\)
\(524\) 6.00000 0.262111
\(525\) 0 0
\(526\) 0 0
\(527\) −4.00000 + 6.92820i −0.174243 + 0.301797i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) −12.0000 + 20.7846i −0.521247 + 0.902826i
\(531\) 36.0000 1.56227
\(532\) 0 0
\(533\) 8.00000 0.346518
\(534\) 0 0
\(535\) −32.0000 55.4256i −1.38348 2.39626i
\(536\) −6.00000 10.3923i −0.259161 0.448879i
\(537\) 0 0
\(538\) −12.0000 −0.517357
\(539\) 0 0
\(540\) 0 0
\(541\) −7.00000 + 12.1244i −0.300954 + 0.521267i −0.976352 0.216186i \(-0.930638\pi\)
0.675399 + 0.737453i \(0.263972\pi\)
\(542\) −10.0000 17.3205i −0.429537 0.743980i
\(543\) 0 0
\(544\) −2.00000 + 3.46410i −0.0857493 + 0.148522i
\(545\) 56.0000 2.39878
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) −3.00000 + 5.19615i −0.128154 + 0.221969i
\(549\) −21.0000 36.3731i −0.896258 1.55236i
\(550\) −5.50000 9.52628i −0.234521 0.406202i
\(551\) −6.00000 + 10.3923i −0.255609 + 0.442727i
\(552\) 0 0
\(553\) 0 0
\(554\) 30.0000 1.27458
\(555\) 0 0
\(556\) −7.00000 12.1244i −0.296866 0.514187i
\(557\) −7.00000 12.1244i −0.296600 0.513725i 0.678756 0.734364i \(-0.262519\pi\)
−0.975356 + 0.220638i \(0.929186\pi\)
\(558\) 3.00000 5.19615i 0.127000 0.219971i
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) −5.00000 + 8.66025i −0.210912 + 0.365311i
\(563\) 17.0000 + 29.4449i 0.716465 + 1.24095i 0.962392 + 0.271665i \(0.0875742\pi\)
−0.245927 + 0.969288i \(0.579092\pi\)
\(564\) 0 0
\(565\) 28.0000 48.4974i 1.17797 2.04030i
\(566\) −6.00000 −0.252199
\(567\) 0 0
\(568\) 8.00000 0.335673
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) 0 0
\(571\) −14.0000 24.2487i −0.585882 1.01478i −0.994765 0.102190i \(-0.967415\pi\)
0.408883 0.912587i \(-0.365918\pi\)
\(572\) 1.00000 1.73205i 0.0418121 0.0724207i
\(573\) 0 0
\(574\) 0 0
\(575\) 44.0000 1.83493
\(576\) 1.50000 2.59808i 0.0625000 0.108253i
\(577\) −7.00000 12.1244i −0.291414 0.504744i 0.682730 0.730670i \(-0.260792\pi\)
−0.974144 + 0.225927i \(0.927459\pi\)
\(578\) −0.500000 0.866025i −0.0207973 0.0360219i
\(579\) 0 0
\(580\) 8.00000 0.332182
\(581\) 0 0
\(582\) 0 0
\(583\) 3.00000 5.19615i 0.124247 0.215203i
\(584\) 2.00000 + 3.46410i 0.0827606 + 0.143346i
\(585\) −12.0000 20.7846i −0.496139 0.859338i
\(586\) 9.00000 15.5885i 0.371787 0.643953i
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) 12.0000 0.494451
\(590\) 24.0000 41.5692i 0.988064 1.71138i
\(591\) 0 0
\(592\) −5.00000 8.66025i −0.205499 0.355934i
\(593\) 6.00000 10.3923i 0.246390 0.426761i −0.716131 0.697966i \(-0.754089\pi\)
0.962522 + 0.271205i \(0.0874221\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 2.00000 0.0819232
\(597\) 0 0
\(598\) 4.00000 + 6.92820i 0.163572 + 0.283315i
\(599\) −12.0000 20.7846i −0.490307 0.849236i 0.509631 0.860393i \(-0.329782\pi\)
−0.999938 + 0.0111569i \(0.996449\pi\)
\(600\) 0 0
\(601\) 8.00000 0.326327 0.163163 0.986599i \(-0.447830\pi\)
0.163163 + 0.986599i \(0.447830\pi\)
\(602\) 0 0
\(603\) 36.0000 1.46603
\(604\) 12.0000 20.7846i 0.488273 0.845714i
\(605\) 2.00000 + 3.46410i 0.0813116 + 0.140836i
\(606\) 0 0
\(607\) −4.00000 + 6.92820i −0.162355 + 0.281207i −0.935713 0.352763i \(-0.885242\pi\)
0.773358 + 0.633970i \(0.218576\pi\)
\(608\) 6.00000 0.243332
\(609\) 0 0
\(610\) −56.0000 −2.26737
\(611\) −2.00000 + 3.46410i −0.0809113 + 0.140143i
\(612\) −6.00000 10.3923i −0.242536 0.420084i
\(613\) −23.0000 39.8372i −0.928961 1.60901i −0.785063 0.619416i \(-0.787370\pi\)
−0.143898 0.989593i \(-0.545964\pi\)
\(614\) −5.00000 + 8.66025i −0.201784 + 0.349499i
\(615\) 0 0
\(616\) 0 0
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) 0 0
\(619\) −4.00000 6.92820i −0.160774 0.278468i 0.774373 0.632730i \(-0.218066\pi\)
−0.935146 + 0.354262i \(0.884732\pi\)
\(620\) −4.00000 6.92820i −0.160644 0.278243i
\(621\) 0 0
\(622\) −14.0000 −0.561349
\(623\) 0 0
\(624\) 0 0
\(625\) −20.5000 + 35.5070i −0.820000 + 1.42028i
\(626\) −1.00000 1.73205i −0.0399680 0.0692267i
\(627\) 0 0
\(628\) 4.00000 6.92820i 0.159617 0.276465i
\(629\) −40.0000 −1.59490
\(630\) 0 0
\(631\) −12.0000 −0.477712 −0.238856 0.971055i \(-0.576772\pi\)
−0.238856 + 0.971055i \(0.576772\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 3.00000 + 5.19615i 0.119145 + 0.206366i
\(635\) 16.0000 27.7128i 0.634941 1.09975i
\(636\) 0 0
\(637\) 0 0
\(638\) −2.00000 −0.0791808
\(639\) −12.0000 + 20.7846i −0.474713 + 0.822226i
\(640\) −2.00000 3.46410i −0.0790569 0.136931i
\(641\) 3.00000 + 5.19615i 0.118493 + 0.205236i 0.919171 0.393860i \(-0.128860\pi\)
−0.800678 + 0.599095i \(0.795527\pi\)
\(642\) 0 0
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 12.0000 20.7846i 0.472134 0.817760i
\(647\) −3.00000 5.19615i −0.117942 0.204282i 0.801010 0.598651i \(-0.204296\pi\)
−0.918952 + 0.394369i \(0.870963\pi\)
\(648\) 4.50000 + 7.79423i 0.176777 + 0.306186i
\(649\) −6.00000 + 10.3923i −0.235521 + 0.407934i
\(650\) −22.0000 −0.862911
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) −5.00000 + 8.66025i −0.195665 + 0.338902i −0.947118 0.320884i \(-0.896020\pi\)
0.751453 + 0.659786i \(0.229353\pi\)
\(654\) 0 0
\(655\) 12.0000 + 20.7846i 0.468879 + 0.812122i
\(656\) −2.00000 + 3.46410i −0.0780869 + 0.135250i
\(657\) −12.0000 −0.468165
\(658\) 0 0
\(659\) −8.00000 −0.311636 −0.155818 0.987786i \(-0.549801\pi\)
−0.155818 + 0.987786i \(0.549801\pi\)
\(660\) 0 0
\(661\) −10.0000 17.3205i −0.388955 0.673690i 0.603354 0.797473i \(-0.293830\pi\)
−0.992309 + 0.123784i \(0.960497\pi\)
\(662\) −10.0000 17.3205i −0.388661 0.673181i
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 30.0000 1.16248
\(667\) 4.00000 6.92820i 0.154881 0.268261i
\(668\) −2.00000 3.46410i −0.0773823 0.134030i
\(669\) 0 0
\(670\) 24.0000 41.5692i 0.927201 1.60596i
\(671\) 14.0000 0.540464
\(672\) 0 0
\(673\) 22.0000 0.848038 0.424019 0.905653i \(-0.360619\pi\)
0.424019 + 0.905653i \(0.360619\pi\)
\(674\) −9.00000 + 15.5885i −0.346667 + 0.600445i
\(675\) 0 0
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) −13.0000 + 22.5167i −0.499631 + 0.865386i −1.00000 0.000426509i \(-0.999864\pi\)
0.500369 + 0.865812i \(0.333198\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −16.0000 −0.613572
\(681\) 0 0
\(682\) 1.00000 + 1.73205i 0.0382920 + 0.0663237i
\(683\) −18.0000 31.1769i −0.688751 1.19295i −0.972242 0.233977i \(-0.924826\pi\)
0.283491 0.958975i \(-0.408507\pi\)
\(684\) −9.00000 + 15.5885i −0.344124 + 0.596040i
\(685\) −24.0000 −0.916993
\(686\) 0 0
\(687\) 0 0
\(688\) 4.00000 6.92820i 0.152499 0.264135i
\(689\) −6.00000 10.3923i −0.228582 0.395915i
\(690\) 0 0
\(691\) −18.0000 + 31.1769i −0.684752 + 1.18603i 0.288762 + 0.957401i \(0.406756\pi\)
−0.973515 + 0.228625i \(0.926577\pi\)
\(692\) −14.0000 −0.532200
\(693\) 0 0
\(694\) −8.00000 −0.303676
\(695\) 28.0000 48.4974i 1.06210 1.83961i
\(696\) 0 0
\(697\) 8.00000 + 13.8564i 0.303022 + 0.524849i
\(698\) −5.00000 + 8.66025i −0.189253 + 0.327795i
\(699\) 0 0
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) 30.0000 + 51.9615i 1.13147 + 1.95977i
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) 0 0
\(708\) 0 0
\(709\) −9.00000 + 15.5885i −0.338002 + 0.585437i −0.984057 0.177854i \(-0.943084\pi\)
0.646055 + 0.763291i \(0.276418\pi\)
\(710\) 16.0000 + 27.7128i 0.600469 + 1.04004i
\(711\) 0 0
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) −8.00000 −0.299602
\(714\) 0 0
\(715\) 8.00000 0.299183
\(716\) −2.00000 + 3.46410i −0.0747435 + 0.129460i
\(717\) 0 0
\(718\) −8.00000 13.8564i −0.298557 0.517116i
\(719\) 13.0000 22.5167i 0.484818 0.839730i −0.515030 0.857172i \(-0.672219\pi\)
0.999848 + 0.0174426i \(0.00555244\pi\)
\(720\) 12.0000 0.447214
\(721\) 0 0
\(722\) −17.0000 −0.632674
\(723\) 0 0
\(724\) −10.0000 17.3205i −0.371647 0.643712i
\(725\) 11.0000 + 19.0526i 0.408530 + 0.707594i
\(726\) 0 0
\(727\) −10.0000 −0.370879 −0.185440 0.982656i \(-0.559371\pi\)
−0.185440 + 0.982656i \(0.559371\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) −8.00000 + 13.8564i −0.296093 + 0.512849i
\(731\) −16.0000 27.7128i −0.591781 1.02500i
\(732\) 0 0
\(733\) 11.0000 19.0526i 0.406294 0.703722i −0.588177 0.808732i \(-0.700154\pi\)
0.994471 + 0.105010i \(0.0334875\pi\)
\(734\) −22.0000 −0.812035
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) −6.00000 + 10.3923i −0.221013 + 0.382805i
\(738\) −6.00000 10.3923i −0.220863 0.382546i
\(739\) 6.00000 + 10.3923i 0.220714 + 0.382287i 0.955025 0.296526i \(-0.0958281\pi\)
−0.734311 + 0.678813i \(0.762495\pi\)
\(740\) 20.0000 34.6410i 0.735215 1.27343i
\(741\) 0 0
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 0 0
\(745\) 4.00000 + 6.92820i 0.146549 + 0.253830i
\(746\) −5.00000 8.66025i −0.183063 0.317074i
\(747\) −9.00000 + 15.5885i −0.329293 + 0.570352i
\(748\) 4.00000 0.146254
\(749\) 0 0
\(750\) 0 0
\(751\) −14.0000 + 24.2487i −0.510867 + 0.884848i 0.489053 + 0.872254i \(0.337342\pi\)
−0.999921 + 0.0125942i \(0.995991\pi\)
\(752\) −1.00000 1.73205i −0.0364662 0.0631614i
\(753\) 0 0
\(754\) −2.00000 + 3.46410i −0.0728357 + 0.126155i
\(755\) 96.0000 3.49380
\(756\) 0 0
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 2.00000 3.46410i 0.0726433 0.125822i
\(759\) 0 0
\(760\) 12.0000 + 20.7846i 0.435286 + 0.753937i
\(761\) 24.0000 41.5692i 0.869999 1.50688i 0.00800331 0.999968i \(-0.497452\pi\)
0.861996 0.506915i \(-0.169214\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −4.00000 −0.144715
\(765\) 24.0000 41.5692i 0.867722 1.50294i
\(766\) −5.00000 8.66025i −0.180657 0.312908i
\(767\) 12.0000 + 20.7846i 0.433295 + 0.750489i
\(768\) 0 0
\(769\) 16.0000 0.576975 0.288487 0.957484i \(-0.406848\pi\)
0.288487 + 0.957484i \(0.406848\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.00000 + 1.73205i −0.0359908 + 0.0623379i
\(773\) 24.0000 + 41.5692i 0.863220 + 1.49514i 0.868804 + 0.495156i \(0.164889\pi\)
−0.00558380 + 0.999984i \(0.501777\pi\)
\(774\) 12.0000 + 20.7846i 0.431331 + 0.747087i
\(775\) 11.0000 19.0526i 0.395132 0.684388i
\(776\) 14.0000 0.502571
\(777\) 0 0
\(778\) 30.0000 1.07555
\(779\) 12.0000 20.7846i 0.429945 0.744686i
\(780\) 0 0
\(781\) −4.00000 6.92820i −0.143131 0.247911i
\(782\) −8.00000 + 13.8564i −0.286079 + 0.495504i
\(783\) 0 0
\(784\) 0 0
\(785\) 32.0000 1.14213
\(786\) 0 0
\(787\) 11.0000 + 19.0526i 0.392108 + 0.679150i 0.992727 0.120384i \(-0.0384127\pi\)
−0.600620 + 0.799535i \(0.705079\pi\)
\(788\) −3.00000 5.19615i −0.106871 0.185105i
\(789\) 0 0