Properties

Label 476.2.i.a.137.1
Level $476$
Weight $2$
Character 476.137
Analytic conductor $3.801$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 476.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.80087913621\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 137.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 476.137
Dual form 476.2.i.a.205.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +(2.00000 + 3.46410i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +(2.00000 + 3.46410i) q^{5} +(-2.00000 + 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{11} -5.00000 q^{13} -4.00000 q^{15} +(0.500000 - 0.866025i) q^{17} +(-3.00000 - 5.19615i) q^{19} +(-0.500000 - 2.59808i) q^{21} +(2.00000 + 3.46410i) q^{23} +(-5.50000 + 9.52628i) q^{25} -5.00000 q^{27} +8.00000 q^{29} +(1.50000 + 2.59808i) q^{33} +(-10.0000 - 3.46410i) q^{35} +(4.00000 + 6.92820i) q^{37} +(2.50000 - 4.33013i) q^{39} -8.00000 q^{41} +10.0000 q^{43} +(-4.00000 + 6.92820i) q^{45} +(1.00000 + 1.73205i) q^{47} +(1.00000 - 6.92820i) q^{49} +(0.500000 + 0.866025i) q^{51} +(-1.50000 + 2.59808i) q^{53} +12.0000 q^{55} +6.00000 q^{57} +(-1.00000 + 1.73205i) q^{59} +(4.00000 + 6.92820i) q^{61} +(-5.00000 - 1.73205i) q^{63} +(-10.0000 - 17.3205i) q^{65} +(-7.00000 + 12.1244i) q^{67} -4.00000 q^{69} +7.00000 q^{71} +(4.00000 - 6.92820i) q^{73} +(-5.50000 - 9.52628i) q^{75} +(1.50000 + 7.79423i) q^{77} +(-7.50000 - 12.9904i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} +4.00000 q^{85} +(-4.00000 + 6.92820i) q^{87} +(-0.500000 - 0.866025i) q^{89} +(10.0000 - 8.66025i) q^{91} +(12.0000 - 20.7846i) q^{95} +18.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{3} + 4 q^{5} - 4 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{3} + 4 q^{5} - 4 q^{7} + 2 q^{9} + 3 q^{11} - 10 q^{13} - 8 q^{15} + q^{17} - 6 q^{19} - q^{21} + 4 q^{23} - 11 q^{25} - 10 q^{27} + 16 q^{29} + 3 q^{33} - 20 q^{35} + 8 q^{37} + 5 q^{39} - 16 q^{41} + 20 q^{43} - 8 q^{45} + 2 q^{47} + 2 q^{49} + q^{51} - 3 q^{53} + 24 q^{55} + 12 q^{57} - 2 q^{59} + 8 q^{61} - 10 q^{63} - 20 q^{65} - 14 q^{67} - 8 q^{69} + 14 q^{71} + 8 q^{73} - 11 q^{75} + 3 q^{77} - 15 q^{79} - q^{81} + 24 q^{83} + 8 q^{85} - 8 q^{87} - q^{89} + 20 q^{91} + 24 q^{95} + 36 q^{97} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/476\mathbb{Z}\right)^\times\).

\(n\) \(239\) \(309\) \(409\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) 0 0
\(5\) 2.00000 + 3.46410i 0.894427 + 1.54919i 0.834512 + 0.550990i \(0.185750\pi\)
0.0599153 + 0.998203i \(0.480917\pi\)
\(6\) 0 0
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) 0 0
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0 0
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) −4.00000 −1.03280
\(16\) 0 0
\(17\) 0.500000 0.866025i 0.121268 0.210042i
\(18\) 0 0
\(19\) −3.00000 5.19615i −0.688247 1.19208i −0.972404 0.233301i \(-0.925047\pi\)
0.284157 0.958778i \(-0.408286\pi\)
\(20\) 0 0
\(21\) −0.500000 2.59808i −0.109109 0.566947i
\(22\) 0 0
\(23\) 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) 0 0
\(25\) −5.50000 + 9.52628i −1.10000 + 1.90526i
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 0 0
\(33\) 1.50000 + 2.59808i 0.261116 + 0.452267i
\(34\) 0 0
\(35\) −10.0000 3.46410i −1.69031 0.585540i
\(36\) 0 0
\(37\) 4.00000 + 6.92820i 0.657596 + 1.13899i 0.981236 + 0.192809i \(0.0617599\pi\)
−0.323640 + 0.946180i \(0.604907\pi\)
\(38\) 0 0
\(39\) 2.50000 4.33013i 0.400320 0.693375i
\(40\) 0 0
\(41\) −8.00000 −1.24939 −0.624695 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) 10.0000 1.52499 0.762493 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) 0 0
\(45\) −4.00000 + 6.92820i −0.596285 + 1.03280i
\(46\) 0 0
\(47\) 1.00000 + 1.73205i 0.145865 + 0.252646i 0.929695 0.368329i \(-0.120070\pi\)
−0.783830 + 0.620975i \(0.786737\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) 0.500000 + 0.866025i 0.0700140 + 0.121268i
\(52\) 0 0
\(53\) −1.50000 + 2.59808i −0.206041 + 0.356873i −0.950464 0.310835i \(-0.899391\pi\)
0.744423 + 0.667708i \(0.232725\pi\)
\(54\) 0 0
\(55\) 12.0000 1.61808
\(56\) 0 0
\(57\) 6.00000 0.794719
\(58\) 0 0
\(59\) −1.00000 + 1.73205i −0.130189 + 0.225494i −0.923749 0.382998i \(-0.874892\pi\)
0.793560 + 0.608492i \(0.208225\pi\)
\(60\) 0 0
\(61\) 4.00000 + 6.92820i 0.512148 + 0.887066i 0.999901 + 0.0140840i \(0.00448323\pi\)
−0.487753 + 0.872982i \(0.662183\pi\)
\(62\) 0 0
\(63\) −5.00000 1.73205i −0.629941 0.218218i
\(64\) 0 0
\(65\) −10.0000 17.3205i −1.24035 2.14834i
\(66\) 0 0
\(67\) −7.00000 + 12.1244i −0.855186 + 1.48123i 0.0212861 + 0.999773i \(0.493224\pi\)
−0.876472 + 0.481452i \(0.840109\pi\)
\(68\) 0 0
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) 7.00000 0.830747 0.415374 0.909651i \(-0.363651\pi\)
0.415374 + 0.909651i \(0.363651\pi\)
\(72\) 0 0
\(73\) 4.00000 6.92820i 0.468165 0.810885i −0.531174 0.847263i \(-0.678249\pi\)
0.999338 + 0.0363782i \(0.0115821\pi\)
\(74\) 0 0
\(75\) −5.50000 9.52628i −0.635085 1.10000i
\(76\) 0 0
\(77\) 1.50000 + 7.79423i 0.170941 + 0.888235i
\(78\) 0 0
\(79\) −7.50000 12.9904i −0.843816 1.46153i −0.886646 0.462450i \(-0.846971\pi\)
0.0428296 0.999082i \(-0.486363\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) 4.00000 0.433861
\(86\) 0 0
\(87\) −4.00000 + 6.92820i −0.428845 + 0.742781i
\(88\) 0 0
\(89\) −0.500000 0.866025i −0.0529999 0.0917985i 0.838308 0.545197i \(-0.183545\pi\)
−0.891308 + 0.453398i \(0.850212\pi\)
\(90\) 0 0
\(91\) 10.0000 8.66025i 1.04828 0.907841i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 12.0000 20.7846i 1.23117 2.13246i
\(96\) 0 0
\(97\) 18.0000 1.82762 0.913812 0.406138i \(-0.133125\pi\)
0.913812 + 0.406138i \(0.133125\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) 0 0
\(103\) −2.00000 3.46410i −0.197066 0.341328i 0.750510 0.660859i \(-0.229808\pi\)
−0.947576 + 0.319531i \(0.896475\pi\)
\(104\) 0 0
\(105\) 8.00000 6.92820i 0.780720 0.676123i
\(106\) 0 0
\(107\) −0.500000 0.866025i −0.0483368 0.0837218i 0.840845 0.541276i \(-0.182059\pi\)
−0.889182 + 0.457555i \(0.848725\pi\)
\(108\) 0 0
\(109\) 4.00000 6.92820i 0.383131 0.663602i −0.608377 0.793648i \(-0.708179\pi\)
0.991508 + 0.130046i \(0.0415126\pi\)
\(110\) 0 0
\(111\) −8.00000 −0.759326
\(112\) 0 0
\(113\) −8.00000 −0.752577 −0.376288 0.926503i \(-0.622800\pi\)
−0.376288 + 0.926503i \(0.622800\pi\)
\(114\) 0 0
\(115\) −8.00000 + 13.8564i −0.746004 + 1.29212i
\(116\) 0 0
\(117\) −5.00000 8.66025i −0.462250 0.800641i
\(118\) 0 0
\(119\) 0.500000 + 2.59808i 0.0458349 + 0.238165i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 4.00000 6.92820i 0.360668 0.624695i
\(124\) 0 0
\(125\) −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 0
\(129\) −5.00000 + 8.66025i −0.440225 + 0.762493i
\(130\) 0 0
\(131\) 2.00000 + 3.46410i 0.174741 + 0.302660i 0.940072 0.340977i \(-0.110758\pi\)
−0.765331 + 0.643637i \(0.777425\pi\)
\(132\) 0 0
\(133\) 15.0000 + 5.19615i 1.30066 + 0.450564i
\(134\) 0 0
\(135\) −10.0000 17.3205i −0.860663 1.49071i
\(136\) 0 0
\(137\) 3.50000 6.06218i 0.299025 0.517927i −0.676888 0.736086i \(-0.736672\pi\)
0.975913 + 0.218159i \(0.0700052\pi\)
\(138\) 0 0
\(139\) −1.00000 −0.0848189 −0.0424094 0.999100i \(-0.513503\pi\)
−0.0424094 + 0.999100i \(0.513503\pi\)
\(140\) 0 0
\(141\) −2.00000 −0.168430
\(142\) 0 0
\(143\) −7.50000 + 12.9904i −0.627182 + 1.08631i
\(144\) 0 0
\(145\) 16.0000 + 27.7128i 1.32873 + 2.30142i
\(146\) 0 0
\(147\) 5.50000 + 4.33013i 0.453632 + 0.357143i
\(148\) 0 0
\(149\) 5.50000 + 9.52628i 0.450578 + 0.780423i 0.998422 0.0561570i \(-0.0178847\pi\)
−0.547844 + 0.836580i \(0.684551\pi\)
\(150\) 0 0
\(151\) −5.00000 + 8.66025i −0.406894 + 0.704761i −0.994540 0.104357i \(-0.966722\pi\)
0.587646 + 0.809118i \(0.300055\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.500000 + 0.866025i −0.0399043 + 0.0691164i −0.885288 0.465044i \(-0.846039\pi\)
0.845383 + 0.534160i \(0.179372\pi\)
\(158\) 0 0
\(159\) −1.50000 2.59808i −0.118958 0.206041i
\(160\) 0 0
\(161\) −10.0000 3.46410i −0.788110 0.273009i
\(162\) 0 0
\(163\) −2.00000 3.46410i −0.156652 0.271329i 0.777007 0.629492i \(-0.216737\pi\)
−0.933659 + 0.358162i \(0.883403\pi\)
\(164\) 0 0
\(165\) −6.00000 + 10.3923i −0.467099 + 0.809040i
\(166\) 0 0
\(167\) −19.0000 −1.47026 −0.735132 0.677924i \(-0.762880\pi\)
−0.735132 + 0.677924i \(0.762880\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 6.00000 10.3923i 0.458831 0.794719i
\(172\) 0 0
\(173\) 1.00000 + 1.73205i 0.0760286 + 0.131685i 0.901533 0.432710i \(-0.142443\pi\)
−0.825505 + 0.564396i \(0.809109\pi\)
\(174\) 0 0
\(175\) −5.50000 28.5788i −0.415761 2.16036i
\(176\) 0 0
\(177\) −1.00000 1.73205i −0.0751646 0.130189i
\(178\) 0 0
\(179\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(180\) 0 0
\(181\) 18.0000 1.33793 0.668965 0.743294i \(-0.266738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) 0 0
\(183\) −8.00000 −0.591377
\(184\) 0 0
\(185\) −16.0000 + 27.7128i −1.17634 + 2.03749i
\(186\) 0 0
\(187\) −1.50000 2.59808i −0.109691 0.189990i
\(188\) 0 0
\(189\) 10.0000 8.66025i 0.727393 0.629941i
\(190\) 0 0
\(191\) −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i \(-0.309616\pi\)
−0.997225 + 0.0744412i \(0.976283\pi\)
\(192\) 0 0
\(193\) 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i \(-0.716141\pi\)
0.987945 + 0.154805i \(0.0494748\pi\)
\(194\) 0 0
\(195\) 20.0000 1.43223
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 3.50000 6.06218i 0.248108 0.429736i −0.714893 0.699234i \(-0.753524\pi\)
0.963001 + 0.269498i \(0.0868577\pi\)
\(200\) 0 0
\(201\) −7.00000 12.1244i −0.493742 0.855186i
\(202\) 0 0
\(203\) −16.0000 + 13.8564i −1.12298 + 0.972529i
\(204\) 0 0
\(205\) −16.0000 27.7128i −1.11749 1.93555i
\(206\) 0 0
\(207\) −4.00000 + 6.92820i −0.278019 + 0.481543i
\(208\) 0 0
\(209\) −18.0000 −1.24509
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) −3.50000 + 6.06218i −0.239816 + 0.415374i
\(214\) 0 0
\(215\) 20.0000 + 34.6410i 1.36399 + 2.36250i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 4.00000 + 6.92820i 0.270295 + 0.468165i
\(220\) 0 0
\(221\) −2.50000 + 4.33013i −0.168168 + 0.291276i
\(222\) 0 0
\(223\) −6.00000 −0.401790 −0.200895 0.979613i \(-0.564385\pi\)
−0.200895 + 0.979613i \(0.564385\pi\)
\(224\) 0 0
\(225\) −22.0000 −1.46667
\(226\) 0 0
\(227\) −12.5000 + 21.6506i −0.829654 + 1.43700i 0.0686556 + 0.997640i \(0.478129\pi\)
−0.898310 + 0.439363i \(0.855204\pi\)
\(228\) 0 0
\(229\) 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i \(-0.0594799\pi\)
−0.652183 + 0.758062i \(0.726147\pi\)
\(230\) 0 0
\(231\) −7.50000 2.59808i −0.493464 0.170941i
\(232\) 0 0
\(233\) −14.0000 24.2487i −0.917170 1.58859i −0.803692 0.595045i \(-0.797134\pi\)
−0.113478 0.993540i \(-0.536199\pi\)
\(234\) 0 0
\(235\) −4.00000 + 6.92820i −0.260931 + 0.451946i
\(236\) 0 0
\(237\) 15.0000 0.974355
\(238\) 0 0
\(239\) 2.00000 0.129369 0.0646846 0.997906i \(-0.479396\pi\)
0.0646846 + 0.997906i \(0.479396\pi\)
\(240\) 0 0
\(241\) 4.00000 6.92820i 0.257663 0.446285i −0.707953 0.706260i \(-0.750381\pi\)
0.965615 + 0.259975i \(0.0837143\pi\)
\(242\) 0 0
\(243\) −8.00000 13.8564i −0.513200 0.888889i
\(244\) 0 0
\(245\) 26.0000 10.3923i 1.66108 0.663940i
\(246\) 0 0
\(247\) 15.0000 + 25.9808i 0.954427 + 1.65312i
\(248\) 0 0
\(249\) −6.00000 + 10.3923i −0.380235 + 0.658586i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 12.0000 0.754434
\(254\) 0 0
\(255\) −2.00000 + 3.46410i −0.125245 + 0.216930i
\(256\) 0 0
\(257\) −1.50000 2.59808i −0.0935674 0.162064i 0.815442 0.578838i \(-0.196494\pi\)
−0.909010 + 0.416775i \(0.863160\pi\)
\(258\) 0 0
\(259\) −20.0000 6.92820i −1.24274 0.430498i
\(260\) 0 0
\(261\) 8.00000 + 13.8564i 0.495188 + 0.857690i
\(262\) 0 0
\(263\) −2.00000 + 3.46410i −0.123325 + 0.213606i −0.921077 0.389380i \(-0.872689\pi\)
0.797752 + 0.602986i \(0.206023\pi\)
\(264\) 0 0
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) 1.00000 0.0611990
\(268\) 0 0
\(269\) 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i \(-0.648441\pi\)
0.998361 0.0572259i \(-0.0182255\pi\)
\(270\) 0 0
\(271\) 12.0000 + 20.7846i 0.728948 + 1.26258i 0.957328 + 0.289003i \(0.0933238\pi\)
−0.228380 + 0.973572i \(0.573343\pi\)
\(272\) 0 0
\(273\) 2.50000 + 12.9904i 0.151307 + 0.786214i
\(274\) 0 0
\(275\) 16.5000 + 28.5788i 0.994987 + 1.72337i
\(276\) 0 0
\(277\) −4.00000 + 6.92820i −0.240337 + 0.416275i −0.960810 0.277207i \(-0.910591\pi\)
0.720473 + 0.693482i \(0.243925\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −19.0000 −1.13344 −0.566722 0.823909i \(-0.691789\pi\)
−0.566722 + 0.823909i \(0.691789\pi\)
\(282\) 0 0
\(283\) −7.50000 + 12.9904i −0.445829 + 0.772198i −0.998110 0.0614601i \(-0.980424\pi\)
0.552281 + 0.833658i \(0.313758\pi\)
\(284\) 0 0
\(285\) 12.0000 + 20.7846i 0.710819 + 1.23117i
\(286\) 0 0
\(287\) 16.0000 13.8564i 0.944450 0.817918i
\(288\) 0 0
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) 0 0
\(291\) −9.00000 + 15.5885i −0.527589 + 0.913812i
\(292\) 0 0
\(293\) −15.0000 −0.876309 −0.438155 0.898900i \(-0.644368\pi\)
−0.438155 + 0.898900i \(0.644368\pi\)
\(294\) 0 0
\(295\) −8.00000 −0.465778
\(296\) 0 0
\(297\) −7.50000 + 12.9904i −0.435194 + 0.753778i
\(298\) 0 0
\(299\) −10.0000 17.3205i −0.578315 1.00167i
\(300\) 0 0
\(301\) −20.0000 + 17.3205i −1.15278 + 0.998337i
\(302\) 0 0
\(303\) 3.00000 + 5.19615i 0.172345 + 0.298511i
\(304\) 0 0
\(305\) −16.0000 + 27.7128i −0.916157 + 1.58683i
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) 0 0
\(311\) 6.50000 11.2583i 0.368581 0.638401i −0.620763 0.783998i \(-0.713177\pi\)
0.989344 + 0.145597i \(0.0465103\pi\)
\(312\) 0 0
\(313\) −15.0000 25.9808i −0.847850 1.46852i −0.883123 0.469142i \(-0.844563\pi\)
0.0352727 0.999378i \(-0.488770\pi\)
\(314\) 0 0
\(315\) −4.00000 20.7846i −0.225374 1.17108i
\(316\) 0 0
\(317\) 1.00000 + 1.73205i 0.0561656 + 0.0972817i 0.892741 0.450570i \(-0.148779\pi\)
−0.836576 + 0.547852i \(0.815446\pi\)
\(318\) 0 0
\(319\) 12.0000 20.7846i 0.671871 1.16371i
\(320\) 0 0
\(321\) 1.00000 0.0558146
\(322\) 0 0
\(323\) −6.00000 −0.333849
\(324\) 0 0
\(325\) 27.5000 47.6314i 1.52543 2.64211i
\(326\) 0 0
\(327\) 4.00000 + 6.92820i 0.221201 + 0.383131i
\(328\) 0 0
\(329\) −5.00000 1.73205i −0.275659 0.0954911i
\(330\) 0 0
\(331\) 3.00000 + 5.19615i 0.164895 + 0.285606i 0.936618 0.350352i \(-0.113938\pi\)
−0.771723 + 0.635959i \(0.780605\pi\)
\(332\) 0 0
\(333\) −8.00000 + 13.8564i −0.438397 + 0.759326i
\(334\) 0 0
\(335\) −56.0000 −3.05961
\(336\) 0 0
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) 0 0
\(339\) 4.00000 6.92820i 0.217250 0.376288i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 0 0
\(345\) −8.00000 13.8564i −0.430706 0.746004i
\(346\) 0 0
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 0 0
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) 25.0000 1.33440
\(352\) 0 0
\(353\) 10.5000 18.1865i 0.558859 0.967972i −0.438733 0.898617i \(-0.644573\pi\)
0.997592 0.0693543i \(-0.0220939\pi\)
\(354\) 0 0
\(355\) 14.0000 + 24.2487i 0.743043 + 1.28699i
\(356\) 0 0
\(357\) −2.50000 0.866025i −0.132314 0.0458349i
\(358\) 0 0
\(359\) −11.0000 19.0526i −0.580558 1.00556i −0.995413 0.0956683i \(-0.969501\pi\)
0.414855 0.909887i \(-0.363832\pi\)
\(360\) 0 0
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) 0 0
\(363\) −2.00000 −0.104973
\(364\) 0 0
\(365\) 32.0000 1.67496
\(366\) 0 0
\(367\) 4.50000 7.79423i 0.234898 0.406855i −0.724345 0.689438i \(-0.757858\pi\)
0.959243 + 0.282582i \(0.0911910\pi\)
\(368\) 0 0
\(369\) −8.00000 13.8564i −0.416463 0.721336i
\(370\) 0 0
\(371\) −1.50000 7.79423i −0.0778761 0.404656i
\(372\) 0 0
\(373\) −15.5000 26.8468i −0.802560 1.39007i −0.917926 0.396751i \(-0.870138\pi\)
0.115367 0.993323i \(-0.463196\pi\)
\(374\) 0 0
\(375\) 12.0000 20.7846i 0.619677 1.07331i
\(376\) 0 0
\(377\) −40.0000 −2.06010
\(378\) 0 0
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) 0 0
\(381\) −4.00000 + 6.92820i −0.204926 + 0.354943i
\(382\) 0 0
\(383\) −1.00000 1.73205i −0.0510976 0.0885037i 0.839345 0.543599i \(-0.182939\pi\)
−0.890443 + 0.455095i \(0.849605\pi\)
\(384\) 0 0
\(385\) −24.0000 + 20.7846i −1.22315 + 1.05928i
\(386\) 0 0
\(387\) 10.0000 + 17.3205i 0.508329 + 0.880451i
\(388\) 0 0
\(389\) 13.5000 23.3827i 0.684477 1.18555i −0.289124 0.957292i \(-0.593364\pi\)
0.973601 0.228257i \(-0.0733028\pi\)
\(390\) 0 0
\(391\) 4.00000 0.202289
\(392\) 0 0
\(393\) −4.00000 −0.201773
\(394\) 0 0
\(395\) 30.0000 51.9615i 1.50946 2.61447i
\(396\) 0 0
\(397\) −13.0000 22.5167i −0.652451 1.13008i −0.982526 0.186124i \(-0.940407\pi\)
0.330075 0.943955i \(-0.392926\pi\)
\(398\) 0 0
\(399\) −12.0000 + 10.3923i −0.600751 + 0.520266i
\(400\) 0 0
\(401\) 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −4.00000 −0.198762
\(406\) 0 0
\(407\) 24.0000 1.18964
\(408\) 0 0
\(409\) −5.50000 + 9.52628i −0.271957 + 0.471044i −0.969363 0.245633i \(-0.921004\pi\)
0.697406 + 0.716677i \(0.254338\pi\)
\(410\) 0 0
\(411\) 3.50000 + 6.06218i 0.172642 + 0.299025i
\(412\) 0 0
\(413\) −1.00000 5.19615i −0.0492068 0.255686i
\(414\) 0 0
\(415\) 24.0000 + 41.5692i 1.17811 + 2.04055i
\(416\) 0 0
\(417\) 0.500000 0.866025i 0.0244851 0.0424094i
\(418\) 0 0
\(419\) 37.0000 1.80757 0.903784 0.427989i \(-0.140778\pi\)
0.903784 + 0.427989i \(0.140778\pi\)
\(420\) 0 0
\(421\) 6.00000 0.292422 0.146211 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) 0 0
\(423\) −2.00000 + 3.46410i −0.0972433 + 0.168430i
\(424\) 0 0
\(425\) 5.50000 + 9.52628i 0.266789 + 0.462092i
\(426\) 0 0
\(427\) −20.0000 6.92820i −0.967868 0.335279i
\(428\) 0 0
\(429\) −7.50000 12.9904i −0.362103 0.627182i
\(430\) 0 0
\(431\) 7.50000 12.9904i 0.361262 0.625725i −0.626907 0.779094i \(-0.715679\pi\)
0.988169 + 0.153370i \(0.0490126\pi\)
\(432\) 0 0
\(433\) −10.0000 −0.480569 −0.240285 0.970702i \(-0.577241\pi\)
−0.240285 + 0.970702i \(0.577241\pi\)
\(434\) 0 0
\(435\) −32.0000 −1.53428
\(436\) 0 0
\(437\) 12.0000 20.7846i 0.574038 0.994263i
\(438\) 0 0
\(439\) 0.500000 + 0.866025i 0.0238637 + 0.0413331i 0.877711 0.479191i \(-0.159070\pi\)
−0.853847 + 0.520524i \(0.825737\pi\)
\(440\) 0 0
\(441\) 13.0000 5.19615i 0.619048 0.247436i
\(442\) 0 0
\(443\) −13.0000 22.5167i −0.617649 1.06980i −0.989914 0.141672i \(-0.954752\pi\)
0.372265 0.928126i \(-0.378581\pi\)
\(444\) 0 0
\(445\) 2.00000 3.46410i 0.0948091 0.164214i
\(446\) 0 0
\(447\) −11.0000 −0.520282
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) −12.0000 + 20.7846i −0.565058 + 0.978709i
\(452\) 0 0
\(453\) −5.00000 8.66025i −0.234920 0.406894i
\(454\) 0 0
\(455\) 50.0000 + 17.3205i 2.34404 + 0.811998i
\(456\) 0 0
\(457\) 13.0000 + 22.5167i 0.608114 + 1.05328i 0.991551 + 0.129718i \(0.0414071\pi\)
−0.383437 + 0.923567i \(0.625260\pi\)
\(458\) 0 0
\(459\) −2.50000 + 4.33013i −0.116690 + 0.202113i
\(460\) 0 0
\(461\) 15.0000 0.698620 0.349310 0.937007i \(-0.386416\pi\)
0.349310 + 0.937007i \(0.386416\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 14.0000 + 24.2487i 0.647843 + 1.12210i 0.983637 + 0.180161i \(0.0576619\pi\)
−0.335794 + 0.941935i \(0.609005\pi\)
\(468\) 0 0
\(469\) −7.00000 36.3731i −0.323230 1.67955i
\(470\) 0 0
\(471\) −0.500000 0.866025i −0.0230388 0.0399043i
\(472\) 0 0
\(473\) 15.0000 25.9808i 0.689701 1.19460i
\(474\) 0 0
\(475\) 66.0000 3.02829
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) −16.0000 + 27.7128i −0.731059 + 1.26623i 0.225372 + 0.974273i \(0.427640\pi\)
−0.956431 + 0.291958i \(0.905693\pi\)
\(480\) 0 0
\(481\) −20.0000 34.6410i −0.911922 1.57949i
\(482\) 0 0
\(483\) 8.00000 6.92820i 0.364013 0.315244i
\(484\) 0 0
\(485\) 36.0000 + 62.3538i 1.63468 + 2.83134i
\(486\) 0 0
\(487\) 2.50000 4.33013i 0.113286 0.196217i −0.803807 0.594890i \(-0.797196\pi\)
0.917093 + 0.398673i \(0.130529\pi\)
\(488\) 0 0
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) −18.0000 −0.812329 −0.406164 0.913800i \(-0.633134\pi\)
−0.406164 + 0.913800i \(0.633134\pi\)
\(492\) 0 0
\(493\) 4.00000 6.92820i 0.180151 0.312031i
\(494\) 0 0
\(495\) 12.0000 + 20.7846i 0.539360 + 0.934199i
\(496\) 0 0
\(497\) −14.0000 + 12.1244i −0.627986 + 0.543852i
\(498\) 0 0
\(499\) −19.5000 33.7750i −0.872940 1.51198i −0.858941 0.512074i \(-0.828877\pi\)
−0.0139987 0.999902i \(-0.504456\pi\)
\(500\) 0 0
\(501\) 9.50000 16.4545i 0.424429 0.735132i
\(502\) 0 0
\(503\) 21.0000 0.936344 0.468172 0.883637i \(-0.344913\pi\)
0.468172 + 0.883637i \(0.344913\pi\)
\(504\) 0 0
\(505\) 24.0000 1.06799
\(506\) 0 0
\(507\) −6.00000 + 10.3923i −0.266469 + 0.461538i
\(508\) 0 0
\(509\) −19.0000 32.9090i −0.842160 1.45866i −0.888065 0.459718i \(-0.847950\pi\)
0.0459045 0.998946i \(-0.485383\pi\)
\(510\) 0 0
\(511\) 4.00000 + 20.7846i 0.176950 + 0.919457i
\(512\) 0 0
\(513\) 15.0000 + 25.9808i 0.662266 + 1.14708i
\(514\) 0 0
\(515\) 8.00000 13.8564i 0.352522 0.610586i
\(516\) 0 0
\(517\) 6.00000 0.263880
\(518\) 0 0
\(519\) −2.00000 −0.0877903
\(520\) 0 0
\(521\) 12.0000 20.7846i 0.525730 0.910590i −0.473821 0.880621i \(-0.657126\pi\)
0.999551 0.0299693i \(-0.00954094\pi\)
\(522\) 0 0
\(523\) −3.00000 5.19615i −0.131181 0.227212i 0.792951 0.609285i \(-0.208544\pi\)
−0.924132 + 0.382073i \(0.875210\pi\)
\(524\) 0 0
\(525\) 27.5000 + 9.52628i 1.20020 + 0.415761i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) 40.0000 1.73259
\(534\) 0 0
\(535\) 2.00000 3.46410i 0.0864675 0.149766i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −16.5000 12.9904i −0.710705 0.559535i
\(540\) 0 0
\(541\) −7.00000 12.1244i −0.300954 0.521267i 0.675399 0.737453i \(-0.263972\pi\)
−0.976352 + 0.216186i \(0.930638\pi\)
\(542\) 0 0
\(543\) −9.00000 + 15.5885i −0.386227 + 0.668965i
\(544\) 0 0
\(545\) 32.0000 1.37073
\(546\) 0 0
\(547\) −13.0000 −0.555840 −0.277920 0.960604i \(-0.589645\pi\)
−0.277920 + 0.960604i \(0.589645\pi\)
\(548\) 0 0
\(549\) −8.00000 + 13.8564i −0.341432 + 0.591377i
\(550\) 0 0
\(551\) −24.0000 41.5692i −1.02243 1.77091i
\(552\) 0 0
\(553\) 37.5000 + 12.9904i 1.59466 + 0.552407i
\(554\) 0 0
\(555\) −16.0000 27.7128i −0.679162 1.17634i
\(556\) 0 0
\(557\) −11.5000 + 19.9186i −0.487271 + 0.843978i −0.999893 0.0146368i \(-0.995341\pi\)
0.512622 + 0.858614i \(0.328674\pi\)
\(558\) 0 0
\(559\) −50.0000 −2.11477
\(560\) 0 0
\(561\) 3.00000 0.126660
\(562\) 0 0
\(563\) −15.0000 + 25.9808i −0.632175 + 1.09496i 0.354932 + 0.934892i \(0.384504\pi\)
−0.987106 + 0.160066i \(0.948829\pi\)
\(564\) 0 0
\(565\) −16.0000 27.7128i −0.673125 1.16589i
\(566\) 0 0
\(567\) −0.500000 2.59808i −0.0209980 0.109109i
\(568\) 0 0
\(569\) −16.5000 28.5788i −0.691716 1.19809i −0.971275 0.237959i \(-0.923522\pi\)
0.279559 0.960128i \(-0.409812\pi\)
\(570\) 0 0
\(571\) −18.0000 + 31.1769i −0.753277 + 1.30471i 0.192950 + 0.981209i \(0.438194\pi\)
−0.946227 + 0.323505i \(0.895139\pi\)
\(572\) 0 0
\(573\) 12.0000 0.501307
\(574\) 0 0
\(575\) −44.0000 −1.83493
\(576\) 0 0
\(577\) −6.50000 + 11.2583i −0.270599 + 0.468690i −0.969015 0.247001i \(-0.920555\pi\)
0.698417 + 0.715691i \(0.253888\pi\)
\(578\) 0 0
\(579\) 5.00000 + 8.66025i 0.207793 + 0.359908i
\(580\) 0 0
\(581\) −24.0000 + 20.7846i −0.995688 + 0.862291i
\(582\) 0 0
\(583\) 4.50000 + 7.79423i 0.186371 + 0.322804i
\(584\) 0 0
\(585\) 20.0000 34.6410i 0.826898 1.43223i
\(586\) 0 0
\(587\) −2.00000 −0.0825488 −0.0412744 0.999148i \(-0.513142\pi\)
−0.0412744 + 0.999148i \(0.513142\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) −9.00000 + 15.5885i −0.370211 + 0.641223i
\(592\) 0 0
\(593\) −10.5000 18.1865i −0.431183 0.746831i 0.565792 0.824548i \(-0.308570\pi\)
−0.996976 + 0.0777165i \(0.975237\pi\)
\(594\) 0 0
\(595\) −8.00000 + 6.92820i −0.327968 + 0.284029i
\(596\) 0 0
\(597\) 3.50000 + 6.06218i 0.143245 + 0.248108i
\(598\) 0 0
\(599\) 17.0000 29.4449i 0.694601 1.20308i −0.275714 0.961240i \(-0.588914\pi\)
0.970315 0.241845i \(-0.0777525\pi\)
\(600\) 0 0
\(601\) −14.0000 −0.571072 −0.285536 0.958368i \(-0.592172\pi\)
−0.285536 + 0.958368i \(0.592172\pi\)
\(602\) 0 0
\(603\) −28.0000 −1.14025
\(604\) 0 0
\(605\) −4.00000 + 6.92820i −0.162623 + 0.281672i
\(606\) 0 0
\(607\) 11.5000 + 19.9186i 0.466771 + 0.808470i 0.999279 0.0379540i \(-0.0120840\pi\)
−0.532509 + 0.846424i \(0.678751\pi\)
\(608\) 0 0
\(609\) −4.00000 20.7846i −0.162088 0.842235i
\(610\) 0 0
\(611\) −5.00000 8.66025i −0.202278 0.350356i
\(612\) 0 0
\(613\) −8.50000 + 14.7224i −0.343312 + 0.594633i −0.985046 0.172294i \(-0.944882\pi\)
0.641734 + 0.766927i \(0.278215\pi\)
\(614\) 0 0
\(615\) 32.0000 1.29036
\(616\) 0 0
\(617\) −36.0000 −1.44931 −0.724653 0.689114i \(-0.758000\pi\)
−0.724653 + 0.689114i \(0.758000\pi\)
\(618\) 0 0
\(619\) 8.50000 14.7224i 0.341644 0.591744i −0.643094 0.765787i \(-0.722350\pi\)
0.984738 + 0.174042i \(0.0556830\pi\)
\(620\) 0 0
\(621\) −10.0000 17.3205i −0.401286 0.695048i
\(622\) 0 0
\(623\) 2.50000 + 0.866025i 0.100160 + 0.0346966i
\(624\) 0 0
\(625\) −20.5000 35.5070i −0.820000 1.42028i
\(626\) 0 0
\(627\) 9.00000 15.5885i 0.359425 0.622543i
\(628\) 0 0
\(629\) 8.00000 0.318981
\(630\) 0 0
\(631\) −30.0000 −1.19428 −0.597141 0.802137i \(-0.703697\pi\)
−0.597141 + 0.802137i \(0.703697\pi\)
\(632\) 0 0
\(633\) 2.00000 3.46410i 0.0794929 0.137686i
\(634\) 0 0
\(635\) 16.0000 + 27.7128i 0.634941 + 1.09975i
\(636\) 0 0
\(637\) −5.00000 + 34.6410i −0.198107 + 1.37253i
\(638\) 0 0
\(639\) 7.00000 + 12.1244i 0.276916 + 0.479632i
\(640\) 0 0
\(641\) −11.0000 + 19.0526i −0.434474 + 0.752531i −0.997253 0.0740768i \(-0.976399\pi\)
0.562779 + 0.826608i \(0.309732\pi\)
\(642\) 0 0
\(643\) −1.00000 −0.0394362 −0.0197181 0.999806i \(-0.506277\pi\)
−0.0197181 + 0.999806i \(0.506277\pi\)
\(644\) 0 0
\(645\) −40.0000 −1.57500
\(646\) 0 0
\(647\) −14.0000 + 24.2487i −0.550397 + 0.953315i 0.447849 + 0.894109i \(0.352190\pi\)
−0.998246 + 0.0592060i \(0.981143\pi\)
\(648\) 0 0
\(649\) 3.00000 + 5.19615i 0.117760 + 0.203967i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5.00000 + 8.66025i 0.195665 + 0.338902i 0.947118 0.320884i \(-0.103980\pi\)
−0.751453 + 0.659786i \(0.770647\pi\)
\(654\) 0 0
\(655\) −8.00000 + 13.8564i −0.312586 + 0.541415i
\(656\) 0 0
\(657\) 16.0000 0.624219
\(658\) 0 0
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 0 0
\(661\) −9.00000 + 15.5885i −0.350059 + 0.606321i −0.986260 0.165203i \(-0.947172\pi\)
0.636200 + 0.771524i \(0.280505\pi\)
\(662\) 0 0
\(663\) −2.50000 4.33013i −0.0970920 0.168168i
\(664\) 0 0
\(665\) 12.0000 + 62.3538i 0.465340 + 2.41798i
\(666\) 0 0
\(667\) 16.0000 + 27.7128i 0.619522 + 1.07304i
\(668\) 0 0
\(669\) 3.00000 5.19615i 0.115987 0.200895i
\(670\) 0 0
\(671\) 24.0000 0.926510
\(672\) 0 0
\(673\) 28.0000 1.07932 0.539660 0.841883i \(-0.318553\pi\)
0.539660 + 0.841883i \(0.318553\pi\)
\(674\) 0 0
\(675\) 27.5000 47.6314i 1.05848 1.83333i
\(676\) 0 0
\(677\) 4.00000 + 6.92820i 0.153732 + 0.266272i 0.932597 0.360920i \(-0.117537\pi\)
−0.778864 + 0.627192i \(0.784204\pi\)
\(678\) 0 0
\(679\) −36.0000 + 31.1769i −1.38155 + 1.19646i
\(680\) 0 0
\(681\) −12.5000 21.6506i −0.479001 0.829654i
\(682\) 0 0
\(683\) 10.5000 18.1865i 0.401771 0.695888i −0.592168 0.805814i \(-0.701728\pi\)
0.993940 + 0.109926i \(0.0350613\pi\)
\(684\) 0 0
\(685\) 28.0000 1.06983
\(686\) 0 0
\(687\) −10.0000 −0.381524
\(688\) 0 0
\(689\) 7.50000 12.9904i 0.285727 0.494894i
\(690\) 0 0
\(691\) −4.00000 6.92820i −0.152167 0.263561i 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) 0 0
\(693\) −12.0000 + 10.3923i −0.455842 + 0.394771i
\(694\) 0 0
\(695\) −2.00000 3.46410i −0.0758643 0.131401i
\(696\) 0 0
\(697\) −4.00000 + 6.92820i −0.151511 + 0.262424i
\(698\) 0 0
\(699\) 28.0000 1.05906
\(700\) 0 0
\(701\) 31.0000 1.17085 0.585427 0.810725i \(-0.300927\pi\)
0.585427 + 0.810725i \(0.300927\pi\)
\(702\) 0 0
\(703\) 24.0000 41.5692i 0.905177 1.56781i
\(704\) 0 0
\(705\) −4.00000 6.92820i −0.150649 0.260931i
\(706\) 0 0
\(707\) 3.00000 + 15.5885i 0.112827 + 0.586264i
\(708\) 0 0
\(709\) 25.0000 + 43.3013i 0.938895 + 1.62621i 0.767537 + 0.641004i \(0.221482\pi\)
0.171358 + 0.985209i \(0.445185\pi\)
\(710\) 0 0
\(711\) 15.0000 25.9808i 0.562544 0.974355i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −60.0000 −2.24387
\(716\) 0 0
\(717\) −1.00000 + 1.73205i −0.0373457 + 0.0646846i
\(718\) 0 0
\(719\) 17.5000 + 30.3109i 0.652640 + 1.13041i 0.982480 + 0.186369i \(0.0596719\pi\)
−0.329840 + 0.944037i \(0.606995\pi\)
\(720\) 0 0
\(721\) 10.0000 + 3.46410i 0.372419 + 0.129010i
\(722\) 0 0
\(723\) 4.00000 + 6.92820i 0.148762 + 0.257663i
\(724\) 0 0
\(725\) −44.0000 + 76.2102i −1.63412 + 2.83038i
\(726\) 0 0
\(727\) 18.0000 0.667583 0.333792 0.942647i \(-0.391672\pi\)
0.333792 + 0.942647i \(0.391672\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 5.00000 8.66025i 0.184932 0.320311i
\(732\) 0 0
\(733\) −1.50000 2.59808i −0.0554038 0.0959621i 0.836993 0.547213i \(-0.184311\pi\)
−0.892397 + 0.451251i \(0.850978\pi\)
\(734\) 0 0
\(735\) −4.00000 + 27.7128i −0.147542 + 1.02220i
\(736\) 0 0
\(737\) 21.0000 + 36.3731i 0.773545 + 1.33982i
\(738\) 0 0
\(739\) −15.0000 + 25.9808i −0.551784 + 0.955718i 0.446362 + 0.894852i \(0.352719\pi\)
−0.998146 + 0.0608653i \(0.980614\pi\)
\(740\) 0 0
\(741\) −30.0000 −1.10208
\(742\) 0 0
\(743\) 1.00000 0.0366864 0.0183432 0.999832i \(-0.494161\pi\)
0.0183432 + 0.999832i \(0.494161\pi\)
\(744\) 0 0
\(745\) −22.0000 + 38.1051i −0.806018 + 1.39606i
\(746\) 0 0
\(747\) 12.0000 + 20.7846i 0.439057 + 0.760469i
\(748\) 0 0
\(749\) 2.50000 + 0.866025i 0.0913480 + 0.0316439i
\(750\) 0 0
\(751\) −1.50000 2.59808i −0.0547358 0.0948051i 0.837359 0.546653i \(-0.184098\pi\)
−0.892095 + 0.451848i \(0.850765\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −40.0000 −1.45575
\(756\) 0 0
\(757\) 9.00000 0.327111 0.163555 0.986534i \(-0.447704\pi\)
0.163555 + 0.986534i \(0.447704\pi\)
\(758\) 0 0
\(759\) −6.00000 + 10.3923i −0.217786 + 0.377217i
\(760\) 0 0
\(761\) −22.5000 38.9711i −0.815624 1.41270i −0.908879 0.417061i \(-0.863060\pi\)
0.0932544 0.995642i \(-0.470273\pi\)
\(762\) 0 0
\(763\) 4.00000 + 20.7846i 0.144810 + 0.752453i
\(764\) 0 0
\(765\) 4.00000 + 6.92820i 0.144620 + 0.250490i
\(766\) 0 0
\(767\) 5.00000 8.66025i 0.180540 0.312704i
\(768\) 0 0
\(769\) 1.00000 0.0360609 0.0180305 0.999837i \(-0.494260\pi\)
0.0180305 + 0.999837i \(0.494260\pi\)
\(770\) 0 0
\(771\) 3.00000 0.108042
\(772\) 0 0
\(773\) −4.50000 + 7.79423i −0.161854 + 0.280339i −0.935534 0.353238i \(-0.885081\pi\)
0.773680 + 0.633577i \(0.218414\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 16.0000 13.8564i 0.573997 0.497096i
\(778\) 0 0
\(779\) 24.0000 + 41.5692i 0.859889 + 1.48937i
\(780\) 0 0
\(781\) 10.5000 18.1865i 0.375720 0.650765i
\(782\) 0 0
\(783\) −40.0000 −1.42948
\(784\) 0 0
\(785\) −4.00000 −0.142766
\(786\) 0 0
\(787\) −2.00000 + 3.46410i −0.0712923 + 0.123482i −0.899468 0.436987i \(-0.856046\pi\)
0.828176 + 0.560469i \(0.189379\pi\)
\(788\) 0 0
\(789\) −2.00000 3.46410i −0.0712019 0.123325i
\(790\) 0 0
\(791\) 16.0000 13.8564i 0.568895 0.492677i
\(792\) 0 0
\(793\) −20.0000 34.6410i −0.710221 1.23014i
\(794\) 0 0