Properties

Label 882.2.g.l.361.2
Level $882$
Weight $2$
Character 882.361
Analytic conductor $7.043$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 98)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.2.g.l.667.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.41421 + 2.44949i) q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.41421 + 2.44949i) q^{5} -1.00000 q^{8} +(-1.41421 + 2.44949i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-0.500000 - 0.866025i) q^{16} +(-0.707107 + 1.22474i) q^{17} +(3.53553 + 6.12372i) q^{19} -2.82843 q^{20} -2.00000 q^{22} +(-2.00000 - 3.46410i) q^{23} +(-1.50000 + 2.59808i) q^{25} -2.00000 q^{29} +(-4.24264 + 7.34847i) q^{31} +(0.500000 - 0.866025i) q^{32} -1.41421 q^{34} +(-5.00000 - 8.66025i) q^{37} +(-3.53553 + 6.12372i) q^{38} +(-1.41421 - 2.44949i) q^{40} +9.89949 q^{41} +2.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(2.00000 - 3.46410i) q^{46} +(1.41421 + 2.44949i) q^{47} -3.00000 q^{50} +(-1.00000 + 1.73205i) q^{53} -5.65685 q^{55} +(-1.00000 - 1.73205i) q^{58} +(-0.707107 + 1.22474i) q^{59} +(-1.41421 - 2.44949i) q^{61} -8.48528 q^{62} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{67} +(-0.707107 - 1.22474i) q^{68} +12.0000 q^{71} +(0.707107 - 1.22474i) q^{73} +(5.00000 - 8.66025i) q^{74} -7.07107 q^{76} +(2.00000 + 3.46410i) q^{79} +(1.41421 - 2.44949i) q^{80} +(4.94975 + 8.57321i) q^{82} -9.89949 q^{83} -4.00000 q^{85} +(1.00000 + 1.73205i) q^{86} +(1.00000 - 1.73205i) q^{88} +(-3.53553 - 6.12372i) q^{89} +4.00000 q^{92} +(-1.41421 + 2.44949i) q^{94} +(-10.0000 + 17.3205i) q^{95} +9.89949 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{4} - 4q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} - 4q^{8} - 4q^{11} - 2q^{16} - 8q^{22} - 8q^{23} - 6q^{25} - 8q^{29} + 2q^{32} - 20q^{37} + 8q^{43} - 4q^{44} + 8q^{46} - 12q^{50} - 4q^{53} - 4q^{58} + 4q^{64} - 24q^{67} + 48q^{71} + 20q^{74} + 8q^{79} - 16q^{85} + 4q^{86} + 4q^{88} + 16q^{92} - 40q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.41421 + 2.44949i 0.632456 + 1.09545i 0.987048 + 0.160424i \(0.0512862\pi\)
−0.354593 + 0.935021i \(0.615380\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.41421 + 2.44949i −0.447214 + 0.774597i
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.707107 + 1.22474i −0.171499 + 0.297044i −0.938944 0.344070i \(-0.888194\pi\)
0.767445 + 0.641114i \(0.221528\pi\)
\(18\) 0 0
\(19\) 3.53553 + 6.12372i 0.811107 + 1.40488i 0.912090 + 0.409991i \(0.134468\pi\)
−0.100983 + 0.994888i \(0.532199\pi\)
\(20\) −2.82843 −0.632456
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) −2.00000 3.46410i −0.417029 0.722315i 0.578610 0.815604i \(-0.303595\pi\)
−0.995639 + 0.0932891i \(0.970262\pi\)
\(24\) 0 0
\(25\) −1.50000 + 2.59808i −0.300000 + 0.519615i
\(26\) 0 0
\(27\) 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
\(31\) −4.24264 + 7.34847i −0.762001 + 1.31982i 0.179817 + 0.983700i \(0.442449\pi\)
−0.941818 + 0.336124i \(0.890884\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −1.41421 −0.242536
\(35\) 0 0
\(36\) 0 0
\(37\) −5.00000 8.66025i −0.821995 1.42374i −0.904194 0.427121i \(-0.859528\pi\)
0.0821995 0.996616i \(-0.473806\pi\)
\(38\) −3.53553 + 6.12372i −0.573539 + 0.993399i
\(39\) 0 0
\(40\) −1.41421 2.44949i −0.223607 0.387298i
\(41\) 9.89949 1.54604 0.773021 0.634381i \(-0.218745\pi\)
0.773021 + 0.634381i \(0.218745\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −1.00000 1.73205i −0.150756 0.261116i
\(45\) 0 0
\(46\) 2.00000 3.46410i 0.294884 0.510754i
\(47\) 1.41421 + 2.44949i 0.206284 + 0.357295i 0.950541 0.310599i \(-0.100530\pi\)
−0.744257 + 0.667893i \(0.767196\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −3.00000 −0.424264
\(51\) 0 0
\(52\) 0 0
\(53\) −1.00000 + 1.73205i −0.137361 + 0.237915i −0.926497 0.376303i \(-0.877195\pi\)
0.789136 + 0.614218i \(0.210529\pi\)
\(54\) 0 0
\(55\) −5.65685 −0.762770
\(56\) 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 \(0.196011\pi\)
\(60\) 0 0
\(61\) −1.41421 2.44949i −0.181071 0.313625i 0.761174 0.648547i \(-0.224623\pi\)
−0.942246 + 0.334922i \(0.891290\pi\)
\(62\) −8.48528 −1.07763
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −6.00000 + 10.3923i −0.733017 + 1.26962i 0.222571 + 0.974916i \(0.428555\pi\)
−0.955588 + 0.294706i \(0.904778\pi\)
\(68\) −0.707107 1.22474i −0.0857493 0.148522i
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) 0.707107 1.22474i 0.0827606 0.143346i −0.821674 0.569958i \(-0.806960\pi\)
0.904435 + 0.426612i \(0.140293\pi\)
\(74\) 5.00000 8.66025i 0.581238 1.00673i
\(75\) 0 0
\(76\) −7.07107 −0.811107
\(77\) 0 0
\(78\) 0 0
\(79\) 2.00000 + 3.46410i 0.225018 + 0.389742i 0.956325 0.292306i \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 1.41421 2.44949i 0.158114 0.273861i
\(81\) 0 0
\(82\) 4.94975 + 8.57321i 0.546608 + 0.946753i
\(83\) −9.89949 −1.08661 −0.543305 0.839535i \(-0.682827\pi\)
−0.543305 + 0.839535i \(0.682827\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 1.00000 + 1.73205i 0.107833 + 0.186772i
\(87\) 0 0
\(88\) 1.00000 1.73205i 0.106600 0.184637i
\(89\) −3.53553 6.12372i −0.374766 0.649113i 0.615526 0.788116i \(-0.288944\pi\)
−0.990292 + 0.139003i \(0.955610\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 4.00000 0.417029
\(93\) 0 0
\(94\) −1.41421 + 2.44949i −0.145865 + 0.252646i
\(95\) −10.0000 + 17.3205i −1.02598 + 1.77705i
\(96\) 0 0
\(97\) 9.89949 1.00514 0.502571 0.864536i \(-0.332388\pi\)
0.502571 + 0.864536i \(0.332388\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.50000 2.59808i −0.150000 0.259808i
\(101\) 4.24264 7.34847i 0.422159 0.731200i −0.573992 0.818861i \(-0.694606\pi\)
0.996150 + 0.0876610i \(0.0279392\pi\)
\(102\) 0 0
\(103\) −1.41421 2.44949i −0.139347 0.241355i 0.787903 0.615800i \(-0.211167\pi\)
−0.927249 + 0.374444i \(0.877834\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −2.00000 −0.194257
\(107\) −2.00000 3.46410i −0.193347 0.334887i 0.753010 0.658009i \(-0.228601\pi\)
−0.946357 + 0.323122i \(0.895268\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) −2.82843 4.89898i −0.269680 0.467099i
\(111\) 0 0
\(112\) 0 0
\(113\) 12.0000 1.12887 0.564433 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) 0 0
\(115\) 5.65685 9.79796i 0.527504 0.913664i
\(116\) 1.00000 1.73205i 0.0928477 0.160817i
\(117\) 0 0
\(118\) −1.41421 −0.130189
\(119\) 0 0
\(120\) 0 0
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 1.41421 2.44949i 0.128037 0.221766i
\(123\) 0 0
\(124\) −4.24264 7.34847i −0.381000 0.659912i
\(125\) 5.65685 0.505964
\(126\) 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
\(129\) 0 0
\(130\) 0 0
\(131\) 6.36396 + 11.0227i 0.556022 + 0.963058i 0.997823 + 0.0659452i \(0.0210063\pi\)
−0.441801 + 0.897113i \(0.645660\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) 0.707107 1.22474i 0.0606339 0.105021i
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 0 0
\(139\) 9.89949 0.839664 0.419832 0.907602i \(-0.362089\pi\)
0.419832 + 0.907602i \(0.362089\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.00000 + 10.3923i 0.503509 + 0.872103i
\(143\) 0 0
\(144\) 0 0
\(145\) −2.82843 4.89898i −0.234888 0.406838i
\(146\) 1.41421 0.117041
\(147\) 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 \(0.698996\pi\)
\(150\) 0 0
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) −3.53553 6.12372i −0.286770 0.496700i
\(153\) 0 0
\(154\) 0 0
\(155\) −24.0000 −1.92773
\(156\) 0 0
\(157\) 5.65685 9.79796i 0.451466 0.781962i −0.547011 0.837125i \(-0.684235\pi\)
0.998477 + 0.0551630i \(0.0175678\pi\)
\(158\) −2.00000 + 3.46410i −0.159111 + 0.275589i
\(159\) 0 0
\(160\) 2.82843 0.223607
\(161\) 0 0
\(162\) 0 0
\(163\) −5.00000 8.66025i −0.391630 0.678323i 0.601035 0.799223i \(-0.294755\pi\)
−0.992665 + 0.120900i \(0.961422\pi\)
\(164\) −4.94975 + 8.57321i −0.386510 + 0.669456i
\(165\) 0 0
\(166\) −4.94975 8.57321i −0.384175 0.665410i
\(167\) 19.7990 1.53209 0.766046 0.642786i \(-0.222221\pi\)
0.766046 + 0.642786i \(0.222221\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) −2.00000 3.46410i −0.153393 0.265684i
\(171\) 0 0
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) −8.48528 14.6969i −0.645124 1.11739i −0.984273 0.176655i \(-0.943472\pi\)
0.339149 0.940733i \(-0.389861\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.00000 0.150756
\(177\) 0 0
\(178\) 3.53553 6.12372i 0.264999 0.458993i
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 2.00000 + 3.46410i 0.147442 + 0.255377i
\(185\) 14.1421 24.4949i 1.03975 1.80090i
\(186\) 0 0
\(187\) −1.41421 2.44949i −0.103418 0.179124i
\(188\) −2.82843 −0.206284
\(189\) 0 0
\(190\) −20.0000 −1.45095
\(191\) −2.00000 3.46410i −0.144715 0.250654i 0.784552 0.620063i \(-0.212893\pi\)
−0.929267 + 0.369410i \(0.879560\pi\)
\(192\) 0 0
\(193\) 8.00000 13.8564i 0.575853 0.997406i −0.420096 0.907480i \(-0.638004\pi\)
0.995948 0.0899262i \(-0.0286631\pi\)
\(194\) 4.94975 + 8.57321i 0.355371 + 0.615521i
\(195\) 0 0
\(196\) 0 0
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) −4.24264 + 7.34847i −0.300753 + 0.520919i −0.976307 0.216391i \(-0.930571\pi\)
0.675554 + 0.737311i \(0.263905\pi\)
\(200\) 1.50000 2.59808i 0.106066 0.183712i
\(201\) 0 0
\(202\) 8.48528 0.597022
\(203\) 0 0
\(204\) 0 0
\(205\) 14.0000 + 24.2487i 0.977802 + 1.69360i
\(206\) 1.41421 2.44949i 0.0985329 0.170664i
\(207\) 0 0
\(208\) 0 0
\(209\) −14.1421 −0.978232
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) −1.00000 1.73205i −0.0686803 0.118958i
\(213\) 0 0
\(214\) 2.00000 3.46410i 0.136717 0.236801i
\(215\) 2.82843 + 4.89898i 0.192897 + 0.334108i
\(216\) 0 0
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) 0 0
\(220\) 2.82843 4.89898i 0.190693 0.330289i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 6.00000 + 10.3923i 0.399114 + 0.691286i
\(227\) −10.6066 + 18.3712i −0.703985 + 1.21934i 0.263072 + 0.964776i \(0.415264\pi\)
−0.967057 + 0.254561i \(0.918069\pi\)
\(228\) 0 0
\(229\) 8.48528 + 14.6969i 0.560723 + 0.971201i 0.997434 + 0.0715988i \(0.0228101\pi\)
−0.436710 + 0.899602i \(0.643857\pi\)
\(230\) 11.3137 0.746004
\(231\) 0 0
\(232\) 2.00000 0.131306
\(233\) 12.0000 + 20.7846i 0.786146 + 1.36165i 0.928312 + 0.371802i \(0.121260\pi\)
−0.142166 + 0.989843i \(0.545407\pi\)
\(234\) 0 0
\(235\) −4.00000 + 6.92820i −0.260931 + 0.451946i
\(236\) −0.707107 1.22474i −0.0460287 0.0797241i
\(237\) 0 0
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) 10.6066 18.3712i 0.683231 1.18339i −0.290758 0.956797i \(-0.593907\pi\)
0.973989 0.226595i \(-0.0727593\pi\)
\(242\) −3.50000 + 6.06218i −0.224989 + 0.389692i
\(243\) 0 0
\(244\) 2.82843 0.181071
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 4.24264 7.34847i 0.269408 0.466628i
\(249\) 0 0
\(250\) 2.82843 + 4.89898i 0.178885 + 0.309839i
\(251\) −9.89949 −0.624851 −0.312425 0.949942i \(-0.601141\pi\)
−0.312425 + 0.949942i \(0.601141\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) 8.00000 + 13.8564i 0.501965 + 0.869428i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.36396 + 11.0227i 0.396973 + 0.687577i 0.993351 0.115126i \(-0.0367273\pi\)
−0.596378 + 0.802704i \(0.703394\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −6.36396 + 11.0227i −0.393167 + 0.680985i
\(263\) 6.00000 10.3923i 0.369976 0.640817i −0.619586 0.784929i \(-0.712699\pi\)
0.989561 + 0.144112i \(0.0460326\pi\)
\(264\) 0 0
\(265\) −5.65685 −0.347498
\(266\) 0 0
\(267\) 0 0
\(268\) −6.00000 10.3923i −0.366508 0.634811i
\(269\) −5.65685 + 9.79796i −0.344904 + 0.597392i −0.985336 0.170623i \(-0.945422\pi\)
0.640432 + 0.768015i \(0.278755\pi\)
\(270\) 0 0
\(271\) −11.3137 19.5959i −0.687259 1.19037i −0.972721 0.231977i \(-0.925480\pi\)
0.285462 0.958390i \(-0.407853\pi\)
\(272\) 1.41421 0.0857493
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) −3.00000 5.19615i −0.180907 0.313340i
\(276\) 0 0
\(277\) 1.00000 1.73205i 0.0600842 0.104069i −0.834419 0.551131i \(-0.814196\pi\)
0.894503 + 0.447062i \(0.147530\pi\)
\(278\) 4.94975 + 8.57321i 0.296866 + 0.514187i
\(279\) 0 0
\(280\) 0 0
\(281\) −16.0000 −0.954480 −0.477240 0.878773i \(-0.658363\pi\)
−0.477240 + 0.878773i \(0.658363\pi\)
\(282\) 0 0
\(283\) 0.707107 1.22474i 0.0420331 0.0728035i −0.844243 0.535960i \(-0.819950\pi\)
0.886277 + 0.463156i \(0.153283\pi\)
\(284\) −6.00000 + 10.3923i −0.356034 + 0.616670i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 7.50000 + 12.9904i 0.441176 + 0.764140i
\(290\) 2.82843 4.89898i 0.166091 0.287678i
\(291\) 0 0
\(292\) 0.707107 + 1.22474i 0.0413803 + 0.0716728i
\(293\) 19.7990 1.15667 0.578335 0.815800i \(-0.303703\pi\)
0.578335 + 0.815800i \(0.303703\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 5.00000 + 8.66025i 0.290619 + 0.503367i
\(297\) 0 0
\(298\) −5.00000 + 8.66025i −0.289642 + 0.501675i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 16.0000 0.920697
\(303\) 0 0
\(304\) 3.53553 6.12372i 0.202777 0.351220i
\(305\) 4.00000 6.92820i 0.229039 0.396708i
\(306\) 0 0
\(307\) −9.89949 −0.564994 −0.282497 0.959268i \(-0.591163\pi\)
−0.282497 + 0.959268i \(0.591163\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −12.0000 20.7846i −0.681554 1.18049i
\(311\) −5.65685 + 9.79796i −0.320771 + 0.555591i −0.980647 0.195783i \(-0.937275\pi\)
0.659877 + 0.751374i \(0.270609\pi\)
\(312\) 0 0
\(313\) −6.36396 11.0227i −0.359712 0.623040i 0.628200 0.778052i \(-0.283792\pi\)
−0.987913 + 0.155012i \(0.950459\pi\)
\(314\) 11.3137 0.638470
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) 5.00000 + 8.66025i 0.280828 + 0.486408i 0.971589 0.236675i \(-0.0760576\pi\)
−0.690761 + 0.723083i \(0.742724\pi\)
\(318\) 0 0
\(319\) 2.00000 3.46410i 0.111979 0.193952i
\(320\) 1.41421 + 2.44949i 0.0790569 + 0.136931i
\(321\) 0 0
\(322\) 0 0
\(323\) −10.0000 −0.556415
\(324\) 0 0
\(325\) 0 0
\(326\) 5.00000 8.66025i 0.276924 0.479647i
\(327\) 0 0
\(328\) −9.89949 −0.546608
\(329\) 0 0
\(330\) 0 0
\(331\) −5.00000 8.66025i −0.274825 0.476011i 0.695266 0.718752i \(-0.255287\pi\)
−0.970091 + 0.242742i \(0.921953\pi\)
\(332\) 4.94975 8.57321i 0.271653 0.470516i
\(333\) 0 0
\(334\) 9.89949 + 17.1464i 0.541676 + 0.938211i
\(335\) −33.9411 −1.85440
\(336\) 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
\(339\) 0 0
\(340\) 2.00000 3.46410i 0.108465 0.187867i
\(341\) −8.48528 14.6969i −0.459504 0.795884i
\(342\) 0 0
\(343\) 0 0
\(344\) −2.00000 −0.107833
\(345\) 0 0
\(346\) 8.48528 14.6969i 0.456172 0.790112i
\(347\) −15.0000 + 25.9808i −0.805242 + 1.39472i 0.110885 + 0.993833i \(0.464631\pi\)
−0.916127 + 0.400887i \(0.868702\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.00000 + 1.73205i 0.0533002 + 0.0923186i
\(353\) −0.707107 + 1.22474i −0.0376355 + 0.0651866i −0.884230 0.467052i \(-0.845316\pi\)
0.846594 + 0.532239i \(0.178649\pi\)
\(354\) 0 0
\(355\) 16.9706 + 29.3939i 0.900704 + 1.56007i
\(356\) 7.07107 0.374766
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) −16.0000 27.7128i −0.844448 1.46263i −0.886100 0.463494i \(-0.846596\pi\)
0.0416523 0.999132i \(-0.486738\pi\)
\(360\) 0 0
\(361\) −15.5000 + 26.8468i −0.815789 + 1.41299i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.00000 0.209370
\(366\) 0 0
\(367\) −14.1421 + 24.4949i −0.738213 + 1.27862i 0.215086 + 0.976595i \(0.430997\pi\)
−0.953299 + 0.302028i \(0.902336\pi\)
\(368\) −2.00000 + 3.46410i −0.104257 + 0.180579i
\(369\) 0 0
\(370\) 28.2843 1.47043
\(371\) 0 0
\(372\) 0 0
\(373\) −5.00000 8.66025i −0.258890 0.448411i 0.707055 0.707159i \(-0.250023\pi\)
−0.965945 + 0.258748i \(0.916690\pi\)
\(374\) 1.41421 2.44949i 0.0731272 0.126660i
\(375\) 0 0
\(376\) −1.41421 2.44949i −0.0729325 0.126323i
\(377\) 0 0
\(378\) 0 0
\(379\) −26.0000 −1.33553 −0.667765 0.744372i \(-0.732749\pi\)
−0.667765 + 0.744372i \(0.732749\pi\)
\(380\) −10.0000 17.3205i −0.512989 0.888523i
\(381\) 0 0
\(382\) 2.00000 3.46410i 0.102329 0.177239i
\(383\) −18.3848 31.8434i −0.939418 1.62712i −0.766559 0.642173i \(-0.778033\pi\)
−0.172859 0.984947i \(-0.555300\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 16.0000 0.814379
\(387\) 0 0
\(388\) −4.94975 + 8.57321i −0.251285 + 0.435239i
\(389\) 13.0000 22.5167i 0.659126 1.14164i −0.321716 0.946836i \(-0.604260\pi\)
0.980842 0.194804i \(-0.0624070\pi\)
\(390\) 0 0
\(391\) 5.65685 0.286079
\(392\) 0 0
\(393\) 0 0
\(394\) −1.00000 1.73205i −0.0503793 0.0872595i
\(395\) −5.65685 + 9.79796i −0.284627 + 0.492989i
\(396\) 0 0
\(397\) −11.3137 19.5959i −0.567819 0.983491i −0.996781 0.0801687i \(-0.974454\pi\)
0.428963 0.903322i \(-0.358879\pi\)
\(398\) −8.48528 −0.425329
\(399\) 0 0
\(400\) 3.00000 0.150000
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 4.24264 + 7.34847i 0.211079 + 0.365600i
\(405\) 0 0
\(406\) 0 0
\(407\) 20.0000 0.991363
\(408\) 0 0
\(409\) −19.0919 + 33.0681i −0.944033 + 1.63511i −0.186357 + 0.982482i \(0.559668\pi\)
−0.757676 + 0.652631i \(0.773665\pi\)
\(410\) −14.0000 + 24.2487i −0.691411 + 1.19756i
\(411\) 0 0
\(412\) 2.82843 0.139347
\(413\) 0 0
\(414\) 0 0
\(415\) −14.0000 24.2487i −0.687233 1.19032i
\(416\) 0 0
\(417\) 0 0
\(418\) −7.07107 12.2474i −0.345857 0.599042i
\(419\) 9.89949 0.483622 0.241811 0.970323i \(-0.422259\pi\)
0.241811 + 0.970323i \(0.422259\pi\)
\(420\) 0 0
\(421\) 30.0000 1.46211 0.731055 0.682318i \(-0.239028\pi\)
0.731055 + 0.682318i \(0.239028\pi\)
\(422\) −6.00000 10.3923i −0.292075 0.505889i
\(423\) 0 0
\(424\) 1.00000 1.73205i 0.0485643 0.0841158i
\(425\) −2.12132 3.67423i −0.102899 0.178227i
\(426\) 0 0
\(427\) 0 0
\(428\) 4.00000 0.193347
\(429\) 0 0
\(430\) −2.82843 + 4.89898i −0.136399 + 0.236250i
\(431\) 6.00000 10.3923i 0.289010 0.500580i −0.684564 0.728953i \(-0.740007\pi\)
0.973574 + 0.228373i \(0.0733406\pi\)
\(432\) 0 0
\(433\) −29.6985 −1.42722 −0.713609 0.700544i \(-0.752941\pi\)
−0.713609 + 0.700544i \(0.752941\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.00000 + 1.73205i 0.0478913 + 0.0829502i
\(437\) 14.1421 24.4949i 0.676510 1.17175i
\(438\) 0 0
\(439\) 8.48528 + 14.6969i 0.404980 + 0.701447i 0.994319 0.106439i \(-0.0339450\pi\)
−0.589339 + 0.807886i \(0.700612\pi\)
\(440\) 5.65685 0.269680
\(441\) 0 0
\(442\) 0 0
\(443\) −2.00000 3.46410i −0.0950229 0.164584i 0.814595 0.580030i \(-0.196959\pi\)
−0.909618 + 0.415445i \(0.863626\pi\)
\(444\) 0 0
\(445\) 10.0000 17.3205i 0.474045 0.821071i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) −9.89949 + 17.1464i −0.466149 + 0.807394i
\(452\) −6.00000 + 10.3923i −0.282216 + 0.488813i
\(453\) 0 0
\(454\) −21.2132 −0.995585
\(455\) 0 0
\(456\) 0 0
\(457\) −12.0000 20.7846i −0.561336 0.972263i −0.997380 0.0723376i \(-0.976954\pi\)
0.436044 0.899925i \(-0.356379\pi\)
\(458\) −8.48528 + 14.6969i −0.396491 + 0.686743i
\(459\) 0 0
\(460\) 5.65685 + 9.79796i 0.263752 + 0.456832i
\(461\) −39.5980 −1.84426 −0.922131 0.386878i \(-0.873553\pi\)
−0.922131 + 0.386878i \(0.873553\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 1.00000 + 1.73205i 0.0464238 + 0.0804084i
\(465\) 0 0
\(466\) −12.0000 + 20.7846i −0.555889 + 0.962828i
\(467\) 16.2635 + 28.1691i 0.752583 + 1.30351i 0.946567 + 0.322507i \(0.104526\pi\)
−0.193984 + 0.981005i \(0.562141\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −8.00000 −0.369012
\(471\) 0 0
\(472\) 0.707107 1.22474i 0.0325472 0.0563735i
\(473\) −2.00000 + 3.46410i −0.0919601 + 0.159280i
\(474\) 0 0
\(475\) −21.2132 −0.973329
\(476\) 0 0
\(477\) 0 0
\(478\) 6.00000 + 10.3923i 0.274434 + 0.475333i
\(479\) −15.5563 + 26.9444i −0.710788 + 1.23112i 0.253774 + 0.967264i \(0.418328\pi\)
−0.964562 + 0.263857i \(0.915005\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 21.2132 0.966235
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) 14.0000 + 24.2487i 0.635707 + 1.10108i
\(486\) 0 0
\(487\) −6.00000 + 10.3923i −0.271886 + 0.470920i −0.969345 0.245705i \(-0.920981\pi\)
0.697459 + 0.716625i \(0.254314\pi\)
\(488\) 1.41421 + 2.44949i 0.0640184 + 0.110883i
\(489\) 0 0
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) 1.41421 2.44949i 0.0636930 0.110319i
\(494\) 0 0
\(495\) 0 0
\(496\) 8.48528 0.381000
\(497\) 0 0
\(498\) 0 0
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) −2.82843 + 4.89898i −0.126491 + 0.219089i
\(501\) 0 0
\(502\) −4.94975 8.57321i −0.220918 0.382641i
\(503\) −39.5980 −1.76559 −0.882793 0.469762i \(-0.844340\pi\)
−0.882793 + 0.469762i \(0.844340\pi\)
\(504\) 0 0
\(505\) 24.0000 1.06799
\(506\) 4.00000 + 6.92820i 0.177822 + 0.307996i
\(507\) 0 0
\(508\) −8.00000 + 13.8564i −0.354943 + 0.614779i
\(509\) 11.3137 + 19.5959i 0.501471 + 0.868574i 0.999999 + 0.00169976i \(0.000541051\pi\)
−0.498527 + 0.866874i \(0.666126\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −6.36396 + 11.0227i −0.280702 + 0.486191i
\(515\) 4.00000 6.92820i 0.176261 0.305293i
\(516\) 0 0
\(517\) −5.65685 −0.248788
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.707107 + 1.22474i −0.0309789 + 0.0536570i −0.881099 0.472931i \(-0.843196\pi\)
0.850120 + 0.526589i \(0.176529\pi\)
\(522\) 0 0
\(523\) −6.36396 11.0227i −0.278277 0.481989i 0.692680 0.721245i \(-0.256430\pi\)
−0.970957 + 0.239256i \(0.923097\pi\)
\(524\) −12.7279 −0.556022
\(525\) 0 0
\(526\) 12.0000 0.523225
\(527\) −6.00000 10.3923i −0.261364 0.452696i
\(528\) 0 0
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) −2.82843 4.89898i −0.122859 0.212798i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 5.65685 9.79796i 0.244567 0.423603i
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) 0 0
\(538\) −11.3137 −0.487769
\(539\) 0 0
\(540\) 0 0
\(541\) −5.00000 8.66025i −0.214967 0.372333i 0.738296 0.674477i \(-0.235631\pi\)
−0.953262 + 0.302144i \(0.902298\pi\)
\(542\) 11.3137 19.5959i 0.485965 0.841717i
\(543\) 0 0
\(544\) 0.707107 + 1.22474i 0.0303170 + 0.0525105i
\(545\) 5.65685 0.242313
\(546\) 0 0
\(547\) −26.0000 −1.11168 −0.555840 0.831289i \(-0.687603\pi\)
−0.555840 + 0.831289i \(0.687603\pi\)
\(548\) 6.00000 + 10.3923i 0.256307 + 0.443937i
\(549\) 0 0
\(550\) 3.00000 5.19615i 0.127920 0.221565i
\(551\) −7.07107 12.2474i −0.301238 0.521759i
\(552\) 0 0
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) −4.94975 + 8.57321i −0.209916 + 0.363585i
\(557\) −15.0000 + 25.9808i −0.635570 + 1.10084i 0.350824 + 0.936442i \(0.385902\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −8.00000 13.8564i −0.337460 0.584497i
\(563\) −0.707107 + 1.22474i −0.0298010 + 0.0516168i −0.880541 0.473970i \(-0.842821\pi\)
0.850740 + 0.525586i \(0.176154\pi\)
\(564\) 0 0
\(565\) 16.9706 + 29.3939i 0.713957 + 1.23661i
\(566\) 1.41421 0.0594438
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) 5.00000 + 8.66025i 0.209611 + 0.363057i 0.951592 0.307364i \(-0.0994469\pi\)
−0.741981 + 0.670421i \(0.766114\pi\)
\(570\) 0 0
\(571\) 1.00000 1.73205i 0.0418487 0.0724841i −0.844342 0.535804i \(-0.820009\pi\)
0.886191 + 0.463320i \(0.153342\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 12.0000 0.500435
\(576\) 0 0
\(577\) 10.6066 18.3712i 0.441559 0.764802i −0.556247 0.831017i \(-0.687759\pi\)
0.997805 + 0.0662152i \(0.0210924\pi\)
\(578\) −7.50000 + 12.9904i −0.311959 + 0.540329i
\(579\) 0 0
\(580\) 5.65685 0.234888
\(581\) 0 0
\(582\) 0 0
\(583\) −2.00000 3.46410i −0.0828315 0.143468i
\(584\) −0.707107 + 1.22474i −0.0292603 + 0.0506803i
\(585\) 0 0
\(586\) 9.89949 + 17.1464i 0.408944 + 0.708312i
\(587\) 29.6985 1.22579 0.612894 0.790165i \(-0.290005\pi\)
0.612894 + 0.790165i \(0.290005\pi\)
\(588\) 0 0
\(589\) −60.0000 −2.47226
\(590\) −2.00000 3.46410i −0.0823387 0.142615i
\(591\) 0 0
\(592\) −5.00000 + 8.66025i −0.205499 + 0.355934i
\(593\) −3.53553 6.12372i −0.145187 0.251471i 0.784256 0.620438i \(-0.213045\pi\)
−0.929443 + 0.368967i \(0.879712\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −10.0000 −0.409616
\(597\) 0 0
\(598\) 0 0
\(599\) −8.00000 + 13.8564i −0.326871 + 0.566157i −0.981889 0.189456i \(-0.939328\pi\)
0.655018 + 0.755613i \(0.272661\pi\)
\(600\) 0 0
\(601\) 29.6985 1.21143 0.605713 0.795683i \(-0.292888\pi\)
0.605713 + 0.795683i \(0.292888\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 8.00000 + 13.8564i 0.325515 + 0.563809i
\(605\) −9.89949 + 17.1464i −0.402472 + 0.697101i
\(606\) 0 0
\(607\) 8.48528 + 14.6969i 0.344407 + 0.596530i 0.985246 0.171145i \(-0.0547467\pi\)
−0.640839 + 0.767675i \(0.721413\pi\)
\(608\) 7.07107 0.286770
\(609\) 0 0
\(610\) 8.00000 0.323911
\(611\) 0 0
\(612\) 0 0
\(613\) 15.0000 25.9808i 0.605844 1.04935i −0.386073 0.922468i \(-0.626169\pi\)
0.991917 0.126885i \(-0.0404979\pi\)
\(614\) −4.94975 8.57321i −0.199756 0.345987i
\(615\) 0 0
\(616\) 0 0
\(617\) 26.0000 1.04672 0.523360 0.852111i \(-0.324678\pi\)
0.523360 + 0.852111i \(0.324678\pi\)
\(618\) 0 0
\(619\) −9.19239 + 15.9217i −0.369473 + 0.639946i −0.989483 0.144647i \(-0.953795\pi\)
0.620010 + 0.784594i \(0.287129\pi\)
\(620\) 12.0000 20.7846i 0.481932 0.834730i
\(621\) 0 0
\(622\) −11.3137 −0.453638
\(623\) 0 0
\(624\) 0 0
\(625\) 15.5000 + 26.8468i 0.620000 + 1.07387i
\(626\) 6.36396 11.0227i 0.254355 0.440556i
\(627\) 0 0
\(628\) 5.65685 + 9.79796i 0.225733 + 0.390981i
\(629\) 14.1421 0.563884
\(630\) 0 0
\(631\) 44.0000 1.75161 0.875806 0.482663i \(-0.160330\pi\)
0.875806 + 0.482663i \(0.160330\pi\)
\(632\) −2.00000 3.46410i −0.0795557 0.137795i
\(633\) 0 0
\(634\) −5.00000 + 8.66025i −0.198575 + 0.343943i
\(635\) 22.6274 + 39.1918i 0.897942 + 1.55528i
\(636\) 0 0
\(637\) 0 0
\(638\) 4.00000 0.158362
\(639\) 0 0
\(640\) −1.41421 + 2.44949i −0.0559017 + 0.0968246i
\(641\) 13.0000 22.5167i 0.513469 0.889355i −0.486409 0.873731i \(-0.661693\pi\)
0.999878 0.0156233i \(-0.00497325\pi\)
\(642\) 0 0
\(643\) 9.89949 0.390398 0.195199 0.980764i \(-0.437465\pi\)
0.195199 + 0.980764i \(0.437465\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −5.00000 8.66025i −0.196722 0.340733i
\(647\) 4.24264 7.34847i 0.166795 0.288898i −0.770496 0.637445i \(-0.779991\pi\)
0.937291 + 0.348547i \(0.113325\pi\)
\(648\) 0 0
\(649\) −1.41421 2.44949i −0.0555127 0.0961509i
\(650\) 0 0
\(651\) 0 0
\(652\) 10.0000 0.391630
\(653\) −9.00000 15.5885i −0.352197 0.610023i 0.634437 0.772975i \(-0.281232\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(654\) 0 0
\(655\) −18.0000 + 31.1769i −0.703318 + 1.21818i
\(656\) −4.94975 8.57321i −0.193255 0.334728i
\(657\) 0 0
\(658\) 0 0
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 0 0
\(661\) −4.24264 + 7.34847i −0.165020 + 0.285822i −0.936662 0.350234i \(-0.886102\pi\)
0.771643 + 0.636056i \(0.219435\pi\)
\(662\) 5.00000 8.66025i 0.194331 0.336590i
\(663\) 0 0
\(664\) 9.89949 0.384175
\(665\) 0 0
\(666\) 0 0
\(667\) 4.00000 + 6.92820i 0.154881 + 0.268261i
\(668\) −9.89949 + 17.1464i −0.383023 + 0.663415i
\(669\) 0 0
\(670\) −16.9706 29.3939i −0.655630 1.13558i
\(671\) 5.65685 0.218380
\(672\) 0 0
\(673\) −12.0000 −0.462566 −0.231283 0.972887i \(-0.574292\pi\)
−0.231283 + 0.972887i \(0.574292\pi\)
\(674\) 1.00000 + 1.73205i 0.0385186 + 0.0667161i
\(675\) 0 0
\(676\) 6.50000 11.2583i 0.250000 0.433013i
\(677\) −8.48528 14.6969i −0.326116 0.564849i 0.655622 0.755090i \(-0.272407\pi\)
−0.981738 + 0.190240i \(0.939073\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 4.00000 0.153393
\(681\) 0 0
\(682\) 8.48528 14.6969i 0.324918 0.562775i
\(683\) 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) 0 0
\(685\) 33.9411 1.29682
\(686\) 0 0
\(687\) 0 0
\(688\) −1.00000 1.73205i −0.0381246 0.0660338i
\(689\) 0 0
\(690\) 0 0
\(691\) −6.36396 11.0227i −0.242096 0.419323i 0.719215 0.694788i \(-0.244502\pi\)
−0.961311 + 0.275464i \(0.911168\pi\)
\(692\) 16.9706 0.645124
\(693\) 0 0
\(694\) −30.0000 −1.13878
\(695\) 14.0000 + 24.2487i 0.531050 + 0.919806i
\(696\) 0 0
\(697\) −7.00000 + 12.1244i −0.265144 + 0.459243i
\(698\) 0 0
\(699\) 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
\(703\) 35.3553 61.2372i 1.33345 2.30961i
\(704\) −1.00000 + 1.73205i −0.0376889 + 0.0652791i
\(705\) 0 0
\(706\) −1.41421 −0.0532246
\(707\) 0 0
\(708\) 0 0
\(709\) −5.00000 8.66025i −0.187779 0.325243i 0.756730 0.653727i \(-0.226796\pi\)
−0.944509 + 0.328484i \(0.893462\pi\)
\(710\) −16.9706 + 29.3939i −0.636894 + 1.10313i
\(711\) 0 0
\(712\) 3.53553 + 6.12372i 0.132500 + 0.229496i
\(713\) 33.9411 1.27111
\(714\) 0 0
\(715\) 0 0
\(716\) 6.00000 + 10.3923i 0.224231 + 0.388379i
\(717\) 0 0
\(718\) 16.0000 27.7128i 0.597115 1.03423i
\(719\) 1.41421 + 2.44949i 0.0527413 + 0.0913506i 0.891191 0.453629i \(-0.149871\pi\)
−0.838449 + 0.544979i \(0.816537\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −31.0000 −1.15370
\(723\) 0 0
\(724\) 0 0
\(725\) 3.00000 5.19615i 0.111417 0.192980i
\(726\) 0 0
\(727\) −19.7990 −0.734304 −0.367152 0.930161i \(-0.619667\pi\)
−0.367152 + 0.930161i \(0.619667\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 2.00000 + 3.46410i 0.0740233 + 0.128212i
\(731\) −1.41421 + 2.44949i −0.0523066 + 0.0905977i
\(732\) 0 0
\(733\) −21.2132 36.7423i −0.783528 1.35711i −0.929875 0.367876i \(-0.880085\pi\)
0.146347 0.989233i \(-0.453248\pi\)
\(734\) −28.2843 −1.04399
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) −12.0000 20.7846i −0.442026 0.765611i
\(738\) 0 0
\(739\) 15.0000 25.9808i 0.551784 0.955718i −0.446362 0.894852i \(-0.647281\pi\)
0.998146 0.0608653i \(-0.0193860\pi\)
\(740\) 14.1421 + 24.4949i 0.519875 + 0.900450i
\(741\) 0 0
\(742\) 0 0
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) 0 0
\(745\) −14.1421 + 24.4949i −0.518128 + 0.897424i
\(746\) 5.00000 8.66025i 0.183063 0.317074i
\(747\) 0 0
\(748\) 2.82843 0.103418
\(749\) 0 0
\(750\) 0 0
\(751\) 2.00000 + 3.46410i 0.0729810 + 0.126407i 0.900207 0.435463i \(-0.143415\pi\)
−0.827225 + 0.561870i \(0.810082\pi\)
\(752\) 1.41421 2.44949i 0.0515711 0.0893237i
\(753\) 0 0
\(754\) 0 0
\(755\) 45.2548 1.64699
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −13.0000 22.5167i −0.472181 0.817842i
\(759\) 0 0
\(760\) 10.0000 17.3205i 0.362738 0.628281i
\(761\) −3.53553 6.12372i −0.128163 0.221985i 0.794802 0.606869i \(-0.207575\pi\)
−0.922965 + 0.384884i \(0.874241\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 4.00000 0.144715
\(765\) 0 0
\(766\) 18.3848 31.8434i 0.664269 1.15055i
\(767\) 0 0
\(768\) 0 0
\(769\) 29.6985 1.07095 0.535477 0.844550i \(-0.320132\pi\)
0.535477 + 0.844550i \(0.320132\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 8.00000 + 13.8564i 0.287926 + 0.498703i
\(773\) 24.0416 41.6413i 0.864717 1.49773i −0.00261021 0.999997i \(-0.500831\pi\)
0.867328 0.497738i \(-0.165836\pi\)
\(774\) 0 0
\(775\) −12.7279 22.0454i −0.457200 0.791894i
\(776\) −9.89949 −0.355371
\(777\) 0 0
\(778\) 26.0000 0.932145
\(779\) 35.0000 + 60.6218i 1.25401 + 2.17200i
\(780\) 0 0
\(781\) −12.0000 + 20.7846i −0.429394 + 0.743732i
\(782\) 2.82843 + 4.89898i 0.101144 + 0.175187i
\(783\) 0 0
\(784\) 0 0
\(785\) 32.0000 1.14213
\(786\) 0 0
\(787\) 0.707107 1.22474i 0.0252056 0.0436574i −0.853147 0.521670i \(-0.825309\pi\)
0.878353 + 0.478012i \(0.158643\pi\)
\(788\) 1.00000 1.73205i 0.0356235 0.0617018i
\(789\) 0 0
\(790\) −11.3137 −0.402524
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 11.3137 19.5959i 0.401508 0.695433i
\(795\) 0 0
\(796\) −4.24264 7.34847i −0.150376 0.260460i
\(797\) 0 0