Properties

Label 567.2.s.d.458.1
Level $567$
Weight $2$
Character 567.458
Analytic conductor $4.528$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 458.1
Root \(-1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 567.458
Dual form 567.2.s.d.26.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +2.44949 q^{5} +(2.50000 - 0.866025i) q^{7} +2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +2.44949 q^{5} +(2.50000 - 0.866025i) q^{7} +2.82843i q^{8} +(-3.00000 - 1.73205i) q^{10} +1.41421i q^{11} +(4.50000 + 2.59808i) q^{13} +(-3.67423 - 0.707107i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-2.44949 + 4.24264i) q^{17} +(1.50000 - 0.866025i) q^{19} +(1.00000 - 1.73205i) q^{22} +5.65685i q^{23} +1.00000 q^{25} +(-3.67423 - 6.36396i) q^{26} +(-2.44949 + 1.41421i) q^{29} +(-1.50000 + 0.866025i) q^{31} +(6.00000 - 3.46410i) q^{34} +(6.12372 - 2.12132i) q^{35} +(0.500000 + 0.866025i) q^{37} -2.44949 q^{38} +6.92820i q^{40} +(3.67423 - 6.36396i) q^{41} +(0.500000 + 0.866025i) q^{43} +(4.00000 - 6.92820i) q^{46} +(6.12372 - 10.6066i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-1.22474 - 0.707107i) q^{50} +(2.44949 + 1.41421i) q^{53} +3.46410i q^{55} +(2.44949 + 7.07107i) q^{56} +4.00000 q^{58} +(-2.44949 - 4.24264i) q^{59} +(3.00000 + 1.73205i) q^{61} +2.44949 q^{62} -8.00000 q^{64} +(11.0227 + 6.36396i) q^{65} +(-5.50000 - 9.52628i) q^{67} +(-9.00000 - 1.73205i) q^{70} -7.07107i q^{71} +(1.50000 + 0.866025i) q^{73} -1.41421i q^{74} +(1.22474 + 3.53553i) q^{77} +(-2.50000 + 4.33013i) q^{79} +(4.89898 - 8.48528i) q^{80} +(-9.00000 + 5.19615i) q^{82} +(-3.67423 - 6.36396i) q^{83} +(-6.00000 + 10.3923i) q^{85} -1.41421i q^{86} -4.00000 q^{88} +(2.44949 + 4.24264i) q^{89} +(13.5000 + 2.59808i) q^{91} +(-15.0000 + 8.66025i) q^{94} +(3.67423 - 2.12132i) q^{95} +(-9.00000 + 5.19615i) q^{97} +(-9.79796 + 1.41421i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 10q^{7} + O(q^{10}) \) \( 4q + 10q^{7} - 12q^{10} + 18q^{13} + 8q^{16} + 6q^{19} + 4q^{22} + 4q^{25} - 6q^{31} + 24q^{34} + 2q^{37} + 2q^{43} + 16q^{46} + 22q^{49} + 16q^{58} + 12q^{61} - 32q^{64} - 22q^{67} - 36q^{70} + 6q^{73} - 10q^{79} - 36q^{82} - 24q^{85} - 16q^{88} + 54q^{91} - 60q^{94} - 36q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 0.707107i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(3\) 0 0
\(4\) 0 0
\(5\) 2.44949 1.09545 0.547723 0.836660i \(-0.315495\pi\)
0.547723 + 0.836660i \(0.315495\pi\)
\(6\) 0 0
\(7\) 2.50000 0.866025i 0.944911 0.327327i
\(8\) 2.82843i 1.00000i
\(9\) 0 0
\(10\) −3.00000 1.73205i −0.948683 0.547723i
\(11\) 1.41421i 0.426401i 0.977008 + 0.213201i \(0.0683888\pi\)
−0.977008 + 0.213201i \(0.931611\pi\)
\(12\) 0 0
\(13\) 4.50000 + 2.59808i 1.24808 + 0.720577i 0.970725 0.240192i \(-0.0772105\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −3.67423 0.707107i −0.981981 0.188982i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −2.44949 + 4.24264i −0.594089 + 1.02899i 0.399586 + 0.916696i \(0.369154\pi\)
−0.993675 + 0.112296i \(0.964180\pi\)
\(18\) 0 0
\(19\) 1.50000 0.866025i 0.344124 0.198680i −0.317970 0.948101i \(-0.603001\pi\)
0.662094 + 0.749421i \(0.269668\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.00000 1.73205i 0.213201 0.369274i
\(23\) 5.65685i 1.17954i 0.807573 + 0.589768i \(0.200781\pi\)
−0.807573 + 0.589768i \(0.799219\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −3.67423 6.36396i −0.720577 1.24808i
\(27\) 0 0
\(28\) 0 0
\(29\) −2.44949 + 1.41421i −0.454859 + 0.262613i −0.709880 0.704323i \(-0.751251\pi\)
0.255021 + 0.966935i \(0.417918\pi\)
\(30\) 0 0
\(31\) −1.50000 + 0.866025i −0.269408 + 0.155543i −0.628619 0.777714i \(-0.716379\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 6.00000 3.46410i 1.02899 0.594089i
\(35\) 6.12372 2.12132i 1.03510 0.358569i
\(36\) 0 0
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) −2.44949 −0.397360
\(39\) 0 0
\(40\) 6.92820i 1.09545i
\(41\) 3.67423 6.36396i 0.573819 0.993884i −0.422350 0.906433i \(-0.638795\pi\)
0.996169 0.0874508i \(-0.0278721\pi\)
\(42\) 0 0
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 4.00000 6.92820i 0.589768 1.02151i
\(47\) 6.12372 10.6066i 0.893237 1.54713i 0.0572655 0.998359i \(-0.481762\pi\)
0.835971 0.548773i \(-0.184905\pi\)
\(48\) 0 0
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) −1.22474 0.707107i −0.173205 0.100000i
\(51\) 0 0
\(52\) 0 0
\(53\) 2.44949 + 1.41421i 0.336463 + 0.194257i 0.658707 0.752400i \(-0.271104\pi\)
−0.322244 + 0.946657i \(0.604437\pi\)
\(54\) 0 0
\(55\) 3.46410i 0.467099i
\(56\) 2.44949 + 7.07107i 0.327327 + 0.944911i
\(57\) 0 0
\(58\) 4.00000 0.525226
\(59\) −2.44949 4.24264i −0.318896 0.552345i 0.661362 0.750067i \(-0.269979\pi\)
−0.980258 + 0.197722i \(0.936646\pi\)
\(60\) 0 0
\(61\) 3.00000 + 1.73205i 0.384111 + 0.221766i 0.679605 0.733578i \(-0.262151\pi\)
−0.295495 + 0.955344i \(0.595484\pi\)
\(62\) 2.44949 0.311086
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 11.0227 + 6.36396i 1.36720 + 0.789352i
\(66\) 0 0
\(67\) −5.50000 9.52628i −0.671932 1.16382i −0.977356 0.211604i \(-0.932131\pi\)
0.305424 0.952217i \(-0.401202\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −9.00000 1.73205i −1.07571 0.207020i
\(71\) 7.07107i 0.839181i −0.907713 0.419591i \(-0.862174\pi\)
0.907713 0.419591i \(-0.137826\pi\)
\(72\) 0 0
\(73\) 1.50000 + 0.866025i 0.175562 + 0.101361i 0.585206 0.810885i \(-0.301014\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) 1.41421i 0.164399i
\(75\) 0 0
\(76\) 0 0
\(77\) 1.22474 + 3.53553i 0.139573 + 0.402911i
\(78\) 0 0
\(79\) −2.50000 + 4.33013i −0.281272 + 0.487177i −0.971698 0.236225i \(-0.924090\pi\)
0.690426 + 0.723403i \(0.257423\pi\)
\(80\) 4.89898 8.48528i 0.547723 0.948683i
\(81\) 0 0
\(82\) −9.00000 + 5.19615i −0.993884 + 0.573819i
\(83\) −3.67423 6.36396i −0.403300 0.698535i 0.590822 0.806802i \(-0.298803\pi\)
−0.994122 + 0.108266i \(0.965470\pi\)
\(84\) 0 0
\(85\) −6.00000 + 10.3923i −0.650791 + 1.12720i
\(86\) 1.41421i 0.152499i
\(87\) 0 0
\(88\) −4.00000 −0.426401
\(89\) 2.44949 + 4.24264i 0.259645 + 0.449719i 0.966147 0.257993i \(-0.0830610\pi\)
−0.706502 + 0.707712i \(0.749728\pi\)
\(90\) 0 0
\(91\) 13.5000 + 2.59808i 1.41518 + 0.272352i
\(92\) 0 0
\(93\) 0 0
\(94\) −15.0000 + 8.66025i −1.54713 + 0.893237i
\(95\) 3.67423 2.12132i 0.376969 0.217643i
\(96\) 0 0
\(97\) −9.00000 + 5.19615i −0.913812 + 0.527589i −0.881656 0.471894i \(-0.843571\pi\)
−0.0321560 + 0.999483i \(0.510237\pi\)
\(98\) −9.79796 + 1.41421i −0.989743 + 0.142857i
\(99\) 0 0
\(100\) 0 0
\(101\) −17.1464 −1.70613 −0.853067 0.521802i \(-0.825260\pi\)
−0.853067 + 0.521802i \(0.825260\pi\)
\(102\) 0 0
\(103\) 8.66025i 0.853320i −0.904412 0.426660i \(-0.859690\pi\)
0.904412 0.426660i \(-0.140310\pi\)
\(104\) −7.34847 + 12.7279i −0.720577 + 1.24808i
\(105\) 0 0
\(106\) −2.00000 3.46410i −0.194257 0.336463i
\(107\) −2.44949 + 1.41421i −0.236801 + 0.136717i −0.613706 0.789535i \(-0.710322\pi\)
0.376905 + 0.926252i \(0.376988\pi\)
\(108\) 0 0
\(109\) 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i \(-0.818083\pi\)
0.888977 + 0.457951i \(0.151417\pi\)
\(110\) 2.44949 4.24264i 0.233550 0.404520i
\(111\) 0 0
\(112\) 2.00000 10.3923i 0.188982 0.981981i
\(113\) −1.22474 0.707107i −0.115214 0.0665190i 0.441285 0.897367i \(-0.354523\pi\)
−0.556500 + 0.830848i \(0.687856\pi\)
\(114\) 0 0
\(115\) 13.8564i 1.29212i
\(116\) 0 0
\(117\) 0 0
\(118\) 6.92820i 0.637793i
\(119\) −2.44949 + 12.7279i −0.224544 + 1.16677i
\(120\) 0 0
\(121\) 9.00000 0.818182
\(122\) −2.44949 4.24264i −0.221766 0.384111i
\(123\) 0 0
\(124\) 0 0
\(125\) −9.79796 −0.876356
\(126\) 0 0
\(127\) 11.0000 0.976092 0.488046 0.872818i \(-0.337710\pi\)
0.488046 + 0.872818i \(0.337710\pi\)
\(128\) 9.79796 + 5.65685i 0.866025 + 0.500000i
\(129\) 0 0
\(130\) −9.00000 15.5885i −0.789352 1.36720i
\(131\) 2.44949 0.214013 0.107006 0.994258i \(-0.465873\pi\)
0.107006 + 0.994258i \(0.465873\pi\)
\(132\) 0 0
\(133\) 3.00000 3.46410i 0.260133 0.300376i
\(134\) 15.5563i 1.34386i
\(135\) 0 0
\(136\) −12.0000 6.92820i −1.02899 0.594089i
\(137\) 11.3137i 0.966595i −0.875456 0.483298i \(-0.839439\pi\)
0.875456 0.483298i \(-0.160561\pi\)
\(138\) 0 0
\(139\) 4.50000 + 2.59808i 0.381685 + 0.220366i 0.678551 0.734553i \(-0.262608\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −5.00000 + 8.66025i −0.419591 + 0.726752i
\(143\) −3.67423 + 6.36396i −0.307255 + 0.532181i
\(144\) 0 0
\(145\) −6.00000 + 3.46410i −0.498273 + 0.287678i
\(146\) −1.22474 2.12132i −0.101361 0.175562i
\(147\) 0 0
\(148\) 0 0
\(149\) 5.65685i 0.463428i 0.972784 + 0.231714i \(0.0744333\pi\)
−0.972784 + 0.231714i \(0.925567\pi\)
\(150\) 0 0
\(151\) −22.0000 −1.79033 −0.895167 0.445730i \(-0.852944\pi\)
−0.895167 + 0.445730i \(0.852944\pi\)
\(152\) 2.44949 + 4.24264i 0.198680 + 0.344124i
\(153\) 0 0
\(154\) 1.00000 5.19615i 0.0805823 0.418718i
\(155\) −3.67423 + 2.12132i −0.295122 + 0.170389i
\(156\) 0 0
\(157\) −15.0000 + 8.66025i −1.19713 + 0.691164i −0.959914 0.280293i \(-0.909568\pi\)
−0.237216 + 0.971457i \(0.576235\pi\)
\(158\) 6.12372 3.53553i 0.487177 0.281272i
\(159\) 0 0
\(160\) 0 0
\(161\) 4.89898 + 14.1421i 0.386094 + 1.11456i
\(162\) 0 0
\(163\) 5.00000 + 8.66025i 0.391630 + 0.678323i 0.992665 0.120900i \(-0.0385779\pi\)
−0.601035 + 0.799223i \(0.705245\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 10.3923i 0.806599i
\(167\) 3.67423 6.36396i 0.284321 0.492458i −0.688123 0.725594i \(-0.741565\pi\)
0.972444 + 0.233136i \(0.0748986\pi\)
\(168\) 0 0
\(169\) 7.00000 + 12.1244i 0.538462 + 0.932643i
\(170\) 14.6969 8.48528i 1.12720 0.650791i
\(171\) 0 0
\(172\) 0 0
\(173\) −4.89898 + 8.48528i −0.372463 + 0.645124i −0.989944 0.141462i \(-0.954820\pi\)
0.617481 + 0.786586i \(0.288153\pi\)
\(174\) 0 0
\(175\) 2.50000 0.866025i 0.188982 0.0654654i
\(176\) 4.89898 + 2.82843i 0.369274 + 0.213201i
\(177\) 0 0
\(178\) 6.92820i 0.519291i
\(179\) −8.57321 4.94975i −0.640792 0.369961i 0.144127 0.989559i \(-0.453962\pi\)
−0.784920 + 0.619598i \(0.787296\pi\)
\(180\) 0 0
\(181\) 15.5885i 1.15868i 0.815086 + 0.579340i \(0.196690\pi\)
−0.815086 + 0.579340i \(0.803310\pi\)
\(182\) −14.6969 12.7279i −1.08941 0.943456i
\(183\) 0 0
\(184\) −16.0000 −1.17954
\(185\) 1.22474 + 2.12132i 0.0900450 + 0.155963i
\(186\) 0 0
\(187\) −6.00000 3.46410i −0.438763 0.253320i
\(188\) 0 0
\(189\) 0 0
\(190\) −6.00000 −0.435286
\(191\) −1.22474 0.707107i −0.0886194 0.0511645i 0.455035 0.890473i \(-0.349627\pi\)
−0.543655 + 0.839309i \(0.682960\pi\)
\(192\) 0 0
\(193\) −5.50000 9.52628i −0.395899 0.685717i 0.597317 0.802005i \(-0.296234\pi\)
−0.993215 + 0.116289i \(0.962900\pi\)
\(194\) 14.6969 1.05518
\(195\) 0 0
\(196\) 0 0
\(197\) 19.7990i 1.41062i −0.708899 0.705310i \(-0.750808\pi\)
0.708899 0.705310i \(-0.249192\pi\)
\(198\) 0 0
\(199\) −12.0000 6.92820i −0.850657 0.491127i 0.0102152 0.999948i \(-0.496748\pi\)
−0.860873 + 0.508821i \(0.830082\pi\)
\(200\) 2.82843i 0.200000i
\(201\) 0 0
\(202\) 21.0000 + 12.1244i 1.47755 + 0.853067i
\(203\) −4.89898 + 5.65685i −0.343841 + 0.397033i
\(204\) 0 0
\(205\) 9.00000 15.5885i 0.628587 1.08875i
\(206\) −6.12372 + 10.6066i −0.426660 + 0.738997i
\(207\) 0 0
\(208\) 18.0000 10.3923i 1.24808 0.720577i
\(209\) 1.22474 + 2.12132i 0.0847174 + 0.146735i
\(210\) 0 0
\(211\) 11.0000 19.0526i 0.757271 1.31163i −0.186966 0.982366i \(-0.559865\pi\)
0.944237 0.329266i \(-0.106801\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 4.00000 0.273434
\(215\) 1.22474 + 2.12132i 0.0835269 + 0.144673i
\(216\) 0 0
\(217\) −3.00000 + 3.46410i −0.203653 + 0.235159i
\(218\) −1.22474 + 0.707107i −0.0829502 + 0.0478913i
\(219\) 0 0
\(220\) 0 0
\(221\) −22.0454 + 12.7279i −1.48293 + 0.856173i
\(222\) 0 0
\(223\) 18.0000 10.3923i 1.20537 0.695920i 0.243625 0.969870i \(-0.421663\pi\)
0.961744 + 0.273949i \(0.0883300\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.00000 + 1.73205i 0.0665190 + 0.115214i
\(227\) 26.9444 1.78836 0.894181 0.447706i \(-0.147759\pi\)
0.894181 + 0.447706i \(0.147759\pi\)
\(228\) 0 0
\(229\) 22.5167i 1.48794i 0.668211 + 0.743971i \(0.267060\pi\)
−0.668211 + 0.743971i \(0.732940\pi\)
\(230\) 9.79796 16.9706i 0.646058 1.11901i
\(231\) 0 0
\(232\) −4.00000 6.92820i −0.262613 0.454859i
\(233\) 8.57321 4.94975i 0.561650 0.324269i −0.192158 0.981364i \(-0.561548\pi\)
0.753807 + 0.657095i \(0.228215\pi\)
\(234\) 0 0
\(235\) 15.0000 25.9808i 0.978492 1.69480i
\(236\) 0 0
\(237\) 0 0
\(238\) 12.0000 13.8564i 0.777844 0.898177i
\(239\) −23.2702 13.4350i −1.50522 0.869040i −0.999982 0.00606055i \(-0.998071\pi\)
−0.505239 0.862979i \(-0.668596\pi\)
\(240\) 0 0
\(241\) 13.8564i 0.892570i 0.894891 + 0.446285i \(0.147253\pi\)
−0.894891 + 0.446285i \(0.852747\pi\)
\(242\) −11.0227 6.36396i −0.708566 0.409091i
\(243\) 0 0
\(244\) 0 0
\(245\) 13.4722 10.6066i 0.860707 0.677631i
\(246\) 0 0
\(247\) 9.00000 0.572656
\(248\) −2.44949 4.24264i −0.155543 0.269408i
\(249\) 0 0
\(250\) 12.0000 + 6.92820i 0.758947 + 0.438178i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) −8.00000 −0.502956
\(254\) −13.4722 7.77817i −0.845321 0.488046i
\(255\) 0 0
\(256\) 0 0
\(257\) 2.44949 0.152795 0.0763975 0.997077i \(-0.475658\pi\)
0.0763975 + 0.997077i \(0.475658\pi\)
\(258\) 0 0
\(259\) 2.00000 + 1.73205i 0.124274 + 0.107624i
\(260\) 0 0
\(261\) 0 0
\(262\) −3.00000 1.73205i −0.185341 0.107006i
\(263\) 14.1421i 0.872041i 0.899937 + 0.436021i \(0.143613\pi\)
−0.899937 + 0.436021i \(0.856387\pi\)
\(264\) 0 0
\(265\) 6.00000 + 3.46410i 0.368577 + 0.212798i
\(266\) −6.12372 + 2.12132i −0.375470 + 0.130066i
\(267\) 0 0
\(268\) 0 0
\(269\) 8.57321 14.8492i 0.522718 0.905374i −0.476932 0.878940i \(-0.658251\pi\)
0.999651 0.0264343i \(-0.00841529\pi\)
\(270\) 0 0
\(271\) −12.0000 + 6.92820i −0.728948 + 0.420858i −0.818037 0.575165i \(-0.804938\pi\)
0.0890891 + 0.996024i \(0.471604\pi\)
\(272\) 9.79796 + 16.9706i 0.594089 + 1.02899i
\(273\) 0 0
\(274\) −8.00000 + 13.8564i −0.483298 + 0.837096i
\(275\) 1.41421i 0.0852803i
\(276\) 0 0
\(277\) 23.0000 1.38194 0.690968 0.722885i \(-0.257185\pi\)
0.690968 + 0.722885i \(0.257185\pi\)
\(278\) −3.67423 6.36396i −0.220366 0.381685i
\(279\) 0 0
\(280\) 6.00000 + 17.3205i 0.358569 + 1.03510i
\(281\) 19.5959 11.3137i 1.16899 0.674919i 0.215551 0.976492i \(-0.430845\pi\)
0.953443 + 0.301573i \(0.0975118\pi\)
\(282\) 0 0
\(283\) −1.50000 + 0.866025i −0.0891657 + 0.0514799i −0.543920 0.839137i \(-0.683060\pi\)
0.454754 + 0.890617i \(0.349727\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 9.00000 5.19615i 0.532181 0.307255i
\(287\) 3.67423 19.0919i 0.216883 1.12696i
\(288\) 0 0
\(289\) −3.50000 6.06218i −0.205882 0.356599i
\(290\) 9.79796 0.575356
\(291\) 0 0
\(292\) 0 0
\(293\) −7.34847 + 12.7279i −0.429302 + 0.743573i −0.996811 0.0797939i \(-0.974574\pi\)
0.567509 + 0.823367i \(0.307907\pi\)
\(294\) 0 0
\(295\) −6.00000 10.3923i −0.349334 0.605063i
\(296\) −2.44949 + 1.41421i −0.142374 + 0.0821995i
\(297\) 0 0
\(298\) 4.00000 6.92820i 0.231714 0.401340i
\(299\) −14.6969 + 25.4558i −0.849946 + 1.47215i
\(300\) 0 0
\(301\) 2.00000 + 1.73205i 0.115278 + 0.0998337i
\(302\) 26.9444 + 15.5563i 1.55048 + 0.895167i
\(303\) 0 0
\(304\) 6.92820i 0.397360i
\(305\) 7.34847 + 4.24264i 0.420772 + 0.242933i
\(306\) 0 0
\(307\) 15.5885i 0.889680i −0.895610 0.444840i \(-0.853260\pi\)
0.895610 0.444840i \(-0.146740\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 6.00000 0.340777
\(311\) 8.57321 + 14.8492i 0.486142 + 0.842023i 0.999873 0.0159282i \(-0.00507031\pi\)
−0.513731 + 0.857951i \(0.671737\pi\)
\(312\) 0 0
\(313\) −10.5000 6.06218i −0.593495 0.342655i 0.172983 0.984925i \(-0.444659\pi\)
−0.766478 + 0.642270i \(0.777993\pi\)
\(314\) 24.4949 1.38233
\(315\) 0 0
\(316\) 0 0
\(317\) −12.2474 7.07107i −0.687885 0.397151i 0.114934 0.993373i \(-0.463334\pi\)
−0.802819 + 0.596222i \(0.796668\pi\)
\(318\) 0 0
\(319\) −2.00000 3.46410i −0.111979 0.193952i
\(320\) −19.5959 −1.09545
\(321\) 0 0
\(322\) 4.00000 20.7846i 0.222911 1.15828i
\(323\) 8.48528i 0.472134i
\(324\) 0 0
\(325\) 4.50000 + 2.59808i 0.249615 + 0.144115i
\(326\) 14.1421i 0.783260i
\(327\) 0 0
\(328\) 18.0000 + 10.3923i 0.993884 + 0.573819i
\(329\) 6.12372 31.8198i 0.337612 1.75428i
\(330\) 0 0
\(331\) 15.5000 26.8468i 0.851957 1.47563i −0.0274825 0.999622i \(-0.508749\pi\)
0.879440 0.476011i \(-0.157918\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −9.00000 + 5.19615i −0.492458 + 0.284321i
\(335\) −13.4722 23.3345i −0.736065 1.27490i
\(336\) 0 0
\(337\) −11.5000 + 19.9186i −0.626445 + 1.08503i 0.361815 + 0.932250i \(0.382157\pi\)
−0.988260 + 0.152784i \(0.951176\pi\)
\(338\) 19.7990i 1.07692i
\(339\) 0 0
\(340\) 0 0
\(341\) −1.22474 2.12132i −0.0663237 0.114876i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) −2.44949 + 1.41421i −0.132068 + 0.0762493i
\(345\) 0 0
\(346\) 12.0000 6.92820i 0.645124 0.372463i
\(347\) 26.9444 15.5563i 1.44645 0.835109i 0.448183 0.893942i \(-0.352071\pi\)
0.998268 + 0.0588334i \(0.0187381\pi\)
\(348\) 0 0
\(349\) −9.00000 + 5.19615i −0.481759 + 0.278144i −0.721149 0.692780i \(-0.756386\pi\)
0.239390 + 0.970923i \(0.423052\pi\)
\(350\) −3.67423 0.707107i −0.196396 0.0377964i
\(351\) 0 0
\(352\) 0 0
\(353\) −17.1464 −0.912612 −0.456306 0.889823i \(-0.650828\pi\)
−0.456306 + 0.889823i \(0.650828\pi\)
\(354\) 0 0
\(355\) 17.3205i 0.919277i
\(356\) 0 0
\(357\) 0 0
\(358\) 7.00000 + 12.1244i 0.369961 + 0.640792i
\(359\) −24.4949 + 14.1421i −1.29279 + 0.746393i −0.979148 0.203148i \(-0.934883\pi\)
−0.313643 + 0.949541i \(0.601550\pi\)
\(360\) 0 0
\(361\) −8.00000 + 13.8564i −0.421053 + 0.729285i
\(362\) 11.0227 19.0919i 0.579340 1.00345i
\(363\) 0 0
\(364\) 0 0
\(365\) 3.67423 + 2.12132i 0.192318 + 0.111035i
\(366\) 0 0
\(367\) 1.73205i 0.0904123i −0.998978 0.0452062i \(-0.985606\pi\)
0.998978 0.0452062i \(-0.0143945\pi\)
\(368\) 19.5959 + 11.3137i 1.02151 + 0.589768i
\(369\) 0 0
\(370\) 3.46410i 0.180090i
\(371\) 7.34847 + 1.41421i 0.381514 + 0.0734223i
\(372\) 0 0
\(373\) 29.0000 1.50156 0.750782 0.660551i \(-0.229677\pi\)
0.750782 + 0.660551i \(0.229677\pi\)
\(374\) 4.89898 + 8.48528i 0.253320 + 0.438763i
\(375\) 0 0
\(376\) 30.0000 + 17.3205i 1.54713 + 0.893237i
\(377\) −14.6969 −0.756931
\(378\) 0 0
\(379\) −7.00000 −0.359566 −0.179783 0.983706i \(-0.557540\pi\)
−0.179783 + 0.983706i \(0.557540\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.00000 + 1.73205i 0.0511645 + 0.0886194i
\(383\) −19.5959 −1.00130 −0.500652 0.865648i \(-0.666906\pi\)
−0.500652 + 0.865648i \(0.666906\pi\)
\(384\) 0 0
\(385\) 3.00000 + 8.66025i 0.152894 + 0.441367i
\(386\) 15.5563i 0.791797i
\(387\) 0 0
\(388\) 0 0
\(389\) 26.8701i 1.36237i 0.732113 + 0.681183i \(0.238534\pi\)
−0.732113 + 0.681183i \(0.761466\pi\)
\(390\) 0 0
\(391\) −24.0000 13.8564i −1.21373 0.700749i
\(392\) 12.2474 + 15.5563i 0.618590 + 0.785714i
\(393\) 0 0
\(394\) −14.0000 + 24.2487i −0.705310 + 1.22163i
\(395\) −6.12372 + 10.6066i −0.308118 + 0.533676i
\(396\) 0 0
\(397\) 1.50000 0.866025i 0.0752828 0.0434646i −0.461886 0.886939i \(-0.652827\pi\)
0.537169 + 0.843475i \(0.319494\pi\)
\(398\) 9.79796 + 16.9706i 0.491127 + 0.850657i
\(399\) 0 0
\(400\) 2.00000 3.46410i 0.100000 0.173205i
\(401\) 19.7990i 0.988714i −0.869259 0.494357i \(-0.835403\pi\)
0.869259 0.494357i \(-0.164597\pi\)
\(402\) 0 0
\(403\) −9.00000 −0.448322
\(404\) 0 0
\(405\) 0 0
\(406\) 10.0000 3.46410i 0.496292 0.171920i
\(407\) −1.22474 + 0.707107i −0.0607083 + 0.0350500i
\(408\) 0 0
\(409\) −28.5000 + 16.4545i −1.40923 + 0.813622i −0.995314 0.0966915i \(-0.969174\pi\)
−0.413920 + 0.910313i \(0.635841\pi\)
\(410\) −22.0454 + 12.7279i −1.08875 + 0.628587i
\(411\) 0 0
\(412\) 0 0
\(413\) −9.79796 8.48528i −0.482126 0.417533i
\(414\) 0 0
\(415\) −9.00000 15.5885i −0.441793 0.765207i
\(416\) 0 0
\(417\) 0 0
\(418\) 3.46410i 0.169435i
\(419\) −18.3712 + 31.8198i −0.897491 + 1.55450i −0.0667989 + 0.997766i \(0.521279\pi\)
−0.830692 + 0.556733i \(0.812055\pi\)
\(420\) 0 0
\(421\) 0.500000 + 0.866025i 0.0243685 + 0.0422075i 0.877952 0.478748i \(-0.158909\pi\)
−0.853584 + 0.520955i \(0.825576\pi\)
\(422\) −26.9444 + 15.5563i −1.31163 + 0.757271i
\(423\) 0 0
\(424\) −4.00000 + 6.92820i −0.194257 + 0.336463i
\(425\) −2.44949 + 4.24264i −0.118818 + 0.205798i
\(426\) 0 0
\(427\) 9.00000 + 1.73205i 0.435541 + 0.0838198i
\(428\) 0 0
\(429\) 0 0
\(430\) 3.46410i 0.167054i
\(431\) 13.4722 + 7.77817i 0.648933 + 0.374661i 0.788047 0.615615i \(-0.211092\pi\)
−0.139114 + 0.990276i \(0.544426\pi\)
\(432\) 0 0
\(433\) 15.5885i 0.749133i 0.927200 + 0.374567i \(0.122209\pi\)
−0.927200 + 0.374567i \(0.877791\pi\)
\(434\) 6.12372 2.12132i 0.293948 0.101827i
\(435\) 0 0
\(436\) 0 0
\(437\) 4.89898 + 8.48528i 0.234350 + 0.405906i
\(438\) 0 0
\(439\) −24.0000 13.8564i −1.14546 0.661330i −0.197681 0.980266i \(-0.563341\pi\)
−0.947776 + 0.318936i \(0.896674\pi\)
\(440\) −9.79796 −0.467099
\(441\) 0 0
\(442\) 36.0000 1.71235
\(443\) −34.2929 19.7990i −1.62930 0.940678i −0.984301 0.176497i \(-0.943523\pi\)
−0.645002 0.764181i \(-0.723143\pi\)
\(444\) 0 0
\(445\) 6.00000 + 10.3923i 0.284427 + 0.492642i
\(446\) −29.3939 −1.39184
\(447\) 0 0
\(448\) −20.0000 + 6.92820i −0.944911 + 0.327327i
\(449\) 7.07107i 0.333704i −0.985982 0.166852i \(-0.946640\pi\)
0.985982 0.166852i \(-0.0533603\pi\)
\(450\) 0 0
\(451\) 9.00000 + 5.19615i 0.423793 + 0.244677i
\(452\) 0 0
\(453\) 0 0
\(454\) −33.0000 19.0526i −1.54877 0.894181i
\(455\) 33.0681 + 6.36396i 1.55026 + 0.298347i
\(456\) 0 0
\(457\) −2.50000 + 4.33013i −0.116945 + 0.202555i −0.918556 0.395292i \(-0.870643\pi\)
0.801611 + 0.597847i \(0.203977\pi\)
\(458\) 15.9217 27.5772i 0.743971 1.28860i
\(459\) 0 0
\(460\) 0 0
\(461\) 7.34847 + 12.7279i 0.342252 + 0.592798i 0.984851 0.173405i \(-0.0554769\pi\)
−0.642598 + 0.766203i \(0.722144\pi\)
\(462\) 0 0
\(463\) 6.50000 11.2583i 0.302081 0.523219i −0.674526 0.738251i \(-0.735652\pi\)
0.976607 + 0.215032i \(0.0689855\pi\)
\(464\) 11.3137i 0.525226i
\(465\) 0 0
\(466\) −14.0000 −0.648537
\(467\) 13.4722 + 23.3345i 0.623419 + 1.07979i 0.988844 + 0.148952i \(0.0475901\pi\)
−0.365426 + 0.930841i \(0.619077\pi\)
\(468\) 0 0
\(469\) −22.0000 19.0526i −1.01587 0.879765i
\(470\) −36.7423 + 21.2132i −1.69480 + 0.978492i
\(471\) 0 0
\(472\) 12.0000 6.92820i 0.552345 0.318896i
\(473\) −1.22474 + 0.707107i −0.0563138 + 0.0325128i
\(474\) 0 0
\(475\) 1.50000 0.866025i 0.0688247 0.0397360i
\(476\) 0 0
\(477\) 0 0
\(478\) 19.0000 + 32.9090i 0.869040 + 1.50522i
\(479\) 4.89898 0.223840 0.111920 0.993717i \(-0.464300\pi\)
0.111920 + 0.993717i \(0.464300\pi\)
\(480\) 0 0
\(481\) 5.19615i 0.236924i
\(482\) 9.79796 16.9706i 0.446285 0.772988i
\(483\) 0 0
\(484\) 0 0
\(485\) −22.0454 + 12.7279i −1.00103 + 0.577945i
\(486\) 0 0
\(487\) −8.50000 + 14.7224i −0.385172 + 0.667137i −0.991793 0.127854i \(-0.959191\pi\)
0.606621 + 0.794991i \(0.292524\pi\)
\(488\) −4.89898 + 8.48528i −0.221766 + 0.384111i
\(489\) 0 0
\(490\) −24.0000 + 3.46410i −1.08421 + 0.156492i
\(491\) 9.79796 + 5.65685i 0.442176 + 0.255290i 0.704520 0.709684i \(-0.251162\pi\)
−0.262344 + 0.964974i \(0.584496\pi\)
\(492\) 0 0
\(493\) 13.8564i 0.624061i
\(494\) −11.0227 6.36396i −0.495935 0.286328i
\(495\) 0 0
\(496\) 6.92820i 0.311086i
\(497\) −6.12372 17.6777i −0.274687 0.792952i
\(498\) 0 0
\(499\) −25.0000 −1.11915 −0.559577 0.828778i \(-0.689036\pi\)
−0.559577 + 0.828778i \(0.689036\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 22.0454 0.982956 0.491478 0.870890i \(-0.336457\pi\)
0.491478 + 0.870890i \(0.336457\pi\)
\(504\) 0 0
\(505\) −42.0000 −1.86898
\(506\) 9.79796 + 5.65685i 0.435572 + 0.251478i
\(507\) 0 0
\(508\) 0 0
\(509\) 2.44949 0.108572 0.0542859 0.998525i \(-0.482712\pi\)
0.0542859 + 0.998525i \(0.482712\pi\)
\(510\) 0 0
\(511\) 4.50000 + 0.866025i 0.199068 + 0.0383107i
\(512\) 22.6274i 1.00000i
\(513\) 0 0
\(514\) −3.00000 1.73205i −0.132324 0.0763975i
\(515\) 21.2132i 0.934765i
\(516\) 0 0
\(517\) 15.0000 + 8.66025i 0.659699 + 0.380878i
\(518\) −1.22474 3.53553i −0.0538122 0.155342i
\(519\) 0 0
\(520\) −18.0000 + 31.1769i −0.789352 + 1.36720i
\(521\) −2.44949 + 4.24264i −0.107314 + 0.185873i −0.914681 0.404176i \(-0.867558\pi\)
0.807367 + 0.590049i \(0.200892\pi\)
\(522\) 0 0
\(523\) 1.50000 0.866025i 0.0655904 0.0378686i −0.466846 0.884339i \(-0.654610\pi\)
0.532437 + 0.846470i \(0.321276\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 10.0000 17.3205i 0.436021 0.755210i
\(527\) 8.48528i 0.369625i
\(528\) 0 0
\(529\) −9.00000 −0.391304
\(530\) −4.89898 8.48528i −0.212798 0.368577i
\(531\) 0 0
\(532\) 0 0
\(533\) 33.0681 19.0919i 1.43234 0.826961i
\(534\) 0 0
\(535\) −6.00000 + 3.46410i −0.259403 + 0.149766i
\(536\) 26.9444 15.5563i 1.16382 0.671932i
\(537\) 0 0
\(538\) −21.0000 + 12.1244i −0.905374 + 0.522718i
\(539\) 6.12372 + 7.77817i 0.263767 + 0.335030i
\(540\) 0 0
\(541\) −8.50000 14.7224i −0.365444 0.632967i 0.623404 0.781900i \(-0.285749\pi\)
−0.988847 + 0.148933i \(0.952416\pi\)
\(542\) 19.5959 0.841717
\(543\) 0 0
\(544\) 0 0
\(545\) 1.22474 2.12132i 0.0524623 0.0908674i
\(546\) 0 0
\(547\) 5.00000 + 8.66025i 0.213785 + 0.370286i 0.952896 0.303298i \(-0.0980876\pi\)
−0.739111 + 0.673583i \(0.764754\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 1.00000 1.73205i 0.0426401 0.0738549i
\(551\) −2.44949 + 4.24264i −0.104352 + 0.180743i
\(552\) 0 0
\(553\) −2.50000 + 12.9904i −0.106311 + 0.552407i
\(554\) −28.1691 16.2635i −1.19679 0.690968i
\(555\) 0 0
\(556\) 0 0
\(557\) 13.4722 + 7.77817i 0.570835 + 0.329572i 0.757483 0.652855i \(-0.226429\pi\)
−0.186648 + 0.982427i \(0.559762\pi\)
\(558\) 0 0
\(559\) 5.19615i 0.219774i
\(560\) 4.89898 25.4558i 0.207020 1.07571i
\(561\) 0 0
\(562\) −32.0000 −1.34984
\(563\) −13.4722 23.3345i −0.567785 0.983433i −0.996785 0.0801281i \(-0.974467\pi\)
0.428999 0.903305i \(-0.358866\pi\)
\(564\) 0 0
\(565\) −3.00000 1.73205i −0.126211 0.0728679i
\(566\) 2.44949 0.102960
\(567\) 0 0
\(568\) 20.0000 0.839181
\(569\) −1.22474 0.707107i −0.0513440 0.0296435i 0.474108 0.880467i \(-0.342771\pi\)
−0.525452 + 0.850823i \(0.676104\pi\)
\(570\) 0 0
\(571\) −5.50000 9.52628i −0.230168 0.398662i 0.727690 0.685907i \(-0.240594\pi\)
−0.957857 + 0.287244i \(0.907261\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −18.0000 + 20.7846i −0.751305 + 0.867533i
\(575\) 5.65685i 0.235907i
\(576\) 0 0
\(577\) 1.50000 + 0.866025i 0.0624458 + 0.0360531i 0.530898 0.847436i \(-0.321855\pi\)
−0.468452 + 0.883489i \(0.655188\pi\)
\(578\) 9.89949i 0.411765i
\(579\) 0 0
\(580\) 0 0
\(581\) −14.6969 12.7279i −0.609732 0.528043i
\(582\) 0 0
\(583\) −2.00000 + 3.46410i −0.0828315 + 0.143468i
\(584\) −2.44949 + 4.24264i −0.101361 + 0.175562i
\(585\) 0 0
\(586\) 18.0000 10.3923i 0.743573 0.429302i
\(587\) 7.34847 + 12.7279i 0.303304 + 0.525338i 0.976882 0.213778i \(-0.0685770\pi\)
−0.673578 + 0.739116i \(0.735244\pi\)
\(588\) 0 0
\(589\) −1.50000 + 2.59808i −0.0618064 + 0.107052i
\(590\) 16.9706i 0.698667i
\(591\) 0 0
\(592\) 4.00000 0.164399
\(593\) −8.57321 14.8492i −0.352060 0.609785i 0.634550 0.772881i \(-0.281185\pi\)
−0.986610 + 0.163096i \(0.947852\pi\)
\(594\) 0 0
\(595\) −6.00000 + 31.1769i −0.245976 + 1.27813i
\(596\) 0 0
\(597\) 0 0
\(598\) 36.0000 20.7846i 1.47215 0.849946i
\(599\) 4.89898 2.82843i 0.200167 0.115566i −0.396566 0.918006i \(-0.629798\pi\)
0.596733 + 0.802440i \(0.296465\pi\)
\(600\) 0 0
\(601\) −22.5000 + 12.9904i −0.917794 + 0.529889i −0.882931 0.469503i \(-0.844433\pi\)
−0.0348635 + 0.999392i \(0.511100\pi\)
\(602\) −1.22474 3.53553i −0.0499169 0.144098i
\(603\) 0 0
\(604\) 0 0
\(605\) 22.0454 0.896273
\(606\) 0 0
\(607\) 39.8372i 1.61694i −0.588537 0.808470i \(-0.700296\pi\)
0.588537 0.808470i \(-0.299704\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −6.00000 10.3923i −0.242933 0.420772i
\(611\) 55.1135 31.8198i 2.22965 1.28729i
\(612\) 0 0
\(613\) −4.00000 + 6.92820i −0.161558 + 0.279827i −0.935428 0.353518i \(-0.884985\pi\)
0.773869 + 0.633345i \(0.218319\pi\)
\(614\) −11.0227 + 19.0919i −0.444840 + 0.770486i
\(615\) 0 0
\(616\) −10.0000 + 3.46410i −0.402911 + 0.139573i
\(617\) 20.8207 + 12.0208i 0.838208 + 0.483940i 0.856655 0.515890i \(-0.172539\pi\)
−0.0184465 + 0.999830i \(0.505872\pi\)
\(618\) 0 0
\(619\) 29.4449i 1.18349i 0.806126 + 0.591744i \(0.201561\pi\)
−0.806126 + 0.591744i \(0.798439\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.2487i 0.972285i
\(623\) 9.79796 + 8.48528i 0.392547 + 0.339956i
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) 8.57321 + 14.8492i 0.342655 + 0.593495i
\(627\) 0 0
\(628\) 0 0
\(629\) −4.89898 −0.195335
\(630\) 0 0
\(631\) 38.0000 1.51276 0.756378 0.654135i \(-0.226967\pi\)
0.756378 + 0.654135i \(0.226967\pi\)
\(632\) −12.2474 7.07107i −0.487177 0.281272i
\(633\) 0 0
\(634\) 10.0000 + 17.3205i 0.397151 + 0.687885i
\(635\) 26.9444 1.06926
\(636\) 0 0
\(637\) 36.0000 5.19615i 1.42637 0.205879i
\(638\) 5.65685i 0.223957i
\(639\) 0 0
\(640\) 24.0000 + 13.8564i 0.948683 + 0.547723i
\(641\) 14.1421i 0.558581i 0.960207 + 0.279290i \(0.0900992\pi\)
−0.960207 + 0.279290i \(0.909901\pi\)
\(642\) 0 0
\(643\) −22.5000 12.9904i −0.887313 0.512291i −0.0142506 0.999898i \(-0.504536\pi\)
−0.873063 + 0.487608i \(0.837870\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6.00000 10.3923i 0.236067 0.408880i
\(647\) 8.57321 14.8492i 0.337048 0.583784i −0.646828 0.762636i \(-0.723905\pi\)
0.983876 + 0.178852i \(0.0572383\pi\)
\(648\) 0 0
\(649\) 6.00000 3.46410i 0.235521 0.135978i
\(650\) −3.67423 6.36396i −0.144115 0.249615i
\(651\) 0 0
\(652\) 0 0
\(653\) 7.07107i 0.276712i −0.990383 0.138356i \(-0.955818\pi\)
0.990383 0.138356i \(-0.0441819\pi\)
\(654\) 0 0
\(655\) 6.00000 0.234439
\(656\) −14.6969 25.4558i −0.573819 0.993884i
\(657\) 0 0
\(658\) −30.0000 + 34.6410i −1.16952 + 1.35045i
\(659\) 19.5959 11.3137i 0.763349 0.440720i −0.0671481 0.997743i \(-0.521390\pi\)
0.830497 + 0.557024i \(0.188057\pi\)
\(660\) 0 0
\(661\) 25.5000 14.7224i 0.991835 0.572636i 0.0860127 0.996294i \(-0.472587\pi\)
0.905822 + 0.423658i \(0.139254\pi\)
\(662\) −37.9671 + 21.9203i −1.47563 + 0.851957i
\(663\) 0 0
\(664\) 18.0000 10.3923i 0.698535 0.403300i
\(665\) 7.34847 8.48528i 0.284961 0.329045i
\(666\) 0 0
\(667\) −8.00000 13.8564i −0.309761 0.536522i
\(668\) 0 0
\(669\) 0 0
\(670\) 38.1051i 1.47213i
\(671\) −2.44949 + 4.24264i −0.0945615 + 0.163785i
\(672\) 0 0
\(673\) −17.5000 30.3109i −0.674575 1.16840i −0.976593 0.215096i \(-0.930993\pi\)
0.302017 0.953302i \(-0.402340\pi\)
\(674\) 28.1691 16.2635i 1.08503 0.626445i
\(675\) 0 0
\(676\) 0 0
\(677\) −4.89898 + 8.48528i −0.188283 + 0.326116i −0.944678 0.327999i \(-0.893626\pi\)
0.756395 + 0.654115i \(0.226959\pi\)
\(678\) 0 0
\(679\) −18.0000 + 20.7846i −0.690777 + 0.797640i
\(680\) −29.3939 16.9706i −1.12720 0.650791i
\(681\) 0 0
\(682\) 3.46410i 0.132647i
\(683\) −41.6413 24.0416i −1.59336 0.919927i −0.992725 0.120405i \(-0.961581\pi\)
−0.600636 0.799522i \(-0.705086\pi\)
\(684\) 0 0
\(685\) 27.7128i 1.05885i
\(686\) −23.2702 + 12.0208i −0.888459 + 0.458957i
\(687\) 0 0
\(688\) 4.00000 0.152499
\(689\) 7.34847 + 12.7279i 0.279954 + 0.484895i
\(690\) 0 0
\(691\) −37.5000 21.6506i −1.42657 0.823629i −0.429719 0.902963i \(-0.641387\pi\)
−0.996848 + 0.0793336i \(0.974721\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −44.0000 −1.67022
\(695\) 11.0227 + 6.36396i 0.418115 + 0.241399i
\(696\) 0 0
\(697\) 18.0000 + 31.1769i 0.681799 + 1.18091i
\(698\) 14.6969 0.556287
\(699\) 0 0
\(700\) 0 0
\(701\) 5.65685i 0.213656i 0.994277 + 0.106828i \(0.0340695\pi\)
−0.994277 + 0.106828i \(0.965931\pi\)
\(702\) 0 0
\(703\) 1.50000 + 0.866025i 0.0565736 + 0.0326628i
\(704\) 11.3137i 0.426401i
\(705\) 0 0
\(706\) 21.0000 + 12.1244i 0.790345 + 0.456306i
\(707\) −42.8661 + 14.8492i −1.61214 + 0.558463i
\(708\) 0 0
\(709\) 20.0000 34.6410i 0.751116 1.30097i −0.196167 0.980571i \(-0.562849\pi\)
0.947282 0.320400i \(-0.103817\pi\)
\(710\) −12.2474 + 21.2132i −0.459639 + 0.796117i
\(711\) 0 0
\(712\) −12.0000 + 6.92820i −0.449719 + 0.259645i
\(713\) −4.89898 8.48528i −0.183468 0.317776i
\(714\) 0 0
\(715\) −9.00000 + 15.5885i −0.336581 + 0.582975i
\(716\) 0 0
\(717\) 0 0
\(718\) 40.0000 1.49279
\(719\) 13.4722 + 23.3345i 0.502428 + 0.870231i 0.999996 + 0.00280593i \(0.000893157\pi\)
−0.497568 + 0.867425i \(0.665774\pi\)
\(720\) 0 0
\(721\) −7.50000 21.6506i −0.279315 0.806312i
\(722\) 19.5959 11.3137i 0.729285 0.421053i
\(723\) 0 0
\(724\) 0 0
\(725\) −2.44949 + 1.41421i −0.0909718 + 0.0525226i
\(726\) 0 0
\(727\) −22.5000 + 12.9904i −0.834479 + 0.481787i −0.855384 0.517995i \(-0.826679\pi\)
0.0209049 + 0.999781i \(0.493345\pi\)
\(728\) −7.34847 + 38.1838i −0.272352 + 1.41518i
\(729\) 0 0
\(730\) −3.00000 5.19615i −0.111035 0.192318i
\(731\) −4.89898 −0.181195
\(732\) 0 0
\(733\) 39.8372i 1.47142i −0.677297 0.735710i \(-0.736849\pi\)
0.677297 0.735710i \(-0.263151\pi\)
\(734\) −1.22474 + 2.12132i −0.0452062 + 0.0782994i
\(735\) 0 0
\(736\) 0 0
\(737\) 13.4722 7.77817i 0.496255 0.286513i
\(738\) 0 0
\(739\) 0.500000 0.866025i 0.0183928 0.0318573i −0.856683 0.515844i \(-0.827478\pi\)
0.875075 + 0.483987i \(0.160812\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −8.00000 6.92820i −0.293689 0.254342i
\(743\) 20.8207 + 12.0208i 0.763836 + 0.441001i 0.830671 0.556763i \(-0.187957\pi\)
−0.0668353 + 0.997764i \(0.521290\pi\)
\(744\) 0 0
\(745\) 13.8564i 0.507659i
\(746\) −35.5176 20.5061i −1.30039 0.750782i
\(747\) 0 0
\(748\) 0 0
\(749\) −4.89898 + 5.65685i −0.179005 + 0.206697i
\(750\) 0 0
\(751\) 29.0000 1.05823 0.529113 0.848552i \(-0.322525\pi\)
0.529113 + 0.848552i \(0.322525\pi\)
\(752\) −24.4949 42.4264i −0.893237 1.54713i
\(753\) 0 0
\(754\) 18.0000 + 10.3923i 0.655521 + 0.378465i
\(755\) −53.8888 −1.96121
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 8.57321 + 4.94975i 0.311393 + 0.179783i
\(759\) 0 0
\(760\) 6.00000 + 10.3923i 0.217643 + 0.376969i
\(761\) 24.4949 0.887939 0.443970 0.896042i \(-0.353570\pi\)
0.443970 + 0.896042i \(0.353570\pi\)
\(762\) 0 0
\(763\) 0.500000 2.59808i 0.0181012 0.0940567i
\(764\) 0 0
\(765\) 0 0
\(766\) 24.0000 + 13.8564i 0.867155 + 0.500652i
\(767\) 25.4558i 0.919157i
\(768\) 0 0
\(769\) −22.5000 12.9904i −0.811371 0.468445i 0.0360609 0.999350i \(-0.488519\pi\)
−0.847432 + 0.530904i \(0.821852\pi\)
\(770\) 2.44949 12.7279i 0.0882735 0.458682i
\(771\) 0 0
\(772\) 0 0
\(773\) −13.4722 + 23.3345i −0.484561 + 0.839284i −0.999843 0.0177365i \(-0.994354\pi\)
0.515282 + 0.857021i \(0.327687\pi\)
\(774\) 0 0
\(775\) −1.50000 + 0.866025i −0.0538816 + 0.0311086i
\(776\) −14.6969 25.4558i −0.527589 0.913812i
\(777\) 0 0
\(778\) 19.0000 32.9090i 0.681183 1.17984i
\(779\) 12.7279i 0.456025i
\(780\) 0 0
\(781\) 10.0000 0.357828
\(782\) 19.5959 + 33.9411i 0.700749 + 1.21373i
\(783\) 0 0
\(784\) −4.00000 27.7128i −0.142857 0.989743i
\(785\) −36.7423 + 21.2132i −1.31139 + 0.757132i
\(786\) 0 0
\(787\) 39.0000 22.5167i 1.39020 0.802632i 0.396863 0.917878i \(-0.370099\pi\)
0.993337 + 0.115246i \(0.0367655\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 15.0000 8.66025i 0.533676 0.308118i
\(791\) −3.67423 0.707107i −0.130641 0.0251418i
\(792\) 0 0