Properties

Label 567.2.i.c.269.2
Level $567$
Weight $2$
Character 567.269
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.i (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: \(\Q(\sqrt{-3}, \sqrt{-5})\)
Defining polynomial: \(x^{4} - 5 x^{2} + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.2
Root \(-1.93649 + 1.11803i\) of defining polynomial
Character \(\chi\) \(=\) 567.269
Dual form 567.2.i.c.215.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.23607i q^{2} -3.00000 q^{4} +(2.50000 - 0.866025i) q^{7} -2.23607i q^{8} +O(q^{10})\) \(q+2.23607i q^{2} -3.00000 q^{4} +(2.50000 - 0.866025i) q^{7} -2.23607i q^{8} +(-3.87298 + 2.23607i) q^{11} +(-1.50000 + 0.866025i) q^{13} +(1.93649 + 5.59017i) q^{14} -1.00000 q^{16} +(-3.87298 + 6.70820i) q^{17} +(-3.00000 + 1.73205i) q^{19} +(-5.00000 - 8.66025i) q^{22} +(3.87298 + 2.23607i) q^{23} +(2.50000 + 4.33013i) q^{25} +(-1.93649 - 3.35410i) q^{26} +(-7.50000 + 2.59808i) q^{28} +(3.87298 + 2.23607i) q^{29} +1.73205i q^{31} -6.70820i q^{32} +(-15.0000 - 8.66025i) q^{34} +(-2.50000 - 4.33013i) q^{37} +(-3.87298 - 6.70820i) q^{38} +(-3.87298 - 6.70820i) q^{41} +(3.50000 - 6.06218i) q^{43} +(11.6190 - 6.70820i) q^{44} +(-5.00000 + 8.66025i) q^{46} +7.74597 q^{47} +(5.50000 - 4.33013i) q^{49} +(-9.68246 + 5.59017i) q^{50} +(4.50000 - 2.59808i) q^{52} +(3.87298 + 2.23607i) q^{53} +(-1.93649 - 5.59017i) q^{56} +(-5.00000 + 8.66025i) q^{58} -7.74597 q^{59} +8.66025i q^{61} -3.87298 q^{62} +13.0000 q^{64} -1.00000 q^{67} +(11.6190 - 20.1246i) q^{68} +8.94427i q^{71} +(6.00000 + 3.46410i) q^{73} +(9.68246 - 5.59017i) q^{74} +(9.00000 - 5.19615i) q^{76} +(-7.74597 + 8.94427i) q^{77} +11.0000 q^{79} +(15.0000 - 8.66025i) q^{82} +(3.87298 - 6.70820i) q^{83} +(13.5554 + 7.82624i) q^{86} +(5.00000 + 8.66025i) q^{88} +(-7.74597 - 13.4164i) q^{89} +(-3.00000 + 3.46410i) q^{91} +(-11.6190 - 6.70820i) q^{92} +17.3205i q^{94} +(-1.50000 - 0.866025i) q^{97} +(9.68246 + 12.2984i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 12q^{4} + 10q^{7} + O(q^{10}) \) \( 4q - 12q^{4} + 10q^{7} - 6q^{13} - 4q^{16} - 12q^{19} - 20q^{22} + 10q^{25} - 30q^{28} - 60q^{34} - 10q^{37} + 14q^{43} - 20q^{46} + 22q^{49} + 18q^{52} - 20q^{58} + 52q^{64} - 4q^{67} + 24q^{73} + 36q^{76} + 44q^{79} + 60q^{82} + 20q^{88} - 12q^{91} - 6q^{97} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.23607i 1.58114i 0.612372 + 0.790569i \(0.290215\pi\)
−0.612372 + 0.790569i \(0.709785\pi\)
\(3\) 0 0
\(4\) −3.00000 −1.50000
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 0 0
\(7\) 2.50000 0.866025i 0.944911 0.327327i
\(8\) 2.23607i 0.790569i
\(9\) 0 0
\(10\) 0 0
\(11\) −3.87298 + 2.23607i −1.16775 + 0.674200i −0.953149 0.302502i \(-0.902178\pi\)
−0.214600 + 0.976702i \(0.568845\pi\)
\(12\) 0 0
\(13\) −1.50000 + 0.866025i −0.416025 + 0.240192i −0.693375 0.720577i \(-0.743877\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 1.93649 + 5.59017i 0.517549 + 1.49404i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −3.87298 + 6.70820i −0.939336 + 1.62698i −0.172624 + 0.984988i \(0.555225\pi\)
−0.766712 + 0.641991i \(0.778109\pi\)
\(18\) 0 0
\(19\) −3.00000 + 1.73205i −0.688247 + 0.397360i −0.802955 0.596040i \(-0.796740\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −5.00000 8.66025i −1.06600 1.84637i
\(23\) 3.87298 + 2.23607i 0.807573 + 0.466252i 0.846112 0.533005i \(-0.178937\pi\)
−0.0385394 + 0.999257i \(0.512271\pi\)
\(24\) 0 0
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) −1.93649 3.35410i −0.379777 0.657794i
\(27\) 0 0
\(28\) −7.50000 + 2.59808i −1.41737 + 0.490990i
\(29\) 3.87298 + 2.23607i 0.719195 + 0.415227i 0.814456 0.580225i \(-0.197035\pi\)
−0.0952614 + 0.995452i \(0.530369\pi\)
\(30\) 0 0
\(31\) 1.73205i 0.311086i 0.987829 + 0.155543i \(0.0497126\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 6.70820i 1.18585i
\(33\) 0 0
\(34\) −15.0000 8.66025i −2.57248 1.48522i
\(35\) 0 0
\(36\) 0 0
\(37\) −2.50000 4.33013i −0.410997 0.711868i 0.584002 0.811752i \(-0.301486\pi\)
−0.994999 + 0.0998840i \(0.968153\pi\)
\(38\) −3.87298 6.70820i −0.628281 1.08821i
\(39\) 0 0
\(40\) 0 0
\(41\) −3.87298 6.70820i −0.604858 1.04765i −0.992074 0.125656i \(-0.959896\pi\)
0.387215 0.921989i \(-0.373437\pi\)
\(42\) 0 0
\(43\) 3.50000 6.06218i 0.533745 0.924473i −0.465478 0.885059i \(-0.654118\pi\)
0.999223 0.0394140i \(-0.0125491\pi\)
\(44\) 11.6190 6.70820i 1.75162 1.01130i
\(45\) 0 0
\(46\) −5.00000 + 8.66025i −0.737210 + 1.27688i
\(47\) 7.74597 1.12987 0.564933 0.825137i \(-0.308902\pi\)
0.564933 + 0.825137i \(0.308902\pi\)
\(48\) 0 0
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) −9.68246 + 5.59017i −1.36931 + 0.790569i
\(51\) 0 0
\(52\) 4.50000 2.59808i 0.624038 0.360288i
\(53\) 3.87298 + 2.23607i 0.531995 + 0.307148i 0.741829 0.670590i \(-0.233959\pi\)
−0.209833 + 0.977737i \(0.567292\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.93649 5.59017i −0.258775 0.747018i
\(57\) 0 0
\(58\) −5.00000 + 8.66025i −0.656532 + 1.13715i
\(59\) −7.74597 −1.00844 −0.504219 0.863576i \(-0.668220\pi\)
−0.504219 + 0.863576i \(0.668220\pi\)
\(60\) 0 0
\(61\) 8.66025i 1.10883i 0.832240 + 0.554416i \(0.187058\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) −3.87298 −0.491869
\(63\) 0 0
\(64\) 13.0000 1.62500
\(65\) 0 0
\(66\) 0 0
\(67\) −1.00000 −0.122169 −0.0610847 0.998133i \(-0.519456\pi\)
−0.0610847 + 0.998133i \(0.519456\pi\)
\(68\) 11.6190 20.1246i 1.40900 2.44047i
\(69\) 0 0
\(70\) 0 0
\(71\) 8.94427i 1.06149i 0.847532 + 0.530745i \(0.178088\pi\)
−0.847532 + 0.530745i \(0.821912\pi\)
\(72\) 0 0
\(73\) 6.00000 + 3.46410i 0.702247 + 0.405442i 0.808184 0.588930i \(-0.200451\pi\)
−0.105937 + 0.994373i \(0.533784\pi\)
\(74\) 9.68246 5.59017i 1.12556 0.649844i
\(75\) 0 0
\(76\) 9.00000 5.19615i 1.03237 0.596040i
\(77\) −7.74597 + 8.94427i −0.882735 + 1.01929i
\(78\) 0 0
\(79\) 11.0000 1.23760 0.618798 0.785550i \(-0.287620\pi\)
0.618798 + 0.785550i \(0.287620\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 15.0000 8.66025i 1.65647 0.956365i
\(83\) 3.87298 6.70820i 0.425115 0.736321i −0.571316 0.820730i \(-0.693567\pi\)
0.996431 + 0.0844091i \(0.0269003\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 13.5554 + 7.82624i 1.46172 + 0.843925i
\(87\) 0 0
\(88\) 5.00000 + 8.66025i 0.533002 + 0.923186i
\(89\) −7.74597 13.4164i −0.821071 1.42214i −0.904886 0.425655i \(-0.860044\pi\)
0.0838147 0.996481i \(-0.473290\pi\)
\(90\) 0 0
\(91\) −3.00000 + 3.46410i −0.314485 + 0.363137i
\(92\) −11.6190 6.70820i −1.21136 0.699379i
\(93\) 0 0
\(94\) 17.3205i 1.78647i
\(95\) 0 0
\(96\) 0 0
\(97\) −1.50000 0.866025i −0.152302 0.0879316i 0.421912 0.906637i \(-0.361359\pi\)
−0.574214 + 0.818705i \(0.694692\pi\)
\(98\) 9.68246 + 12.2984i 0.978076 + 1.24232i
\(99\) 0 0
\(100\) −7.50000 12.9904i −0.750000 1.29904i
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0 0
\(103\) 4.50000 + 2.59808i 0.443398 + 0.255996i 0.705038 0.709170i \(-0.250930\pi\)
−0.261640 + 0.965166i \(0.584263\pi\)
\(104\) 1.93649 + 3.35410i 0.189889 + 0.328897i
\(105\) 0 0
\(106\) −5.00000 + 8.66025i −0.485643 + 0.841158i
\(107\) −3.87298 + 2.23607i −0.374415 + 0.216169i −0.675386 0.737465i \(-0.736023\pi\)
0.300970 + 0.953634i \(0.402690\pi\)
\(108\) 0 0
\(109\) 0.500000 0.866025i 0.0478913 0.0829502i −0.841086 0.540901i \(-0.818083\pi\)
0.888977 + 0.457951i \(0.151417\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.50000 + 0.866025i −0.236228 + 0.0818317i
\(113\) 7.74597 4.47214i 0.728679 0.420703i −0.0892596 0.996008i \(-0.528450\pi\)
0.817939 + 0.575305i \(0.195117\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −11.6190 6.70820i −1.07879 0.622841i
\(117\) 0 0
\(118\) 17.3205i 1.59448i
\(119\) −3.87298 + 20.1246i −0.355036 + 1.84482i
\(120\) 0 0
\(121\) 4.50000 7.79423i 0.409091 0.708566i
\(122\) −19.3649 −1.75322
\(123\) 0 0
\(124\) 5.19615i 0.466628i
\(125\) 0 0
\(126\) 0 0
\(127\) −1.00000 −0.0887357 −0.0443678 0.999015i \(-0.514127\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) 15.6525i 1.38350i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) 0 0
\(133\) −6.00000 + 6.92820i −0.520266 + 0.600751i
\(134\) 2.23607i 0.193167i
\(135\) 0 0
\(136\) 15.0000 + 8.66025i 1.28624 + 0.742611i
\(137\) −3.87298 + 2.23607i −0.330891 + 0.191040i −0.656237 0.754555i \(-0.727853\pi\)
0.325345 + 0.945595i \(0.394519\pi\)
\(138\) 0 0
\(139\) 7.50000 4.33013i 0.636142 0.367277i −0.146985 0.989139i \(-0.546957\pi\)
0.783127 + 0.621862i \(0.213624\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −20.0000 −1.67836
\(143\) 3.87298 6.70820i 0.323875 0.560968i
\(144\) 0 0
\(145\) 0 0
\(146\) −7.74597 + 13.4164i −0.641061 + 1.11035i
\(147\) 0 0
\(148\) 7.50000 + 12.9904i 0.616496 + 1.06780i
\(149\) 15.4919 + 8.94427i 1.26915 + 0.732743i 0.974827 0.222963i \(-0.0715729\pi\)
0.294322 + 0.955706i \(0.404906\pi\)
\(150\) 0 0
\(151\) 6.50000 + 11.2583i 0.528962 + 0.916190i 0.999430 + 0.0337724i \(0.0107521\pi\)
−0.470467 + 0.882418i \(0.655915\pi\)
\(152\) 3.87298 + 6.70820i 0.314140 + 0.544107i
\(153\) 0 0
\(154\) −20.0000 17.3205i −1.61165 1.39573i
\(155\) 0 0
\(156\) 0 0
\(157\) 13.8564i 1.10586i −0.833227 0.552931i \(-0.813509\pi\)
0.833227 0.552931i \(-0.186491\pi\)
\(158\) 24.5967i 1.95681i
\(159\) 0 0
\(160\) 0 0
\(161\) 11.6190 + 2.23607i 0.915702 + 0.176227i
\(162\) 0 0
\(163\) 6.50000 + 11.2583i 0.509119 + 0.881820i 0.999944 + 0.0105623i \(0.00336213\pi\)
−0.490825 + 0.871258i \(0.663305\pi\)
\(164\) 11.6190 + 20.1246i 0.907288 + 1.57147i
\(165\) 0 0
\(166\) 15.0000 + 8.66025i 1.16423 + 0.672166i
\(167\) −3.87298 6.70820i −0.299700 0.519096i 0.676367 0.736565i \(-0.263553\pi\)
−0.976067 + 0.217468i \(0.930220\pi\)
\(168\) 0 0
\(169\) −5.00000 + 8.66025i −0.384615 + 0.666173i
\(170\) 0 0
\(171\) 0 0
\(172\) −10.5000 + 18.1865i −0.800617 + 1.38671i
\(173\) −15.4919 −1.17783 −0.588915 0.808195i \(-0.700445\pi\)
−0.588915 + 0.808195i \(0.700445\pi\)
\(174\) 0 0
\(175\) 10.0000 + 8.66025i 0.755929 + 0.654654i
\(176\) 3.87298 2.23607i 0.291937 0.168550i
\(177\) 0 0
\(178\) 30.0000 17.3205i 2.24860 1.29823i
\(179\) −7.74597 4.47214i −0.578961 0.334263i 0.181760 0.983343i \(-0.441821\pi\)
−0.760720 + 0.649080i \(0.775154\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) −7.74597 6.70820i −0.574169 0.497245i
\(183\) 0 0
\(184\) 5.00000 8.66025i 0.368605 0.638442i
\(185\) 0 0
\(186\) 0 0
\(187\) 34.6410i 2.53320i
\(188\) −23.2379 −1.69480
\(189\) 0 0
\(190\) 0 0
\(191\) 17.8885i 1.29437i −0.762333 0.647185i \(-0.775946\pi\)
0.762333 0.647185i \(-0.224054\pi\)
\(192\) 0 0
\(193\) −7.00000 −0.503871 −0.251936 0.967744i \(-0.581067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(194\) 1.93649 3.35410i 0.139032 0.240810i
\(195\) 0 0
\(196\) −16.5000 + 12.9904i −1.17857 + 0.927884i
\(197\) 8.94427i 0.637253i 0.947880 + 0.318626i \(0.103222\pi\)
−0.947880 + 0.318626i \(0.896778\pi\)
\(198\) 0 0
\(199\) 19.5000 + 11.2583i 1.38232 + 0.798082i 0.992434 0.122782i \(-0.0391815\pi\)
0.389885 + 0.920864i \(0.372515\pi\)
\(200\) 9.68246 5.59017i 0.684653 0.395285i
\(201\) 0 0
\(202\) 0 0
\(203\) 11.6190 + 2.23607i 0.815490 + 0.156941i
\(204\) 0 0
\(205\) 0 0
\(206\) −5.80948 + 10.0623i −0.404765 + 0.701074i
\(207\) 0 0
\(208\) 1.50000 0.866025i 0.104006 0.0600481i
\(209\) 7.74597 13.4164i 0.535800 0.928032i
\(210\) 0 0
\(211\) 9.50000 + 16.4545i 0.654007 + 1.13277i 0.982142 + 0.188142i \(0.0602466\pi\)
−0.328135 + 0.944631i \(0.606420\pi\)
\(212\) −11.6190 6.70820i −0.797993 0.460721i
\(213\) 0 0
\(214\) −5.00000 8.66025i −0.341793 0.592003i
\(215\) 0 0
\(216\) 0 0
\(217\) 1.50000 + 4.33013i 0.101827 + 0.293948i
\(218\) 1.93649 + 1.11803i 0.131156 + 0.0757228i
\(219\) 0 0
\(220\) 0 0
\(221\) 13.4164i 0.902485i
\(222\) 0 0
\(223\) 21.0000 + 12.1244i 1.40626 + 0.811907i 0.995025 0.0996209i \(-0.0317630\pi\)
0.411239 + 0.911528i \(0.365096\pi\)
\(224\) −5.80948 16.7705i −0.388162 1.12053i
\(225\) 0 0
\(226\) 10.0000 + 17.3205i 0.665190 + 1.15214i
\(227\) −11.6190 20.1246i −0.771177 1.33572i −0.936918 0.349548i \(-0.886335\pi\)
0.165742 0.986169i \(-0.446998\pi\)
\(228\) 0 0
\(229\) −22.5000 12.9904i −1.48684 0.858429i −0.486954 0.873427i \(-0.661892\pi\)
−0.999888 + 0.0149989i \(0.995226\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 5.00000 8.66025i 0.328266 0.568574i
\(233\) 7.74597 4.47214i 0.507455 0.292979i −0.224332 0.974513i \(-0.572020\pi\)
0.731787 + 0.681533i \(0.238687\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 23.2379 1.51266
\(237\) 0 0
\(238\) −45.0000 8.66025i −2.91692 0.561361i
\(239\) 7.74597 4.47214i 0.501045 0.289278i −0.228100 0.973638i \(-0.573251\pi\)
0.729145 + 0.684359i \(0.239918\pi\)
\(240\) 0 0
\(241\) −13.5000 + 7.79423i −0.869611 + 0.502070i −0.867219 0.497927i \(-0.834095\pi\)
−0.00239235 + 0.999997i \(0.500762\pi\)
\(242\) 17.4284 + 10.0623i 1.12034 + 0.646830i
\(243\) 0 0
\(244\) 25.9808i 1.66325i
\(245\) 0 0
\(246\) 0 0
\(247\) 3.00000 5.19615i 0.190885 0.330623i
\(248\) 3.87298 0.245935
\(249\) 0 0
\(250\) 0 0
\(251\) 23.2379 1.46676 0.733382 0.679817i \(-0.237941\pi\)
0.733382 + 0.679817i \(0.237941\pi\)
\(252\) 0 0
\(253\) −20.0000 −1.25739
\(254\) 2.23607i 0.140303i
\(255\) 0 0
\(256\) −9.00000 −0.562500
\(257\) −11.6190 + 20.1246i −0.724770 + 1.25534i 0.234298 + 0.972165i \(0.424721\pi\)
−0.959069 + 0.283174i \(0.908613\pi\)
\(258\) 0 0
\(259\) −10.0000 8.66025i −0.621370 0.538122i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3.87298 + 2.23607i −0.238818 + 0.137882i −0.614634 0.788813i \(-0.710696\pi\)
0.375815 + 0.926695i \(0.377363\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −15.4919 13.4164i −0.949871 0.822613i
\(267\) 0 0
\(268\) 3.00000 0.183254
\(269\) 7.74597 13.4164i 0.472280 0.818013i −0.527217 0.849731i \(-0.676764\pi\)
0.999497 + 0.0317179i \(0.0100978\pi\)
\(270\) 0 0
\(271\) 1.50000 0.866025i 0.0911185 0.0526073i −0.453748 0.891130i \(-0.649914\pi\)
0.544867 + 0.838523i \(0.316580\pi\)
\(272\) 3.87298 6.70820i 0.234834 0.406745i
\(273\) 0 0
\(274\) −5.00000 8.66025i −0.302061 0.523185i
\(275\) −19.3649 11.1803i −1.16775 0.674200i
\(276\) 0 0
\(277\) −2.50000 4.33013i −0.150210 0.260172i 0.781094 0.624413i \(-0.214662\pi\)
−0.931305 + 0.364241i \(0.881328\pi\)
\(278\) 9.68246 + 16.7705i 0.580715 + 1.00583i
\(279\) 0 0
\(280\) 0 0
\(281\) 15.4919 + 8.94427i 0.924171 + 0.533571i 0.884963 0.465661i \(-0.154183\pi\)
0.0392078 + 0.999231i \(0.487517\pi\)
\(282\) 0 0
\(283\) 12.1244i 0.720718i 0.932814 + 0.360359i \(0.117346\pi\)
−0.932814 + 0.360359i \(0.882654\pi\)
\(284\) 26.8328i 1.59223i
\(285\) 0 0
\(286\) 15.0000 + 8.66025i 0.886969 + 0.512092i
\(287\) −15.4919 13.4164i −0.914460 0.791946i
\(288\) 0 0
\(289\) −21.5000 37.2391i −1.26471 2.19053i
\(290\) 0 0
\(291\) 0 0
\(292\) −18.0000 10.3923i −1.05337 0.608164i
\(293\) −3.87298 6.70820i −0.226262 0.391897i 0.730435 0.682982i \(-0.239317\pi\)
−0.956697 + 0.291084i \(0.905984\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −9.68246 + 5.59017i −0.562781 + 0.324922i
\(297\) 0 0
\(298\) −20.0000 + 34.6410i −1.15857 + 2.00670i
\(299\) −7.74597 −0.447961
\(300\) 0 0
\(301\) 3.50000 18.1865i 0.201737 1.04825i
\(302\) −25.1744 + 14.5344i −1.44862 + 0.836363i
\(303\) 0 0
\(304\) 3.00000 1.73205i 0.172062 0.0993399i
\(305\) 0 0
\(306\) 0 0
\(307\) 5.19615i 0.296560i 0.988945 + 0.148280i \(0.0473737\pi\)
−0.988945 + 0.148280i \(0.952626\pi\)
\(308\) 23.2379 26.8328i 1.32410 1.52894i
\(309\) 0 0
\(310\) 0 0
\(311\) 15.4919 0.878467 0.439233 0.898373i \(-0.355250\pi\)
0.439233 + 0.898373i \(0.355250\pi\)
\(312\) 0 0
\(313\) 13.8564i 0.783210i 0.920133 + 0.391605i \(0.128080\pi\)
−0.920133 + 0.391605i \(0.871920\pi\)
\(314\) 30.9839 1.74852
\(315\) 0 0
\(316\) −33.0000 −1.85640
\(317\) 4.47214i 0.251180i −0.992082 0.125590i \(-0.959918\pi\)
0.992082 0.125590i \(-0.0400824\pi\)
\(318\) 0 0
\(319\) −20.0000 −1.11979
\(320\) 0 0
\(321\) 0 0
\(322\) −5.00000 + 25.9808i −0.278639 + 1.44785i
\(323\) 26.8328i 1.49302i
\(324\) 0 0
\(325\) −7.50000 4.33013i −0.416025 0.240192i
\(326\) −25.1744 + 14.5344i −1.39428 + 0.804988i
\(327\) 0 0
\(328\) −15.0000 + 8.66025i −0.828236 + 0.478183i
\(329\) 19.3649 6.70820i 1.06762 0.369835i
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) −11.6190 + 20.1246i −0.637673 + 1.10448i
\(333\) 0 0
\(334\) 15.0000 8.66025i 0.820763 0.473868i
\(335\) 0 0
\(336\) 0 0
\(337\) 5.00000 + 8.66025i 0.272367 + 0.471754i 0.969468 0.245220i \(-0.0788601\pi\)
−0.697100 + 0.716974i \(0.745527\pi\)
\(338\) −19.3649 11.1803i −1.05331 0.608130i
\(339\) 0 0
\(340\) 0 0
\(341\) −3.87298 6.70820i −0.209734 0.363270i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) −13.5554 7.82624i −0.730860 0.421962i
\(345\) 0 0
\(346\) 34.6410i 1.86231i
\(347\) 8.94427i 0.480154i 0.970754 + 0.240077i \(0.0771726\pi\)
−0.970754 + 0.240077i \(0.922827\pi\)
\(348\) 0 0
\(349\) −19.5000 11.2583i −1.04381 0.602645i −0.122901 0.992419i \(-0.539220\pi\)
−0.920910 + 0.389774i \(0.872553\pi\)
\(350\) −19.3649 + 22.3607i −1.03510 + 1.19523i
\(351\) 0 0
\(352\) 15.0000 + 25.9808i 0.799503 + 1.38478i
\(353\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 23.2379 + 40.2492i 1.23161 + 2.13320i
\(357\) 0 0
\(358\) 10.0000 17.3205i 0.528516 0.915417i
\(359\) −3.87298 + 2.23607i −0.204408 + 0.118015i −0.598710 0.800966i \(-0.704320\pi\)
0.394302 + 0.918981i \(0.370986\pi\)
\(360\) 0 0
\(361\) −3.50000 + 6.06218i −0.184211 + 0.319062i
\(362\) 0 0
\(363\) 0 0
\(364\) 9.00000 10.3923i 0.471728 0.544705i
\(365\) 0 0
\(366\) 0 0
\(367\) 9.00000 5.19615i 0.469796 0.271237i −0.246358 0.969179i \(-0.579234\pi\)
0.716154 + 0.697942i \(0.245901\pi\)
\(368\) −3.87298 2.23607i −0.201893 0.116563i
\(369\) 0 0
\(370\) 0 0
\(371\) 11.6190 + 2.23607i 0.603226 + 0.116091i
\(372\) 0 0
\(373\) −1.00000 + 1.73205i −0.0517780 + 0.0896822i −0.890753 0.454488i \(-0.849822\pi\)
0.838975 + 0.544170i \(0.183156\pi\)
\(374\) 77.4597 4.00534
\(375\) 0 0
\(376\) 17.3205i 0.893237i
\(377\) −7.74597 −0.398938
\(378\) 0 0
\(379\) 17.0000 0.873231 0.436616 0.899648i \(-0.356177\pi\)
0.436616 + 0.899648i \(0.356177\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 40.0000 2.04658
\(383\) −11.6190 + 20.1246i −0.593701 + 1.02832i 0.400028 + 0.916503i \(0.369000\pi\)
−0.993729 + 0.111817i \(0.964333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 15.6525i 0.796690i
\(387\) 0 0
\(388\) 4.50000 + 2.59808i 0.228453 + 0.131897i
\(389\) 7.74597 4.47214i 0.392736 0.226746i −0.290609 0.956842i \(-0.593858\pi\)
0.683345 + 0.730096i \(0.260525\pi\)
\(390\) 0 0
\(391\) −30.0000 + 17.3205i −1.51717 + 0.875936i
\(392\) −9.68246 12.2984i −0.489038 0.621162i
\(393\) 0 0
\(394\) −20.0000 −1.00759
\(395\) 0 0
\(396\) 0 0
\(397\) −25.5000 + 14.7224i −1.27981 + 0.738898i −0.976813 0.214094i \(-0.931320\pi\)
−0.302995 + 0.952992i \(0.597987\pi\)
\(398\) −25.1744 + 43.6033i −1.26188 + 2.18564i
\(399\) 0 0
\(400\) −2.50000 4.33013i −0.125000 0.216506i
\(401\) −19.3649 11.1803i −0.967038 0.558320i −0.0687059 0.997637i \(-0.521887\pi\)
−0.898332 + 0.439317i \(0.855220\pi\)
\(402\) 0 0
\(403\) −1.50000 2.59808i −0.0747203 0.129419i
\(404\) 0 0
\(405\) 0 0
\(406\) −5.00000 + 25.9808i −0.248146 + 1.28940i
\(407\) 19.3649 + 11.1803i 0.959883 + 0.554189i
\(408\) 0 0
\(409\) 22.5167i 1.11338i 0.830721 + 0.556689i \(0.187928\pi\)
−0.830721 + 0.556689i \(0.812072\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −13.5000 7.79423i −0.665097 0.383994i
\(413\) −19.3649 + 6.70820i −0.952885 + 0.330089i
\(414\) 0 0
\(415\) 0 0
\(416\) 5.80948 + 10.0623i 0.284833 + 0.493345i
\(417\) 0 0
\(418\) 30.0000 + 17.3205i 1.46735 + 0.847174i
\(419\) 7.74597 + 13.4164i 0.378415 + 0.655434i 0.990832 0.135101i \(-0.0431358\pi\)
−0.612417 + 0.790535i \(0.709802\pi\)
\(420\) 0 0
\(421\) 17.0000 29.4449i 0.828529 1.43505i −0.0706626 0.997500i \(-0.522511\pi\)
0.899192 0.437555i \(-0.144155\pi\)
\(422\) −36.7933 + 21.2426i −1.79107 + 1.03408i
\(423\) 0 0
\(424\) 5.00000 8.66025i 0.242821 0.420579i
\(425\) −38.7298 −1.87867
\(426\) 0 0
\(427\) 7.50000 + 21.6506i 0.362950 + 1.04775i
\(428\) 11.6190 6.70820i 0.561623 0.324253i
\(429\) 0 0
\(430\) 0 0
\(431\) 27.1109 + 15.6525i 1.30589 + 0.753953i 0.981407 0.191940i \(-0.0614778\pi\)
0.324479 + 0.945893i \(0.394811\pi\)
\(432\) 0 0
\(433\) 15.5885i 0.749133i −0.927200 0.374567i \(-0.877791\pi\)
0.927200 0.374567i \(-0.122209\pi\)
\(434\) −9.68246 + 3.35410i −0.464773 + 0.161002i
\(435\) 0 0
\(436\) −1.50000 + 2.59808i −0.0718370 + 0.124425i
\(437\) −15.4919 −0.741080
\(438\) 0 0
\(439\) 3.46410i 0.165333i 0.996577 + 0.0826663i \(0.0263436\pi\)
−0.996577 + 0.0826663i \(0.973656\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 30.0000 1.42695
\(443\) 35.7771i 1.69982i 0.526927 + 0.849910i \(0.323344\pi\)
−0.526927 + 0.849910i \(0.676656\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −27.1109 + 46.9574i −1.28374 + 2.22350i
\(447\) 0 0
\(448\) 32.5000 11.2583i 1.53548 0.531906i
\(449\) 8.94427i 0.422106i 0.977475 + 0.211053i \(0.0676893\pi\)
−0.977475 + 0.211053i \(0.932311\pi\)
\(450\) 0 0
\(451\) 30.0000 + 17.3205i 1.41264 + 0.815591i
\(452\) −23.2379 + 13.4164i −1.09302 + 0.631055i
\(453\) 0 0
\(454\) 45.0000 25.9808i 2.11195 1.21934i
\(455\) 0 0
\(456\) 0 0
\(457\) 11.0000 0.514558 0.257279 0.966337i \(-0.417174\pi\)
0.257279 + 0.966337i \(0.417174\pi\)
\(458\) 29.0474 50.3115i 1.35729 2.35090i
\(459\) 0 0
\(460\) 0 0
\(461\) 3.87298 6.70820i 0.180383 0.312432i −0.761628 0.648014i \(-0.775600\pi\)
0.942011 + 0.335582i \(0.108933\pi\)
\(462\) 0 0
\(463\) −4.00000 6.92820i −0.185896 0.321981i 0.757982 0.652275i \(-0.226185\pi\)
−0.943878 + 0.330294i \(0.892852\pi\)
\(464\) −3.87298 2.23607i −0.179799 0.103807i
\(465\) 0 0
\(466\) 10.0000 + 17.3205i 0.463241 + 0.802357i
\(467\) 15.4919 + 26.8328i 0.716881 + 1.24167i 0.962229 + 0.272240i \(0.0877643\pi\)
−0.245348 + 0.969435i \(0.578902\pi\)
\(468\) 0 0
\(469\) −2.50000 + 0.866025i −0.115439 + 0.0399893i
\(470\) 0 0
\(471\) 0 0
\(472\) 17.3205i 0.797241i
\(473\) 31.3050i 1.43940i
\(474\) 0 0
\(475\) −15.0000 8.66025i −0.688247 0.397360i
\(476\) 11.6190 60.3738i 0.532554 2.76723i
\(477\) 0 0
\(478\) 10.0000 + 17.3205i 0.457389 + 0.792222i
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 0 0
\(481\) 7.50000 + 4.33013i 0.341971 + 0.197437i
\(482\) −17.4284 30.1869i −0.793843 1.37498i
\(483\) 0 0
\(484\) −13.5000 + 23.3827i −0.613636 + 1.06285i
\(485\) 0 0
\(486\) 0 0
\(487\) 20.0000 34.6410i 0.906287 1.56973i 0.0871056 0.996199i \(-0.472238\pi\)
0.819181 0.573535i \(-0.194428\pi\)
\(488\) 19.3649 0.876609
\(489\) 0 0
\(490\) 0 0
\(491\) 19.3649 11.1803i 0.873926 0.504562i 0.00527540 0.999986i \(-0.498321\pi\)
0.868651 + 0.495424i \(0.164987\pi\)
\(492\) 0 0
\(493\) −30.0000 + 17.3205i −1.35113 + 0.780076i
\(494\) 11.6190 + 6.70820i 0.522761 + 0.301816i
\(495\) 0 0
\(496\) 1.73205i 0.0777714i
\(497\) 7.74597 + 22.3607i 0.347454 + 1.00301i
\(498\) 0 0
\(499\) 15.5000 26.8468i 0.693875 1.20183i −0.276683 0.960961i \(-0.589235\pi\)
0.970558 0.240866i \(-0.0774314\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 51.9615i 2.31916i
\(503\) −23.2379 −1.03613 −0.518063 0.855342i \(-0.673347\pi\)
−0.518063 + 0.855342i \(0.673347\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 44.7214i 1.98811i
\(507\) 0 0
\(508\) 3.00000 0.133103
\(509\) 11.6190 20.1246i 0.515001 0.892008i −0.484848 0.874599i \(-0.661125\pi\)
0.999848 0.0174091i \(-0.00554175\pi\)
\(510\) 0 0
\(511\) 18.0000 + 3.46410i 0.796273 + 0.153243i
\(512\) 11.1803i 0.494106i
\(513\) 0 0
\(514\) −45.0000 25.9808i −1.98486 1.14596i
\(515\) 0 0
\(516\) 0 0
\(517\) −30.0000 + 17.3205i −1.31940 + 0.761755i
\(518\) 19.3649 22.3607i 0.850846 0.982472i
\(519\) 0 0
\(520\) 0 0
\(521\) −3.87298 + 6.70820i −0.169678 + 0.293892i −0.938307 0.345804i \(-0.887606\pi\)
0.768628 + 0.639696i \(0.220940\pi\)
\(522\) 0 0
\(523\) −16.5000 + 9.52628i −0.721495 + 0.416555i −0.815303 0.579035i \(-0.803429\pi\)
0.0938079 + 0.995590i \(0.470096\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −5.00000 8.66025i −0.218010 0.377605i
\(527\) −11.6190 6.70820i −0.506129 0.292214i
\(528\) 0 0
\(529\) −1.50000 2.59808i −0.0652174 0.112960i
\(530\) 0 0
\(531\) 0 0
\(532\) 18.0000 20.7846i 0.780399 0.901127i
\(533\) 11.6190 + 6.70820i 0.503273 + 0.290565i
\(534\) 0 0
\(535\) 0 0
\(536\) 2.23607i 0.0965834i
\(537\) 0 0
\(538\) 30.0000 + 17.3205i 1.29339 + 0.746740i
\(539\) −11.6190 + 29.0689i −0.500464 + 1.25209i
\(540\) 0 0
\(541\) −7.00000 12.1244i −0.300954 0.521267i 0.675399 0.737453i \(-0.263972\pi\)
−0.976352 + 0.216186i \(0.930638\pi\)
\(542\) 1.93649 + 3.35410i 0.0831794 + 0.144071i
\(543\) 0 0
\(544\) 45.0000 + 25.9808i 1.92936 + 1.11392i
\(545\) 0 0
\(546\) 0 0
\(547\) −5.50000 + 9.52628i −0.235163 + 0.407314i −0.959320 0.282321i \(-0.908896\pi\)
0.724157 + 0.689635i \(0.242229\pi\)
\(548\) 11.6190 6.70820i 0.496337 0.286560i
\(549\) 0 0
\(550\) 25.0000 43.3013i 1.06600 1.84637i
\(551\) −15.4919 −0.659979
\(552\) 0 0
\(553\) 27.5000 9.52628i 1.16942 0.405099i
\(554\) 9.68246 5.59017i 0.411368 0.237504i
\(555\) 0 0
\(556\) −22.5000 + 12.9904i −0.954213 + 0.550915i
\(557\) −30.9839 17.8885i −1.31283 0.757962i −0.330265 0.943888i \(-0.607138\pi\)
−0.982564 + 0.185926i \(0.940471\pi\)
\(558\) 0 0
\(559\) 12.1244i 0.512806i
\(560\) 0 0
\(561\) 0 0
\(562\) −20.0000 + 34.6410i −0.843649 + 1.46124i
\(563\) −7.74597 −0.326454 −0.163227 0.986589i \(-0.552190\pi\)
−0.163227 + 0.986589i \(0.552190\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −27.1109 −1.13956
\(567\) 0 0
\(568\) 20.0000 0.839181
\(569\) 17.8885i 0.749927i −0.927040 0.374963i \(-0.877655\pi\)
0.927040 0.374963i \(-0.122345\pi\)
\(570\) 0 0
\(571\) −16.0000 −0.669579 −0.334790 0.942293i \(-0.608665\pi\)
−0.334790 + 0.942293i \(0.608665\pi\)
\(572\) −11.6190 + 20.1246i −0.485813 + 0.841452i
\(573\) 0 0
\(574\) 30.0000 34.6410i 1.25218 1.44589i
\(575\) 22.3607i 0.932505i
\(576\) 0 0
\(577\) −34.5000 19.9186i −1.43625 0.829222i −0.438667 0.898650i \(-0.644549\pi\)
−0.997587 + 0.0694283i \(0.977883\pi\)
\(578\) 83.2691 48.0755i 3.46354 1.99968i
\(579\) 0 0
\(580\) 0 0
\(581\) 3.87298 20.1246i 0.160678 0.834910i
\(582\) 0 0
\(583\) −20.0000 −0.828315
\(584\) 7.74597 13.4164i 0.320530 0.555175i
\(585\) 0 0
\(586\) 15.0000 8.66025i 0.619644 0.357752i
\(587\) 15.4919 26.8328i 0.639421 1.10751i −0.346140 0.938183i \(-0.612508\pi\)
0.985560 0.169326i \(-0.0541590\pi\)
\(588\) 0 0
\(589\) −3.00000 5.19615i −0.123613 0.214104i
\(590\) 0 0
\(591\) 0 0
\(592\) 2.50000 + 4.33013i 0.102749 + 0.177967i
\(593\) 15.4919 + 26.8328i 0.636177 + 1.10189i 0.986264 + 0.165174i \(0.0528187\pi\)
−0.350087 + 0.936717i \(0.613848\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −46.4758 26.8328i −1.90372 1.09911i
\(597\) 0 0
\(598\) 17.3205i 0.708288i
\(599\) 8.94427i 0.365453i 0.983164 + 0.182727i \(0.0584923\pi\)
−0.983164 + 0.182727i \(0.941508\pi\)
\(600\) 0 0
\(601\) −37.5000 21.6506i −1.52966 0.883148i −0.999376 0.0353259i \(-0.988753\pi\)
−0.530281 0.847822i \(-0.677914\pi\)
\(602\) 40.6663 + 7.82624i 1.65744 + 0.318974i
\(603\) 0 0
\(604\) −19.5000 33.7750i −0.793444 1.37428i
\(605\) 0 0
\(606\) 0 0
\(607\) −27.0000 15.5885i −1.09590 0.632716i −0.160756 0.986994i \(-0.551393\pi\)
−0.935140 + 0.354278i \(0.884727\pi\)
\(608\) 11.6190 + 20.1246i 0.471211 + 0.816161i
\(609\) 0 0
\(610\) 0 0
\(611\) −11.6190 + 6.70820i −0.470052 + 0.271385i
\(612\) 0 0
\(613\) −11.5000 + 19.9186i −0.464481 + 0.804504i −0.999178 0.0405396i \(-0.987092\pi\)
0.534697 + 0.845044i \(0.320426\pi\)
\(614\) −11.6190 −0.468903
\(615\) 0 0
\(616\) 20.0000 + 17.3205i 0.805823 + 0.697863i
\(617\) 19.3649 11.1803i 0.779602 0.450104i −0.0566871 0.998392i \(-0.518054\pi\)
0.836289 + 0.548288i \(0.184720\pi\)
\(618\) 0 0
\(619\) −4.50000 + 2.59808i −0.180870 + 0.104425i −0.587701 0.809078i \(-0.699967\pi\)
0.406831 + 0.913503i \(0.366634\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 34.6410i 1.38898i
\(623\) −30.9839 26.8328i −1.24134 1.07503i
\(624\) 0 0
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) −30.9839 −1.23836
\(627\) 0 0
\(628\) 41.5692i 1.65879i
\(629\) 38.7298 1.54426
\(630\) 0 0
\(631\) 29.0000 1.15447 0.577236 0.816577i \(-0.304131\pi\)
0.577236 + 0.816577i \(0.304131\pi\)
\(632\) 24.5967i 0.978406i
\(633\) 0 0
\(634\) 10.0000 0.397151
\(635\) 0 0
\(636\) 0 0
\(637\) −4.50000 + 11.2583i −0.178296 + 0.446071i
\(638\) 44.7214i 1.77054i
\(639\) 0 0
\(640\) 0 0
\(641\) −3.87298 + 2.23607i −0.152974 + 0.0883194i −0.574533 0.818481i \(-0.694816\pi\)
0.421559 + 0.906801i \(0.361483\pi\)
\(642\) 0 0
\(643\) 16.5000 9.52628i 0.650696 0.375680i −0.138027 0.990429i \(-0.544076\pi\)
0.788723 + 0.614749i \(0.210743\pi\)
\(644\) −34.8569 6.70820i −1.37355 0.264340i
\(645\) 0 0
\(646\) 60.0000 2.36067
\(647\) 7.74597 13.4164i 0.304525 0.527453i −0.672630 0.739979i \(-0.734835\pi\)
0.977156 + 0.212525i \(0.0681688\pi\)
\(648\) 0 0
\(649\) 30.0000 17.3205i 1.17760 0.679889i
\(650\) 9.68246 16.7705i 0.379777 0.657794i
\(651\) 0 0
\(652\) −19.5000 33.7750i −0.763679 1.32273i
\(653\) −19.3649 11.1803i −0.757808 0.437521i 0.0707003 0.997498i \(-0.477477\pi\)
−0.828508 + 0.559977i \(0.810810\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 3.87298 + 6.70820i 0.151215 + 0.261911i
\(657\) 0 0
\(658\) 15.0000 + 43.3013i 0.584761 + 1.68806i
\(659\) 15.4919 + 8.94427i 0.603480 + 0.348419i 0.770409 0.637549i \(-0.220052\pi\)
−0.166929 + 0.985969i \(0.553385\pi\)
\(660\) 0 0
\(661\) 27.7128i 1.07790i 0.842337 + 0.538952i \(0.181179\pi\)
−0.842337 + 0.538952i \(0.818821\pi\)
\(662\) 8.94427i 0.347629i
\(663\) 0 0
\(664\) −15.0000 8.66025i −0.582113 0.336083i
\(665\) 0 0
\(666\) 0 0
\(667\) 10.0000 + 17.3205i 0.387202 + 0.670653i
\(668\) 11.6190 + 20.1246i 0.449551 + 0.778645i
\(669\) 0 0
\(670\) 0 0
\(671\) −19.3649 33.5410i −0.747574 1.29484i
\(672\) 0 0
\(673\) −1.00000 + 1.73205i −0.0385472 + 0.0667657i −0.884655 0.466246i \(-0.845606\pi\)
0.846108 + 0.533011i \(0.178940\pi\)
\(674\) −19.3649 + 11.1803i −0.745909 + 0.430651i
\(675\) 0 0
\(676\) 15.0000 25.9808i 0.576923 0.999260i
\(677\) 30.9839 1.19081 0.595403 0.803427i \(-0.296992\pi\)
0.595403 + 0.803427i \(0.296992\pi\)
\(678\) 0 0
\(679\) −4.50000 0.866025i −0.172694 0.0332350i
\(680\) 0 0
\(681\) 0 0
\(682\) 15.0000 8.66025i 0.574380 0.331618i
\(683\) −30.9839 17.8885i −1.18556 0.684486i −0.228269 0.973598i \(-0.573307\pi\)
−0.957295 + 0.289112i \(0.906640\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 34.8569 + 22.3607i 1.33084 + 0.853735i
\(687\) 0 0
\(688\) −3.50000 + 6.06218i −0.133436 + 0.231118i
\(689\) −7.74597 −0.295098
\(690\) 0 0
\(691\) 32.9090i 1.25192i −0.779857 0.625958i \(-0.784708\pi\)
0.779857 0.625958i \(-0.215292\pi\)
\(692\) 46.4758 1.76674
\(693\) 0 0
\(694\) −20.0000 −0.759190
\(695\) 0 0
\(696\) 0 0
\(697\) 60.0000 2.27266
\(698\) 25.1744 43.6033i 0.952865 1.65041i
\(699\) 0 0
\(700\) −30.0000 25.9808i −1.13389 0.981981i
\(701\) 8.94427i 0.337820i 0.985631 + 0.168910i \(0.0540248\pi\)
−0.985631 + 0.168910i \(0.945975\pi\)
\(702\) 0 0
\(703\) 15.0000 + 8.66025i 0.565736 + 0.326628i
\(704\) −50.3488 + 29.0689i −1.89759 + 1.09557i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 11.0000 0.413114 0.206557 0.978435i \(-0.433774\pi\)
0.206557 + 0.978435i \(0.433774\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −30.0000 + 17.3205i −1.12430 + 0.649113i
\(713\) −3.87298 + 6.70820i −0.145044 + 0.251224i
\(714\) 0 0
\(715\) 0 0
\(716\) 23.2379 + 13.4164i 0.868441 + 0.501395i
\(717\) 0 0
\(718\) −5.00000 8.66025i −0.186598 0.323198i
\(719\) −7.74597 13.4164i −0.288876 0.500348i 0.684666 0.728857i \(-0.259948\pi\)
−0.973542 + 0.228509i \(0.926615\pi\)
\(720\) 0 0
\(721\) 13.5000 + 2.59808i 0.502766 + 0.0967574i
\(722\) −13.5554 7.82624i −0.504481 0.291262i
\(723\) 0 0
\(724\) 0 0
\(725\) 22.3607i 0.830455i
\(726\) 0 0
\(727\) 16.5000 + 9.52628i 0.611951 + 0.353310i 0.773729 0.633517i \(-0.218389\pi\)
−0.161778 + 0.986827i \(0.551723\pi\)
\(728\) 7.74597 + 6.70820i 0.287085 + 0.248623i
\(729\) 0 0
\(730\) 0 0
\(731\) 27.1109 + 46.9574i 1.00273 + 1.73678i
\(732\) 0 0
\(733\) −31.5000 18.1865i −1.16348 0.671735i −0.211344 0.977412i \(-0.567784\pi\)
−0.952135 + 0.305677i \(0.901117\pi\)
\(734\) 11.6190 + 20.1246i 0.428863 + 0.742813i
\(735\) 0 0
\(736\) 15.0000 25.9808i 0.552907 0.957664i
\(737\) 3.87298 2.23607i 0.142663 0.0823666i
\(738\) 0 0
\(739\) −11.5000 + 19.9186i −0.423034 + 0.732717i −0.996235 0.0866983i \(-0.972368\pi\)
0.573200 + 0.819415i \(0.305702\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −5.00000 + 25.9808i −0.183556 + 0.953784i
\(743\) −27.1109 + 15.6525i −0.994602 + 0.574234i −0.906647 0.421891i \(-0.861367\pi\)
−0.0879552 + 0.996124i \(0.528033\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −3.87298 2.23607i −0.141800 0.0818683i
\(747\) 0 0
\(748\) 103.923i 3.79980i
\(749\) −7.74597 + 8.94427i −0.283031 + 0.326817i
\(750\) 0 0
\(751\) 8.00000 13.8564i 0.291924 0.505627i −0.682341 0.731034i \(-0.739038\pi\)
0.974265 + 0.225407i \(0.0723712\pi\)
\(752\) −7.74597 −0.282466
\(753\) 0 0
\(754\) 17.3205i 0.630776i
\(755\) 0 0
\(756\) 0 0
\(757\) −25.0000 −0.908640 −0.454320 0.890838i \(-0.650118\pi\)
−0.454320 + 0.890838i \(0.650118\pi\)
\(758\) 38.0132i 1.38070i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(762\) 0 0
\(763\) 0.500000 2.59808i 0.0181012 0.0940567i
\(764\) 53.6656i 1.94155i
\(765\) 0 0
\(766\) −45.0000 25.9808i −1.62592 0.938723i
\(767\) 11.6190 6.70820i 0.419536 0.242219i
\(768\) 0 0
\(769\) 30.0000 17.3205i 1.08183 0.624593i 0.150439 0.988619i \(-0.451931\pi\)
0.931389 + 0.364026i \(0.118598\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 21.0000 0.755807
\(773\) −15.4919 + 26.8328i −0.557206 + 0.965109i 0.440522 + 0.897742i \(0.354793\pi\)
−0.997728 + 0.0673675i \(0.978540\pi\)
\(774\) 0 0
\(775\) −7.50000 + 4.33013i −0.269408 + 0.155543i
\(776\) −1.93649 + 3.35410i −0.0695160 + 0.120405i
\(777\) 0 0
\(778\) 10.0000 + 17.3205i 0.358517 + 0.620970i
\(779\) 23.2379 + 13.4164i 0.832584 + 0.480693i
\(780\) 0 0
\(781\) −20.0000 34.6410i −0.715656 1.23955i
\(782\) −38.7298 67.0820i −1.38498 2.39885i
\(783\) 0 0
\(784\) −5.50000 + 4.33013i −0.196429 + 0.154647i
\(785\) 0 0
\(786\) 0 0
\(787\) 19.0526i 0.679150i −0.940579 0.339575i \(-0.889717\pi\)
0.940579 0.339575i \(-0.110283\pi\)
\(788\) 26.8328i 0.955879i
\(789\) 0 0
\(790\) 0 0
\(791\) 15.4919 17.8885i 0.550830 0.636043i
\(792\) 0 0