Properties

Label 1183.2.e.b.508.1
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.b.170.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.500000 + 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-2.50000 + 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-3.50000 + 6.06218i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(-3.50000 - 6.06218i) q^{19} -3.00000 q^{22} +(3.00000 + 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} +(2.00000 + 1.73205i) q^{28} -5.00000 q^{29} +(2.50000 - 4.33013i) q^{32} -7.00000 q^{34} +3.00000 q^{36} +(4.00000 + 6.92820i) q^{37} +(3.50000 - 6.06218i) q^{38} +2.00000 q^{43} +(1.50000 + 2.59808i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(3.50000 + 6.06218i) q^{47} +(-6.50000 - 2.59808i) q^{49} +5.00000 q^{50} +(1.50000 - 2.59808i) q^{53} +(-1.50000 + 7.79423i) q^{56} +(-2.50000 - 4.33013i) q^{58} +(-3.50000 + 6.06218i) q^{59} +(3.50000 + 6.06218i) q^{61} +(-7.50000 + 2.59808i) q^{63} +7.00000 q^{64} +(-1.50000 + 2.59808i) q^{67} +(3.50000 + 6.06218i) q^{68} +5.00000 q^{71} +(4.50000 + 7.79423i) q^{72} +(7.00000 - 12.1244i) q^{73} +(-4.00000 + 6.92820i) q^{74} -7.00000 q^{76} +(-6.00000 - 5.19615i) q^{77} +(3.00000 + 5.19615i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(1.00000 + 1.73205i) q^{86} +(-4.50000 + 7.79423i) q^{88} +6.00000 q^{92} +(-3.50000 + 6.06218i) q^{94} +14.0000 q^{97} +(-1.00000 - 6.92820i) q^{98} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{4} - q^{7} + 6 q^{8} + 3 q^{9} + O(q^{10}) \) \( 2 q + q^{2} + q^{4} - q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{11} - 5 q^{14} + q^{16} - 7 q^{17} - 3 q^{18} - 7 q^{19} - 6 q^{22} + 6 q^{23} + 5 q^{25} + 4 q^{28} - 10 q^{29} + 5 q^{32} - 14 q^{34} + 6 q^{36} + 8 q^{37} + 7 q^{38} + 4 q^{43} + 3 q^{44} - 6 q^{46} + 7 q^{47} - 13 q^{49} + 10 q^{50} + 3 q^{53} - 3 q^{56} - 5 q^{58} - 7 q^{59} + 7 q^{61} - 15 q^{63} + 14 q^{64} - 3 q^{67} + 7 q^{68} + 10 q^{71} + 9 q^{72} + 14 q^{73} - 8 q^{74} - 14 q^{76} - 12 q^{77} + 6 q^{79} - 9 q^{81} + 2 q^{86} - 9 q^{88} + 12 q^{92} - 7 q^{94} + 28 q^{97} - 2 q^{98} - 18 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0.986869 0.161521i \(-0.0516399\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0 0
\(7\) −0.500000 + 2.59808i −0.188982 + 0.981981i
\(8\) 3.00000 1.06066
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) −2.50000 + 0.866025i −0.668153 + 0.231455i
\(15\) 0 0
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −3.50000 + 6.06218i −0.848875 + 1.47029i 0.0333386 + 0.999444i \(0.489386\pi\)
−0.882213 + 0.470850i \(0.843947\pi\)
\(18\) −1.50000 + 2.59808i −0.353553 + 0.612372i
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(-0.463407\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −3.00000 −0.639602
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 0 0
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) 0 0
\(27\) 0 0
\(28\) 2.00000 + 1.73205i 0.377964 + 0.327327i
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 2.50000 4.33013i 0.441942 0.765466i
\(33\) 0 0
\(34\) −7.00000 −1.20049
\(35\) 0 0
\(36\) 3.00000 0.500000
\(37\) 4.00000 + 6.92820i 0.657596 + 1.13899i 0.981236 + 0.192809i \(0.0617599\pi\)
−0.323640 + 0.946180i \(0.604907\pi\)
\(38\) 3.50000 6.06218i 0.567775 0.983415i
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) 0 0
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) 3.50000 + 6.06218i 0.510527 + 0.884260i 0.999926 + 0.0121990i \(0.00388317\pi\)
−0.489398 + 0.872060i \(0.662783\pi\)
\(48\) 0 0
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 5.00000 0.707107
\(51\) 0 0
\(52\) 0 0
\(53\) 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i \(-0.767275\pi\)
0.950464 + 0.310835i \(0.100609\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.50000 + 7.79423i −0.200446 + 1.04155i
\(57\) 0 0
\(58\) −2.50000 4.33013i −0.328266 0.568574i
\(59\) −3.50000 + 6.06218i −0.455661 + 0.789228i −0.998726 0.0504625i \(-0.983930\pi\)
0.543065 + 0.839691i \(0.317264\pi\)
\(60\) 0 0
\(61\) 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i \(-0.0187572\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(62\) 0 0
\(63\) −7.50000 + 2.59808i −0.944911 + 0.327327i
\(64\) 7.00000 0.875000
\(65\) 0 0
\(66\) 0 0
\(67\) −1.50000 + 2.59808i −0.183254 + 0.317406i −0.942987 0.332830i \(-0.891996\pi\)
0.759733 + 0.650236i \(0.225330\pi\)
\(68\) 3.50000 + 6.06218i 0.424437 + 0.735147i
\(69\) 0 0
\(70\) 0 0
\(71\) 5.00000 0.593391 0.296695 0.954972i \(-0.404115\pi\)
0.296695 + 0.954972i \(0.404115\pi\)
\(72\) 4.50000 + 7.79423i 0.530330 + 0.918559i
\(73\) 7.00000 12.1244i 0.819288 1.41905i −0.0869195 0.996215i \(-0.527702\pi\)
0.906208 0.422833i \(-0.138964\pi\)
\(74\) −4.00000 + 6.92820i −0.464991 + 0.805387i
\(75\) 0 0
\(76\) −7.00000 −0.802955
\(77\) −6.00000 5.19615i −0.683763 0.592157i
\(78\) 0 0
\(79\) 3.00000 + 5.19615i 0.337526 + 0.584613i 0.983967 0.178352i \(-0.0570765\pi\)
−0.646440 + 0.762964i \(0.723743\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.00000 + 1.73205i 0.107833 + 0.186772i
\(87\) 0 0
\(88\) −4.50000 + 7.79423i −0.479702 + 0.830868i
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 0 0
\(94\) −3.50000 + 6.06218i −0.360997 + 0.625266i
\(95\) 0 0
\(96\) 0 0
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) −1.00000 6.92820i −0.101015 0.699854i
\(99\) −9.00000 −0.904534
\(100\) −2.50000 4.33013i −0.250000 0.433013i
\(101\) 7.00000 12.1244i 0.696526 1.20642i −0.273138 0.961975i \(-0.588061\pi\)
0.969664 0.244443i \(-0.0786053\pi\)
\(102\) 0 0
\(103\) −7.00000 12.1244i −0.689730 1.19465i −0.971925 0.235291i \(-0.924396\pi\)
0.282194 0.959357i \(-0.408938\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 3.00000 0.291386
\(107\) −4.00000 6.92820i −0.386695 0.669775i 0.605308 0.795991i \(-0.293050\pi\)
−0.992003 + 0.126217i \(0.959717\pi\)
\(108\) 0 0
\(109\) 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i \(-0.771977\pi\)
0.945769 + 0.324840i \(0.105310\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.50000 + 0.866025i −0.236228 + 0.0818317i
\(113\) 9.00000 0.846649 0.423324 0.905978i \(-0.360863\pi\)
0.423324 + 0.905978i \(0.360863\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −2.50000 + 4.33013i −0.232119 + 0.402042i
\(117\) 0 0
\(118\) −7.00000 −0.644402
\(119\) −14.0000 12.1244i −1.28338 1.11144i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −3.50000 + 6.06218i −0.316875 + 0.548844i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −6.00000 5.19615i −0.534522 0.462910i
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) −1.50000 2.59808i −0.132583 0.229640i
\(129\) 0 0
\(130\) 0 0
\(131\) −7.00000 12.1244i −0.611593 1.05931i −0.990972 0.134069i \(-0.957196\pi\)
0.379379 0.925241i \(-0.376138\pi\)
\(132\) 0 0
\(133\) 17.5000 6.06218i 1.51744 0.525657i
\(134\) −3.00000 −0.259161
\(135\) 0 0
\(136\) −10.5000 + 18.1865i −0.900368 + 1.55948i
\(137\) 2.00000 3.46410i 0.170872 0.295958i −0.767853 0.640626i \(-0.778675\pi\)
0.938725 + 0.344668i \(0.112008\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2.50000 + 4.33013i 0.209795 + 0.363376i
\(143\) 0 0
\(144\) −1.50000 + 2.59808i −0.125000 + 0.216506i
\(145\) 0 0
\(146\) 14.0000 1.15865
\(147\) 0 0
\(148\) 8.00000 0.657596
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) −1.50000 + 2.59808i −0.122068 + 0.211428i −0.920583 0.390547i \(-0.872286\pi\)
0.798515 + 0.601975i \(0.205619\pi\)
\(152\) −10.5000 18.1865i −0.851662 1.47512i
\(153\) −21.0000 −1.69775
\(154\) 1.50000 7.79423i 0.120873 0.628077i
\(155\) 0 0
\(156\) 0 0
\(157\) −3.50000 + 6.06218i −0.279330 + 0.483814i −0.971219 0.238190i \(-0.923446\pi\)
0.691888 + 0.722005i \(0.256779\pi\)
\(158\) −3.00000 + 5.19615i −0.238667 + 0.413384i
\(159\) 0 0
\(160\) 0 0
\(161\) −15.0000 + 5.19615i −1.18217 + 0.409514i
\(162\) −9.00000 −0.707107
\(163\) −6.50000 11.2583i −0.509119 0.881820i −0.999944 0.0105623i \(-0.996638\pi\)
0.490825 0.871258i \(-0.336695\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 7.00000 0.541676 0.270838 0.962625i \(-0.412699\pi\)
0.270838 + 0.962625i \(0.412699\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 10.5000 18.1865i 0.802955 1.39076i
\(172\) 1.00000 1.73205i 0.0762493 0.132068i
\(173\) −3.50000 6.06218i −0.266100 0.460899i 0.701751 0.712422i \(-0.252402\pi\)
−0.967851 + 0.251523i \(0.919068\pi\)
\(174\) 0 0
\(175\) 10.0000 + 8.66025i 0.755929 + 0.654654i
\(176\) −3.00000 −0.226134
\(177\) 0 0
\(178\) 0 0
\(179\) 5.00000 8.66025i 0.373718 0.647298i −0.616417 0.787420i \(-0.711416\pi\)
0.990134 + 0.140122i \(0.0447496\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 9.00000 + 15.5885i 0.663489 + 1.14920i
\(185\) 0 0
\(186\) 0 0
\(187\) −10.5000 18.1865i −0.767836 1.32993i
\(188\) 7.00000 0.510527
\(189\) 0 0
\(190\) 0 0
\(191\) 10.0000 + 17.3205i 0.723575 + 1.25327i 0.959558 + 0.281511i \(0.0908356\pi\)
−0.235983 + 0.971757i \(0.575831\pi\)
\(192\) 0 0
\(193\) 2.00000 3.46410i 0.143963 0.249351i −0.785022 0.619467i \(-0.787349\pi\)
0.928986 + 0.370116i \(0.120682\pi\)
\(194\) 7.00000 + 12.1244i 0.502571 + 0.870478i
\(195\) 0 0
\(196\) −5.50000 + 4.33013i −0.392857 + 0.309295i
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) −4.50000 7.79423i −0.319801 0.553912i
\(199\) 7.00000 12.1244i 0.496217 0.859473i −0.503774 0.863836i \(-0.668055\pi\)
0.999990 + 0.00436292i \(0.00138876\pi\)
\(200\) 7.50000 12.9904i 0.530330 0.918559i
\(201\) 0 0
\(202\) 14.0000 0.985037
\(203\) 2.50000 12.9904i 0.175466 0.911746i
\(204\) 0 0
\(205\) 0 0
\(206\) 7.00000 12.1244i 0.487713 0.844744i
\(207\) −9.00000 + 15.5885i −0.625543 + 1.08347i
\(208\) 0 0
\(209\) 21.0000 1.45260
\(210\) 0 0
\(211\) −26.0000 −1.78991 −0.894957 0.446153i \(-0.852794\pi\)
−0.894957 + 0.446153i \(0.852794\pi\)
\(212\) −1.50000 2.59808i −0.103020 0.178437i
\(213\) 0 0
\(214\) 4.00000 6.92820i 0.273434 0.473602i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 4.00000 0.270914
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −21.0000 −1.40626 −0.703132 0.711059i \(-0.748216\pi\)
−0.703132 + 0.711059i \(0.748216\pi\)
\(224\) 10.0000 + 8.66025i 0.668153 + 0.578638i
\(225\) 15.0000 1.00000
\(226\) 4.50000 + 7.79423i 0.299336 + 0.518464i
\(227\) −14.0000 + 24.2487i −0.929213 + 1.60944i −0.144571 + 0.989494i \(0.546180\pi\)
−0.784642 + 0.619949i \(0.787153\pi\)
\(228\) 0 0
\(229\) 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i \(-0.0135930\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −15.0000 −0.984798
\(233\) 13.5000 + 23.3827i 0.884414 + 1.53185i 0.846383 + 0.532574i \(0.178775\pi\)
0.0380310 + 0.999277i \(0.487891\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 3.50000 + 6.06218i 0.227831 + 0.394614i
\(237\) 0 0
\(238\) 3.50000 18.1865i 0.226871 1.17886i
\(239\) 19.0000 1.22901 0.614504 0.788914i \(-0.289356\pi\)
0.614504 + 0.788914i \(0.289356\pi\)
\(240\) 0 0
\(241\) 14.0000 24.2487i 0.901819 1.56200i 0.0766885 0.997055i \(-0.475565\pi\)
0.825131 0.564942i \(-0.191101\pi\)
\(242\) −1.00000 + 1.73205i −0.0642824 + 0.111340i
\(243\) 0 0
\(244\) 7.00000 0.448129
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −14.0000 −0.883672 −0.441836 0.897096i \(-0.645673\pi\)
−0.441836 + 0.897096i \(0.645673\pi\)
\(252\) −1.50000 + 7.79423i −0.0944911 + 0.490990i
\(253\) −18.0000 −1.13165
\(254\) 1.00000 + 1.73205i 0.0627456 + 0.108679i
\(255\) 0 0
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) 7.00000 + 12.1244i 0.436648 + 0.756297i 0.997429 0.0716680i \(-0.0228322\pi\)
−0.560781 + 0.827964i \(0.689499\pi\)
\(258\) 0 0
\(259\) −20.0000 + 6.92820i −1.24274 + 0.430498i
\(260\) 0 0
\(261\) −7.50000 12.9904i −0.464238 0.804084i
\(262\) 7.00000 12.1244i 0.432461 0.749045i
\(263\) 12.0000 20.7846i 0.739952 1.28163i −0.212565 0.977147i \(-0.568182\pi\)
0.952517 0.304487i \(-0.0984850\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 14.0000 + 12.1244i 0.858395 + 0.743392i
\(267\) 0 0
\(268\) 1.50000 + 2.59808i 0.0916271 + 0.158703i
\(269\) 10.5000 18.1865i 0.640196 1.10885i −0.345192 0.938532i \(-0.612186\pi\)
0.985389 0.170321i \(-0.0544803\pi\)
\(270\) 0 0
\(271\) −3.50000 6.06218i −0.212610 0.368251i 0.739921 0.672694i \(-0.234863\pi\)
−0.952531 + 0.304443i \(0.901530\pi\)
\(272\) −7.00000 −0.424437
\(273\) 0 0
\(274\) 4.00000 0.241649
\(275\) 7.50000 + 12.9904i 0.452267 + 0.783349i
\(276\) 0 0
\(277\) 8.50000 14.7224i 0.510716 0.884585i −0.489207 0.872167i \(-0.662714\pi\)
0.999923 0.0124177i \(-0.00395278\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 12.0000 0.715860 0.357930 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 0 0
\(283\) 7.00000 12.1244i 0.416107 0.720718i −0.579437 0.815017i \(-0.696728\pi\)
0.995544 + 0.0942988i \(0.0300609\pi\)
\(284\) 2.50000 4.33013i 0.148348 0.256946i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 15.0000 0.883883
\(289\) −16.0000 27.7128i −0.941176 1.63017i
\(290\) 0 0
\(291\) 0 0
\(292\) −7.00000 12.1244i −0.409644 0.709524i
\(293\) −14.0000 −0.817889 −0.408944 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 12.0000 + 20.7846i 0.697486 + 1.20808i
\(297\) 0 0
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) 0 0
\(300\) 0 0
\(301\) −1.00000 + 5.19615i −0.0576390 + 0.299501i
\(302\) −3.00000 −0.172631
\(303\) 0 0
\(304\) 3.50000 6.06218i 0.200739 0.347690i
\(305\) 0 0
\(306\) −10.5000 18.1865i −0.600245 1.03965i
\(307\) −21.0000 −1.19853 −0.599267 0.800549i \(-0.704541\pi\)
−0.599267 + 0.800549i \(0.704541\pi\)
\(308\) −7.50000 + 2.59808i −0.427352 + 0.148039i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0 0
\(313\) 7.00000 + 12.1244i 0.395663 + 0.685309i 0.993186 0.116543i \(-0.0371814\pi\)
−0.597522 + 0.801852i \(0.703848\pi\)
\(314\) −7.00000 −0.395033
\(315\) 0 0
\(316\) 6.00000 0.337526
\(317\) −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i \(-0.220558\pi\)
−0.937892 + 0.346929i \(0.887225\pi\)
\(318\) 0 0
\(319\) 7.50000 12.9904i 0.419919 0.727322i
\(320\) 0 0
\(321\) 0 0
\(322\) −12.0000 10.3923i −0.668734 0.579141i
\(323\) 49.0000 2.72643
\(324\) 4.50000 + 7.79423i 0.250000 + 0.433013i
\(325\) 0 0
\(326\) 6.50000 11.2583i 0.360002 0.623541i
\(327\) 0 0
\(328\) 0 0
\(329\) −17.5000 + 6.06218i −0.964806 + 0.334219i
\(330\) 0 0
\(331\) −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i \(-0.981428\pi\)
0.448649 0.893708i \(-0.351905\pi\)
\(332\) 0 0
\(333\) −12.0000 + 20.7846i −0.657596 + 1.13899i
\(334\) 3.50000 + 6.06218i 0.191511 + 0.331708i
\(335\) 0 0
\(336\) 0 0
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 21.0000 1.13555
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 6.00000 0.323498
\(345\) 0 0
\(346\) 3.50000 6.06218i 0.188161 0.325905i
\(347\) −2.00000 + 3.46410i −0.107366 + 0.185963i −0.914702 0.404128i \(-0.867575\pi\)
0.807337 + 0.590091i \(0.200908\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) −2.50000 + 12.9904i −0.133631 + 0.694365i
\(351\) 0 0
\(352\) 7.50000 + 12.9904i 0.399751 + 0.692390i
\(353\) 7.00000 12.1244i 0.372572 0.645314i −0.617388 0.786659i \(-0.711809\pi\)
0.989960 + 0.141344i \(0.0451425\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 10.0000 0.528516
\(359\) 4.00000 + 6.92820i 0.211112 + 0.365657i 0.952063 0.305903i \(-0.0989582\pi\)
−0.740951 + 0.671559i \(0.765625\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) −3.50000 6.06218i −0.183956 0.318621i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −7.00000 + 12.1244i −0.365397 + 0.632886i −0.988840 0.148983i \(-0.952400\pi\)
0.623443 + 0.781869i \(0.285733\pi\)
\(368\) −3.00000 + 5.19615i −0.156386 + 0.270868i
\(369\) 0 0
\(370\) 0 0
\(371\) 6.00000 + 5.19615i 0.311504 + 0.269771i
\(372\) 0 0
\(373\) −7.50000 12.9904i −0.388335 0.672616i 0.603890 0.797067i \(-0.293616\pi\)
−0.992226 + 0.124451i \(0.960283\pi\)
\(374\) 10.5000 18.1865i 0.542942 0.940403i
\(375\) 0 0
\(376\) 10.5000 + 18.1865i 0.541496 + 0.937899i
\(377\) 0 0
\(378\) 0 0
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −10.0000 + 17.3205i −0.511645 + 0.886194i
\(383\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 4.00000 0.203595
\(387\) 3.00000 + 5.19615i 0.152499 + 0.264135i
\(388\) 7.00000 12.1244i 0.355371 0.615521i
\(389\) 1.50000 2.59808i 0.0760530 0.131728i −0.825491 0.564416i \(-0.809102\pi\)
0.901544 + 0.432688i \(0.142435\pi\)
\(390\) 0 0
\(391\) −42.0000 −2.12403
\(392\) −19.5000 7.79423i −0.984899 0.393668i
\(393\) 0 0
\(394\) −1.00000 1.73205i −0.0503793 0.0872595i
\(395\) 0 0
\(396\) −4.50000 + 7.79423i −0.226134 + 0.391675i
\(397\) 7.00000 + 12.1244i 0.351320 + 0.608504i 0.986481 0.163876i \(-0.0523996\pi\)
−0.635161 + 0.772380i \(0.719066\pi\)
\(398\) 14.0000 0.701757
\(399\) 0 0
\(400\) 5.00000 0.250000
\(401\) 11.0000 + 19.0526i 0.549314 + 0.951439i 0.998322 + 0.0579116i \(0.0184442\pi\)
−0.449008 + 0.893528i \(0.648223\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −7.00000 12.1244i −0.348263 0.603209i
\(405\) 0 0
\(406\) 12.5000 4.33013i 0.620365 0.214901i
\(407\) −24.0000 −1.18964
\(408\) 0 0
\(409\) −14.0000 + 24.2487i −0.692255 + 1.19902i 0.278842 + 0.960337i \(0.410050\pi\)
−0.971097 + 0.238685i \(0.923284\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −14.0000 −0.689730
\(413\) −14.0000 12.1244i −0.688895 0.596601i
\(414\) −18.0000 −0.884652
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 10.5000 + 18.1865i 0.513572 + 0.889532i
\(419\) 14.0000 0.683945 0.341972 0.939710i \(-0.388905\pi\)
0.341972 + 0.939710i \(0.388905\pi\)
\(420\) 0 0
\(421\) −30.0000 −1.46211 −0.731055 0.682318i \(-0.760972\pi\)
−0.731055 + 0.682318i \(0.760972\pi\)
\(422\) −13.0000 22.5167i −0.632830 1.09609i
\(423\) −10.5000 + 18.1865i −0.510527 + 0.884260i
\(424\) 4.50000 7.79423i 0.218539 0.378521i
\(425\) 17.5000 + 30.3109i 0.848875 + 1.47029i
\(426\) 0 0
\(427\) −17.5000 + 6.06218i −0.846884 + 0.293369i
\(428\) −8.00000 −0.386695
\(429\) 0 0
\(430\) 0 0
\(431\) −12.0000 + 20.7846i −0.578020 + 1.00116i 0.417687 + 0.908591i \(0.362841\pi\)
−0.995706 + 0.0925683i \(0.970492\pi\)
\(432\) 0 0
\(433\) 21.0000 1.00920 0.504598 0.863355i \(-0.331641\pi\)
0.504598 + 0.863355i \(0.331641\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −2.00000 3.46410i −0.0957826 0.165900i
\(437\) 21.0000 36.3731i 1.00457 1.73996i
\(438\) 0 0
\(439\) −7.00000 12.1244i −0.334092 0.578664i 0.649218 0.760602i \(-0.275096\pi\)
−0.983310 + 0.181938i \(0.941763\pi\)
\(440\) 0 0
\(441\) −3.00000 20.7846i −0.142857 0.989743i
\(442\) 0 0
\(443\) 10.0000 + 17.3205i 0.475114 + 0.822922i 0.999594 0.0285009i \(-0.00907336\pi\)
−0.524479 + 0.851423i \(0.675740\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −10.5000 18.1865i −0.497189 0.861157i
\(447\) 0 0
\(448\) −3.50000 + 18.1865i −0.165359 + 0.859233i
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 7.50000 + 12.9904i 0.353553 + 0.612372i
\(451\) 0 0
\(452\) 4.50000 7.79423i 0.211662 0.366610i
\(453\) 0 0
\(454\) −28.0000 −1.31411
\(455\) 0 0
\(456\) 0 0
\(457\) −3.00000 5.19615i −0.140334 0.243066i 0.787288 0.616585i \(-0.211484\pi\)
−0.927622 + 0.373519i \(0.878151\pi\)
\(458\) −7.00000 + 12.1244i −0.327089 + 0.566534i
\(459\) 0 0
\(460\) 0 0
\(461\) 28.0000 1.30409 0.652045 0.758180i \(-0.273911\pi\)
0.652045 + 0.758180i \(0.273911\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) −2.50000 4.33013i −0.116060 0.201021i
\(465\) 0 0
\(466\) −13.5000 + 23.3827i −0.625375 + 1.08318i
\(467\) −7.00000 12.1244i −0.323921 0.561048i 0.657372 0.753566i \(-0.271668\pi\)
−0.981293 + 0.192518i \(0.938335\pi\)
\(468\) 0 0
\(469\) −6.00000 5.19615i −0.277054 0.239936i
\(470\) 0 0
\(471\) 0 0
\(472\) −10.5000 + 18.1865i −0.483302 + 0.837103i
\(473\) −3.00000 + 5.19615i −0.137940 + 0.238919i
\(474\) 0 0
\(475\) −35.0000 −1.60591
\(476\) −17.5000 + 6.06218i −0.802111 + 0.277859i
\(477\) 9.00000 0.412082
\(478\) 9.50000 + 16.4545i 0.434520 + 0.752611i
\(479\) 3.50000 6.06218i 0.159919 0.276988i −0.774920 0.632059i \(-0.782210\pi\)
0.934839 + 0.355071i \(0.115543\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 28.0000 1.27537
\(483\) 0 0
\(484\) 2.00000 0.0909091
\(485\) 0 0
\(486\) 0 0
\(487\) 12.5000 21.6506i 0.566429 0.981084i −0.430486 0.902597i \(-0.641658\pi\)
0.996915 0.0784867i \(-0.0250088\pi\)
\(488\) 10.5000 + 18.1865i 0.475313 + 0.823266i
\(489\) 0 0
\(490\) 0 0
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) 0 0
\(493\) 17.5000 30.3109i 0.788160 1.36513i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.50000 + 12.9904i −0.112140 + 0.582698i
\(498\) 0 0
\(499\) 4.00000 + 6.92820i 0.179065 + 0.310149i 0.941560 0.336844i \(-0.109360\pi\)
−0.762496 + 0.646993i \(0.776026\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −7.00000 12.1244i −0.312425 0.541136i
\(503\) −28.0000 −1.24846 −0.624229 0.781241i \(-0.714587\pi\)
−0.624229 + 0.781241i \(0.714587\pi\)
\(504\) −22.5000 + 7.79423i −1.00223 + 0.347183i
\(505\) 0 0
\(506\) −9.00000 15.5885i −0.400099 0.692991i
\(507\) 0 0
\(508\) 1.00000 1.73205i 0.0443678 0.0768473i
\(509\) −14.0000 24.2487i −0.620539 1.07481i −0.989385 0.145315i \(-0.953580\pi\)
0.368846 0.929490i \(-0.379753\pi\)
\(510\) 0 0
\(511\) 28.0000 + 24.2487i 1.23865 + 1.07270i
\(512\) 11.0000 0.486136
\(513\) 0 0
\(514\) −7.00000 + 12.1244i −0.308757 + 0.534782i
\(515\) 0 0
\(516\) 0 0
\(517\) −21.0000 −0.923579
\(518\) −16.0000 13.8564i −0.703000 0.608816i
\(519\) 0 0
\(520\) 0 0
\(521\) 7.00000 12.1244i 0.306676 0.531178i −0.670957 0.741496i \(-0.734117\pi\)
0.977633 + 0.210318i \(0.0674500\pi\)
\(522\) 7.50000 12.9904i 0.328266 0.568574i
\(523\) 7.00000 + 12.1244i 0.306089 + 0.530161i 0.977503 0.210921i \(-0.0676463\pi\)
−0.671414 + 0.741082i \(0.734313\pi\)
\(524\) −14.0000 −0.611593
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) −21.0000 −0.911322
\(532\) 3.50000 18.1865i 0.151744 0.788486i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −4.50000 + 7.79423i −0.194370 + 0.336659i
\(537\) 0 0
\(538\) 21.0000 0.905374
\(539\) 16.5000 12.9904i 0.710705 0.559535i
\(540\) 0 0
\(541\) 4.00000 + 6.92820i 0.171973 + 0.297867i 0.939110 0.343617i \(-0.111652\pi\)
−0.767136 + 0.641484i \(0.778319\pi\)
\(542\) 3.50000 6.06218i 0.150338 0.260393i
\(543\) 0 0
\(544\) 17.5000 + 30.3109i 0.750306 + 1.29957i
\(545\) 0 0
\(546\) 0 0
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) −2.00000 3.46410i −0.0854358 0.147979i
\(549\) −10.5000 + 18.1865i −0.448129 + 0.776182i
\(550\) −7.50000 + 12.9904i −0.319801 + 0.553912i
\(551\) 17.5000 + 30.3109i 0.745525 + 1.29129i
\(552\) 0 0
\(553\) −15.0000 + 5.19615i −0.637865 + 0.220963i
\(554\) 17.0000 0.722261
\(555\) 0 0
\(556\) 0 0
\(557\) 9.00000 15.5885i 0.381342 0.660504i −0.609912 0.792469i \(-0.708795\pi\)
0.991254 + 0.131965i \(0.0421286\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 6.00000 + 10.3923i 0.253095 + 0.438373i
\(563\) −14.0000 + 24.2487i −0.590030 + 1.02196i 0.404198 + 0.914671i \(0.367551\pi\)
−0.994228 + 0.107290i \(0.965783\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 14.0000 0.588464
\(567\) −18.0000 15.5885i −0.755929 0.654654i
\(568\) 15.0000 0.629386
\(569\) −0.500000 0.866025i −0.0209611 0.0363057i 0.855355 0.518043i \(-0.173339\pi\)
−0.876316 + 0.481737i \(0.840006\pi\)
\(570\) 0 0
\(571\) −2.00000 + 3.46410i −0.0836974 + 0.144968i −0.904835 0.425762i \(-0.860006\pi\)
0.821138 + 0.570730i \(0.193340\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 30.0000 1.25109
\(576\) 10.5000 + 18.1865i 0.437500 + 0.757772i
\(577\) 7.00000 12.1244i 0.291414 0.504744i −0.682730 0.730670i \(-0.739208\pi\)
0.974144 + 0.225927i \(0.0725410\pi\)
\(578\) 16.0000 27.7128i 0.665512 1.15270i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 4.50000 + 7.79423i 0.186371 + 0.322804i
\(584\) 21.0000 36.3731i 0.868986 1.50513i
\(585\) 0 0
\(586\) −7.00000 12.1244i −0.289167 0.500853i
\(587\) −21.0000 −0.866763 −0.433381 0.901211i \(-0.642680\pi\)
−0.433381 + 0.901211i \(0.642680\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −4.00000 + 6.92820i −0.164399 + 0.284747i
\(593\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 0 0
\(598\) 0 0
\(599\) −16.0000 + 27.7128i −0.653742 + 1.13231i 0.328465 + 0.944516i \(0.393469\pi\)
−0.982208 + 0.187799i \(0.939865\pi\)
\(600\) 0 0
\(601\) −7.00000 −0.285536 −0.142768 0.989756i \(-0.545600\pi\)
−0.142768 + 0.989756i \(0.545600\pi\)
\(602\) −5.00000 + 1.73205i −0.203785 + 0.0705931i
\(603\) −9.00000 −0.366508
\(604\) 1.50000 + 2.59808i 0.0610341 + 0.105714i
\(605\) 0 0
\(606\) 0 0
\(607\) −7.00000 12.1244i −0.284121 0.492112i 0.688274 0.725450i \(-0.258368\pi\)
−0.972396 + 0.233338i \(0.925035\pi\)
\(608\) −35.0000 −1.41944
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −10.5000 + 18.1865i −0.424437 + 0.735147i
\(613\) 16.0000 27.7128i 0.646234 1.11931i −0.337781 0.941225i \(-0.609676\pi\)
0.984015 0.178085i \(-0.0569903\pi\)
\(614\) −10.5000 18.1865i −0.423746 0.733949i
\(615\) 0 0
\(616\) −18.0000 15.5885i −0.725241 0.628077i
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 0 0
\(619\) −14.0000 + 24.2487i −0.562708 + 0.974638i 0.434551 + 0.900647i \(0.356907\pi\)
−0.997259 + 0.0739910i \(0.976426\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) −7.00000 + 12.1244i −0.279776 + 0.484587i
\(627\) 0 0
\(628\) 3.50000 + 6.06218i 0.139665 + 0.241907i
\(629\) −56.0000 −2.23287
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 9.00000 + 15.5885i 0.358001 + 0.620076i
\(633\) 0 0
\(634\) 3.00000 5.19615i 0.119145 0.206366i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 15.0000 0.593856
\(639\) 7.50000 + 12.9904i 0.296695 + 0.513892i
\(640\) 0 0
\(641\) −9.00000 + 15.5885i −0.355479 + 0.615707i −0.987200 0.159489i \(-0.949015\pi\)
0.631721 + 0.775196i \(0.282349\pi\)
\(642\) 0 0
\(643\) 7.00000 0.276053 0.138027 0.990429i \(-0.455924\pi\)
0.138027 + 0.990429i \(0.455924\pi\)
\(644\) −3.00000 + 15.5885i −0.118217 + 0.614271i
\(645\) 0 0
\(646\) 24.5000 + 42.4352i 0.963940 + 1.66959i
\(647\) 21.0000 36.3731i 0.825595 1.42997i −0.0758684 0.997118i \(-0.524173\pi\)
0.901464 0.432855i \(-0.142494\pi\)
\(648\) −13.5000 + 23.3827i −0.530330 + 0.918559i
\(649\) −10.5000 18.1865i −0.412161 0.713884i
\(650\) 0 0
\(651\) 0 0
\(652\) −13.0000 −0.509119
\(653\) 3.00000 + 5.19615i 0.117399 + 0.203341i 0.918736 0.394872i \(-0.129211\pi\)
−0.801337 + 0.598213i \(0.795878\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 42.0000 1.63858
\(658\) −14.0000 12.1244i −0.545777 0.472657i
\(659\) −40.0000 −1.55818 −0.779089 0.626913i \(-0.784318\pi\)
−0.779089 + 0.626913i \(0.784318\pi\)
\(660\) 0 0
\(661\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(662\) 10.0000 17.3205i 0.388661 0.673181i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −24.0000 −0.929981
\(667\) −15.0000 25.9808i −0.580802 1.00598i
\(668\) 3.50000 6.06218i 0.135419 0.234553i
\(669\) 0 0
\(670\) 0 0
\(671\) −21.0000 −0.810696
\(672\) 0 0
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) 11.5000 + 19.9186i 0.442963 + 0.767235i
\(675\) 0 0
\(676\) 0 0
\(677\) 17.5000 + 30.3109i 0.672580 + 1.16494i 0.977170 + 0.212459i \(0.0681471\pi\)
−0.304590 + 0.952483i \(0.598520\pi\)
\(678\) 0 0
\(679\) −7.00000 + 36.3731i −0.268635 + 1.39587i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −12.0000 + 20.7846i −0.459167 + 0.795301i −0.998917 0.0465244i \(-0.985185\pi\)
0.539750 + 0.841825i \(0.318519\pi\)
\(684\) −10.5000 18.1865i −0.401478 0.695379i
\(685\) 0 0
\(686\) 18.5000 + 0.866025i 0.706333 + 0.0330650i
\(687\) 0 0
\(688\) 1.00000 + 1.73205i 0.0381246 + 0.0660338i
\(689\) 0 0
\(690\) 0 0
\(691\) 17.5000 + 30.3109i 0.665731 + 1.15308i 0.979086 + 0.203445i \(0.0652137\pi\)
−0.313355 + 0.949636i \(0.601453\pi\)
\(692\) −7.00000 −0.266100
\(693\) 4.50000 23.3827i 0.170941 0.888235i
\(694\) −4.00000 −0.151838
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −7.00000 12.1244i −0.264954 0.458914i
\(699\) 0 0
\(700\) 12.5000 4.33013i 0.472456 0.163663i
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 28.0000 48.4974i 1.05604 1.82911i
\(704\) −10.5000 + 18.1865i −0.395734 + 0.685431i
\(705\) 0 0
\(706\) 14.0000 0.526897
\(707\) 28.0000 + 24.2487i 1.05305 + 0.911967i
\(708\) 0 0
\(709\) 25.0000 + 43.3013i 0.938895 + 1.62621i 0.767537 + 0.641004i \(0.221482\pi\)
0.171358 + 0.985209i \(0.445185\pi\)
\(710\) 0 0
\(711\) −9.00000 + 15.5885i −0.337526 + 0.584613i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −5.00000 8.66025i −0.186859 0.323649i
\(717\) 0 0
\(718\) −4.00000 + 6.92820i −0.149279 + 0.258558i
\(719\) 21.0000 + 36.3731i 0.783168 + 1.35649i 0.930087 + 0.367338i \(0.119731\pi\)
−0.146920 + 0.989148i \(0.546936\pi\)
\(720\) 0 0
\(721\) 35.0000 12.1244i 1.30347 0.451535i
\(722\) −30.0000 −1.11648
\(723\) 0 0
\(724\) −3.50000 + 6.06218i −0.130076 + 0.225299i
\(725\) −12.5000 + 21.6506i −0.464238 + 0.804084i
\(726\) 0 0
\(727\) 28.0000 1.03846 0.519231 0.854634i \(-0.326218\pi\)
0.519231 + 0.854634i \(0.326218\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −7.00000 + 12.1244i −0.258904 + 0.448435i
\(732\) 0 0
\(733\) 21.0000 + 36.3731i 0.775653 + 1.34347i 0.934427 + 0.356155i \(0.115912\pi\)
−0.158774 + 0.987315i \(0.550754\pi\)
\(734\) −14.0000 −0.516749
\(735\) 0 0
\(736\) 30.0000 1.10581
\(737\) −4.50000 7.79423i −0.165760 0.287104i
\(738\) 0 0
\(739\) 2.00000 3.46410i 0.0735712 0.127429i −0.826893 0.562360i \(-0.809894\pi\)
0.900464 + 0.434930i \(0.143227\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −1.50000 + 7.79423i −0.0550667 + 0.286135i
\(743\) −9.00000 −0.330178 −0.165089 0.986279i \(-0.552791\pi\)
−0.165089 + 0.986279i \(0.552791\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 7.50000 12.9904i 0.274595 0.475612i
\(747\) 0 0
\(748\) −21.0000 −0.767836
\(749\) 20.0000 6.92820i 0.730784 0.253151i
\(750\) 0 0
\(751\) 10.0000 + 17.3205i 0.364905 + 0.632034i 0.988761 0.149505i \(-0.0477681\pi\)
−0.623856 + 0.781540i \(0.714435\pi\)
\(752\) −3.50000 + 6.06218i −0.127632 + 0.221065i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 9.00000 0.327111 0.163555 0.986534i \(-0.447704\pi\)
0.163555 + 0.986534i \(0.447704\pi\)
\(758\) 6.00000 + 10.3923i 0.217930 + 0.377466i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(762\) 0 0
\(763\) 8.00000 + 6.92820i 0.289619 + 0.250818i
\(764\) 20.0000 0.723575
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2.00000 3.46410i −0.0719816 0.124676i
\(773\) 21.0000 36.3731i 0.755318 1.30825i −0.189899 0.981804i \(-0.560816\pi\)
0.945216 0.326445i \(-0.105851\pi\)
\(774\) −3.00000 + 5.19615i −0.107833 + 0.186772i
\(775\) 0 0
\(776\) 42.0000 1.50771
\(777\) 0 0
\(778\) 3.00000 0.107555
\(779\) 0 0
\(780\) 0 0
\(781\) −7.50000 + 12.9904i −0.268371 + 0.464832i
\(782\) −21.0000 36.3731i −0.750958 1.30070i
\(783\) 0 0
\(784\) −1.00000 6.92820i −0.0357143 0.247436i
\(785\) 0 0
\(786\) 0 0
\(787\) 3.50000 6.06218i 0.124762 0.216093i −0.796878 0.604140i \(-0.793517\pi\)
0.921640 + 0.388047i \(0.126850\pi\)
\(788\) −1.00000 + 1.73205i −0.0356235 + 0.0617018i
\(789\) 0 0
\(790\) 0 0
\(791\) −4.50000 + 23.3827i −0.160002 + 0.831393i
\(792\) −27.0000 −0.959403
\(793\) 0 0
\(794\) −7.00000 + 12.1244i −0.248421 + 0.430277i
\(795\) 0