Properties

Label 1134.2.h.d.109.1
Level $1134$
Weight $2$
Character 1134.109
Analytic conductor $9.055$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
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 378)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.109
Dual form 1134.2.h.d.541.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} -6.00000 q^{11} +(-2.50000 + 4.33013i) q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(2.00000 + 3.46410i) q^{19} +(3.00000 - 5.19615i) q^{22} -6.00000 q^{23} -5.00000 q^{25} +(-2.50000 - 4.33013i) q^{26} +(-0.500000 - 2.59808i) q^{28} +(3.00000 + 5.19615i) q^{29} +(0.500000 + 0.866025i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{34} +(0.500000 + 0.866025i) q^{37} -4.00000 q^{38} +(-3.00000 + 5.19615i) q^{41} +(0.500000 + 0.866025i) q^{43} +(3.00000 + 5.19615i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-3.00000 + 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +(2.50000 - 4.33013i) q^{50} +5.00000 q^{52} +(-3.00000 + 5.19615i) q^{53} +(2.50000 + 0.866025i) q^{56} -6.00000 q^{58} +(-3.00000 - 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{61} -1.00000 q^{62} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{67} -6.00000 q^{68} -12.0000 q^{71} +(-1.00000 + 1.73205i) q^{73} -1.00000 q^{74} +(2.00000 - 3.46410i) q^{76} +(-15.0000 - 5.19615i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-3.00000 - 5.19615i) q^{82} +(3.00000 + 5.19615i) q^{83} -1.00000 q^{86} -6.00000 q^{88} +(-10.0000 + 8.66025i) q^{91} +(3.00000 + 5.19615i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(-8.50000 - 14.7224i) q^{97} +(-6.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} + 5q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} + 5q^{7} + 2q^{8} - 12q^{11} - 5q^{13} - 4q^{14} - q^{16} + 6q^{17} + 4q^{19} + 6q^{22} - 12q^{23} - 10q^{25} - 5q^{26} - q^{28} + 6q^{29} + q^{31} - q^{32} + 6q^{34} + q^{37} - 8q^{38} - 6q^{41} + q^{43} + 6q^{44} + 6q^{46} - 6q^{47} + 11q^{49} + 5q^{50} + 10q^{52} - 6q^{53} + 5q^{56} - 12q^{58} - 6q^{59} + q^{61} - 2q^{62} + 2q^{64} + q^{67} - 12q^{68} - 24q^{71} - 2q^{73} - 2q^{74} + 4q^{76} - 30q^{77} + q^{79} - 6q^{82} + 6q^{83} - 2q^{86} - 12q^{88} - 20q^{91} + 6q^{92} - 6q^{94} - 17q^{97} - 13q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 2.50000 + 0.866025i 0.944911 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −6.00000 −1.80907 −0.904534 0.426401i \(-0.859781\pi\)
−0.904534 + 0.426401i \(0.859781\pi\)
\(12\) 0 0
\(13\) −2.50000 + 4.33013i −0.693375 + 1.20096i 0.277350 + 0.960769i \(0.410544\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) −2.00000 + 1.73205i −0.534522 + 0.462910i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i \(-0.573966\pi\)
0.957892 0.287129i \(-0.0927008\pi\)
\(18\) 0 0
\(19\) 2.00000 + 3.46410i 0.458831 + 0.794719i 0.998899 0.0469020i \(-0.0149348\pi\)
−0.540068 + 0.841621i \(0.681602\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 3.00000 5.19615i 0.639602 1.10782i
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) −2.50000 4.33013i −0.490290 0.849208i
\(27\) 0 0
\(28\) −0.500000 2.59808i −0.0944911 0.490990i
\(29\) 3.00000 + 5.19615i 0.557086 + 0.964901i 0.997738 + 0.0672232i \(0.0214140\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.0898027 + 0.155543i 0.907428 0.420208i \(-0.138043\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 3.00000 + 5.19615i 0.514496 + 0.891133i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.500000 + 0.866025i 0.0821995 + 0.142374i 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) −4.00000 −0.648886
\(39\) 0 0
\(40\) 0 0
\(41\) −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i \(-0.988546\pi\)
0.530831 + 0.847477i \(0.321880\pi\)
\(42\) 0 0
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) 3.00000 + 5.19615i 0.452267 + 0.783349i
\(45\) 0 0
\(46\) 3.00000 5.19615i 0.442326 0.766131i
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 0 0
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) 2.50000 4.33013i 0.353553 0.612372i
\(51\) 0 0
\(52\) 5.00000 0.693375
\(53\) −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.50000 + 0.866025i 0.334077 + 0.115728i
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) −3.00000 5.19615i −0.390567 0.676481i 0.601958 0.798528i \(-0.294388\pi\)
−0.992524 + 0.122047i \(0.961054\pi\)
\(60\) 0 0
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) −1.00000 −0.127000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 0.500000 + 0.866025i 0.0610847 + 0.105802i 0.894951 0.446165i \(-0.147211\pi\)
−0.833866 + 0.551967i \(0.813877\pi\)
\(68\) −6.00000 −0.727607
\(69\) 0 0
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) −1.00000 + 1.73205i −0.117041 + 0.202721i −0.918594 0.395203i \(-0.870674\pi\)
0.801553 + 0.597924i \(0.204008\pi\)
\(74\) −1.00000 −0.116248
\(75\) 0 0
\(76\) 2.00000 3.46410i 0.229416 0.397360i
\(77\) −15.0000 5.19615i −1.70941 0.592157i
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −3.00000 5.19615i −0.331295 0.573819i
\(83\) 3.00000 + 5.19615i 0.329293 + 0.570352i 0.982372 0.186938i \(-0.0598564\pi\)
−0.653079 + 0.757290i \(0.726523\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.00000 −0.107833
\(87\) 0 0
\(88\) −6.00000 −0.639602
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 0 0
\(91\) −10.0000 + 8.66025i −1.04828 + 0.907841i
\(92\) 3.00000 + 5.19615i 0.312772 + 0.541736i
\(93\) 0 0
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) 0 0
\(96\) 0 0
\(97\) −8.50000 14.7224i −0.863044 1.49484i −0.868976 0.494854i \(-0.835222\pi\)
0.00593185 0.999982i \(-0.498112\pi\)
\(98\) −6.50000 + 2.59808i −0.656599 + 0.262445i
\(99\) 0 0
\(100\) 2.50000 + 4.33013i 0.250000 + 0.433013i
\(101\) −12.0000 −1.19404 −0.597022 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) 0 0
\(103\) −19.0000 −1.87213 −0.936063 0.351833i \(-0.885559\pi\)
−0.936063 + 0.351833i \(0.885559\pi\)
\(104\) −2.50000 + 4.33013i −0.245145 + 0.424604i
\(105\) 0 0
\(106\) −3.00000 5.19615i −0.291386 0.504695i
\(107\) 9.00000 + 15.5885i 0.870063 + 1.50699i 0.861931 + 0.507026i \(0.169255\pi\)
0.00813215 + 0.999967i \(0.497411\pi\)
\(108\) 0 0
\(109\) −2.50000 + 4.33013i −0.239457 + 0.414751i −0.960558 0.278078i \(-0.910303\pi\)
0.721102 + 0.692829i \(0.243636\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.00000 + 1.73205i −0.188982 + 0.163663i
\(113\) 6.00000 10.3923i 0.564433 0.977626i −0.432670 0.901553i \(-0.642428\pi\)
0.997102 0.0760733i \(-0.0242383\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) 0 0
\(118\) 6.00000 0.552345
\(119\) 12.0000 10.3923i 1.10004 0.952661i
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) 0.500000 + 0.866025i 0.0452679 + 0.0784063i
\(123\) 0 0
\(124\) 0.500000 0.866025i 0.0449013 0.0777714i
\(125\) 0 0
\(126\) 0 0
\(127\) −13.0000 −1.15356 −0.576782 0.816898i \(-0.695692\pi\)
−0.576782 + 0.816898i \(0.695692\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 2.00000 + 10.3923i 0.173422 + 0.901127i
\(134\) −1.00000 −0.0863868
\(135\) 0 0
\(136\) 3.00000 5.19615i 0.257248 0.445566i
\(137\) 6.00000 0.512615 0.256307 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 0 0
\(139\) 3.50000 6.06218i 0.296866 0.514187i −0.678551 0.734553i \(-0.737392\pi\)
0.975417 + 0.220366i \(0.0707252\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.00000 10.3923i 0.503509 0.872103i
\(143\) 15.0000 25.9808i 1.25436 2.17262i
\(144\) 0 0
\(145\) 0 0
\(146\) −1.00000 1.73205i −0.0827606 0.143346i
\(147\) 0 0
\(148\) 0.500000 0.866025i 0.0410997 0.0711868i
\(149\) 12.0000 0.983078 0.491539 0.870855i \(-0.336434\pi\)
0.491539 + 0.870855i \(0.336434\pi\)
\(150\) 0 0
\(151\) 17.0000 1.38344 0.691720 0.722166i \(-0.256853\pi\)
0.691720 + 0.722166i \(0.256853\pi\)
\(152\) 2.00000 + 3.46410i 0.162221 + 0.280976i
\(153\) 0 0
\(154\) 12.0000 10.3923i 0.966988 0.837436i
\(155\) 0 0
\(156\) 0 0
\(157\) 11.0000 + 19.0526i 0.877896 + 1.52056i 0.853646 + 0.520854i \(0.174386\pi\)
0.0242497 + 0.999706i \(0.492280\pi\)
\(158\) 0.500000 + 0.866025i 0.0397779 + 0.0688973i
\(159\) 0 0
\(160\) 0 0
\(161\) −15.0000 5.19615i −1.18217 0.409514i
\(162\) 0 0
\(163\) −5.50000 9.52628i −0.430793 0.746156i 0.566149 0.824303i \(-0.308433\pi\)
−0.996942 + 0.0781474i \(0.975100\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) −6.00000 −0.465690
\(167\) −9.00000 + 15.5885i −0.696441 + 1.20627i 0.273252 + 0.961943i \(0.411901\pi\)
−0.969693 + 0.244328i \(0.921432\pi\)
\(168\) 0 0
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.500000 0.866025i 0.0381246 0.0660338i
\(173\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 0 0
\(175\) −12.5000 4.33013i −0.944911 0.327327i
\(176\) 3.00000 5.19615i 0.226134 0.391675i
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) −2.50000 12.9904i −0.185312 0.962911i
\(183\) 0 0
\(184\) −6.00000 −0.442326
\(185\) 0 0
\(186\) 0 0
\(187\) −18.0000 + 31.1769i −1.31629 + 2.27988i
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) 0 0
\(193\) 0.500000 + 0.866025i 0.0359908 + 0.0623379i 0.883460 0.468507i \(-0.155208\pi\)
−0.847469 + 0.530845i \(0.821875\pi\)
\(194\) 17.0000 1.22053
\(195\) 0 0
\(196\) 1.00000 6.92820i 0.0714286 0.494872i
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) −5.50000 + 9.52628i −0.389885 + 0.675300i −0.992434 0.122782i \(-0.960818\pi\)
0.602549 + 0.798082i \(0.294152\pi\)
\(200\) −5.00000 −0.353553
\(201\) 0 0
\(202\) 6.00000 10.3923i 0.422159 0.731200i
\(203\) 3.00000 + 15.5885i 0.210559 + 1.09410i
\(204\) 0 0
\(205\) 0 0
\(206\) 9.50000 16.4545i 0.661896 1.14644i
\(207\) 0 0
\(208\) −2.50000 4.33013i −0.173344 0.300240i
\(209\) −12.0000 20.7846i −0.830057 1.43770i
\(210\) 0 0
\(211\) 6.50000 11.2583i 0.447478 0.775055i −0.550743 0.834675i \(-0.685655\pi\)
0.998221 + 0.0596196i \(0.0189888\pi\)
\(212\) 6.00000 0.412082
\(213\) 0 0
\(214\) −18.0000 −1.23045
\(215\) 0 0
\(216\) 0 0
\(217\) 0.500000 + 2.59808i 0.0339422 + 0.176369i
\(218\) −2.50000 4.33013i −0.169321 0.293273i
\(219\) 0 0
\(220\) 0 0
\(221\) 15.0000 + 25.9808i 1.00901 + 1.74766i
\(222\) 0 0
\(223\) −4.00000 6.92820i −0.267860 0.463947i 0.700449 0.713702i \(-0.252983\pi\)
−0.968309 + 0.249756i \(0.919650\pi\)
\(224\) −0.500000 2.59808i −0.0334077 0.173591i
\(225\) 0 0
\(226\) 6.00000 + 10.3923i 0.399114 + 0.691286i
\(227\) 6.00000 0.398234 0.199117 0.979976i \(-0.436193\pi\)
0.199117 + 0.979976i \(0.436193\pi\)
\(228\) 0 0
\(229\) 5.00000 0.330409 0.165205 0.986259i \(-0.447172\pi\)
0.165205 + 0.986259i \(0.447172\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 3.00000 + 5.19615i 0.196960 + 0.341144i
\(233\) 12.0000 + 20.7846i 0.786146 + 1.36165i 0.928312 + 0.371802i \(0.121260\pi\)
−0.142166 + 0.989843i \(0.545407\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −3.00000 + 5.19615i −0.195283 + 0.338241i
\(237\) 0 0
\(238\) 3.00000 + 15.5885i 0.194461 + 1.01045i
\(239\) 12.0000 20.7846i 0.776215 1.34444i −0.157893 0.987456i \(-0.550470\pi\)
0.934109 0.356988i \(-0.116196\pi\)
\(240\) 0 0
\(241\) 17.0000 1.09507 0.547533 0.836784i \(-0.315567\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) −12.5000 + 21.6506i −0.803530 + 1.39176i
\(243\) 0 0
\(244\) −1.00000 −0.0640184
\(245\) 0 0
\(246\) 0 0
\(247\) −20.0000 −1.27257
\(248\) 0.500000 + 0.866025i 0.0317500 + 0.0549927i
\(249\) 0 0
\(250\) 0 0
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 0 0
\(253\) 36.0000 2.26330
\(254\) 6.50000 11.2583i 0.407846 0.706410i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) 0.500000 + 2.59808i 0.0310685 + 0.161437i
\(260\) 0 0
\(261\) 0 0
\(262\) −6.00000 + 10.3923i −0.370681 + 0.642039i
\(263\) −6.00000 −0.369976 −0.184988 0.982741i \(-0.559225\pi\)
−0.184988 + 0.982741i \(0.559225\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −10.0000 3.46410i −0.613139 0.212398i
\(267\) 0 0
\(268\) 0.500000 0.866025i 0.0305424 0.0529009i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 0 0
\(271\) 3.50000 + 6.06218i 0.212610 + 0.368251i 0.952531 0.304443i \(-0.0984703\pi\)
−0.739921 + 0.672694i \(0.765137\pi\)
\(272\) 3.00000 + 5.19615i 0.181902 + 0.315063i
\(273\) 0 0
\(274\) −3.00000 + 5.19615i −0.181237 + 0.313911i
\(275\) 30.0000 1.80907
\(276\) 0 0
\(277\) 17.0000 1.02143 0.510716 0.859750i \(-0.329381\pi\)
0.510716 + 0.859750i \(0.329381\pi\)
\(278\) 3.50000 + 6.06218i 0.209916 + 0.363585i
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000 + 10.3923i 0.357930 + 0.619953i 0.987615 0.156898i \(-0.0501493\pi\)
−0.629685 + 0.776851i \(0.716816\pi\)
\(282\) 0 0
\(283\) 6.50000 + 11.2583i 0.386385 + 0.669238i 0.991960 0.126550i \(-0.0403903\pi\)
−0.605575 + 0.795788i \(0.707057\pi\)
\(284\) 6.00000 + 10.3923i 0.356034 + 0.616670i
\(285\) 0 0
\(286\) 15.0000 + 25.9808i 0.886969 + 1.53627i
\(287\) −12.0000 + 10.3923i −0.708338 + 0.613438i
\(288\) 0 0
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 0 0
\(291\) 0 0
\(292\) 2.00000 0.117041
\(293\) 9.00000 15.5885i 0.525786 0.910687i −0.473763 0.880652i \(-0.657105\pi\)
0.999549 0.0300351i \(-0.00956192\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.500000 + 0.866025i 0.0290619 + 0.0503367i
\(297\) 0 0
\(298\) −6.00000 + 10.3923i −0.347571 + 0.602010i
\(299\) 15.0000 25.9808i 0.867472 1.50251i
\(300\) 0 0
\(301\) 0.500000 + 2.59808i 0.0288195 + 0.149751i
\(302\) −8.50000 + 14.7224i −0.489120 + 0.847181i
\(303\) 0 0
\(304\) −4.00000 −0.229416
\(305\) 0 0
\(306\) 0 0
\(307\) 17.0000 0.970241 0.485121 0.874447i \(-0.338776\pi\)
0.485121 + 0.874447i \(0.338776\pi\)
\(308\) 3.00000 + 15.5885i 0.170941 + 0.888235i
\(309\) 0 0
\(310\) 0 0
\(311\) −6.00000 10.3923i −0.340229 0.589294i 0.644246 0.764818i \(-0.277171\pi\)
−0.984475 + 0.175525i \(0.943838\pi\)
\(312\) 0 0
\(313\) 11.0000 19.0526i 0.621757 1.07691i −0.367402 0.930062i \(-0.619753\pi\)
0.989158 0.146852i \(-0.0469141\pi\)
\(314\) −22.0000 −1.24153
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) 0 0
\(319\) −18.0000 31.1769i −1.00781 1.74557i
\(320\) 0 0
\(321\) 0 0
\(322\) 12.0000 10.3923i 0.668734 0.579141i
\(323\) 24.0000 1.33540
\(324\) 0 0
\(325\) 12.5000 21.6506i 0.693375 1.20096i
\(326\) 11.0000 0.609234
\(327\) 0 0
\(328\) −3.00000 + 5.19615i −0.165647 + 0.286910i
\(329\) −12.0000 + 10.3923i −0.661581 + 0.572946i
\(330\) 0 0
\(331\) −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i \(0.351905\pi\)
−0.998298 + 0.0583130i \(0.981428\pi\)
\(332\) 3.00000 5.19615i 0.164646 0.285176i
\(333\) 0 0
\(334\) −9.00000 15.5885i −0.492458 0.852962i
\(335\) 0 0
\(336\) 0 0
\(337\) −1.00000 + 1.73205i −0.0544735 + 0.0943508i −0.891976 0.452082i \(-0.850681\pi\)
0.837503 + 0.546433i \(0.184015\pi\)
\(338\) 12.0000 0.652714
\(339\) 0 0
\(340\) 0 0
\(341\) −3.00000 5.19615i −0.162459 0.281387i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 0.500000 + 0.866025i 0.0269582 + 0.0466930i
\(345\) 0 0
\(346\) 0 0
\(347\) −12.0000 20.7846i −0.644194 1.11578i −0.984487 0.175457i \(-0.943860\pi\)
0.340293 0.940319i \(-0.389474\pi\)
\(348\) 0 0
\(349\) 0.500000 + 0.866025i 0.0267644 + 0.0463573i 0.879097 0.476642i \(-0.158146\pi\)
−0.852333 + 0.523000i \(0.824813\pi\)
\(350\) 10.0000 8.66025i 0.534522 0.462910i
\(351\) 0 0
\(352\) 3.00000 + 5.19615i 0.159901 + 0.276956i
\(353\) 36.0000 1.91609 0.958043 0.286623i \(-0.0925328\pi\)
0.958043 + 0.286623i \(0.0925328\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.00000 + 5.19615i 0.158334 + 0.274242i 0.934268 0.356572i \(-0.116054\pi\)
−0.775934 + 0.630814i \(0.782721\pi\)
\(360\) 0 0
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) 5.00000 8.66025i 0.262794 0.455173i
\(363\) 0 0
\(364\) 12.5000 + 4.33013i 0.655178 + 0.226960i
\(365\) 0 0
\(366\) 0 0
\(367\) −28.0000 −1.46159 −0.730794 0.682598i \(-0.760850\pi\)
−0.730794 + 0.682598i \(0.760850\pi\)
\(368\) 3.00000 5.19615i 0.156386 0.270868i
\(369\) 0 0
\(370\) 0 0
\(371\) −12.0000 + 10.3923i −0.623009 + 0.539542i
\(372\) 0 0
\(373\) 26.0000 1.34623 0.673114 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) −18.0000 31.1769i −0.930758 1.61212i
\(375\) 0 0
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) −30.0000 −1.54508
\(378\) 0 0
\(379\) −1.00000 −0.0513665 −0.0256833 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6.00000 −0.306586 −0.153293 0.988181i \(-0.548988\pi\)
−0.153293 + 0.988181i \(0.548988\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −1.00000 −0.0508987
\(387\) 0 0
\(388\) −8.50000 + 14.7224i −0.431522 + 0.747418i
\(389\) 12.0000 0.608424 0.304212 0.952604i \(-0.401607\pi\)
0.304212 + 0.952604i \(0.401607\pi\)
\(390\) 0 0
\(391\) −18.0000 + 31.1769i −0.910299 + 1.57668i
\(392\) 5.50000 + 4.33013i 0.277792 + 0.218704i
\(393\) 0 0
\(394\) −6.00000 + 10.3923i −0.302276 + 0.523557i
\(395\) 0 0
\(396\) 0 0
\(397\) 6.50000 + 11.2583i 0.326226 + 0.565039i 0.981760 0.190126i \(-0.0608897\pi\)
−0.655534 + 0.755166i \(0.727556\pi\)
\(398\) −5.50000 9.52628i −0.275690 0.477509i
\(399\) 0 0
\(400\) 2.50000 4.33013i 0.125000 0.216506i
\(401\) 6.00000 0.299626 0.149813 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) 0 0
\(403\) −5.00000 −0.249068
\(404\) 6.00000 + 10.3923i 0.298511 + 0.517036i
\(405\) 0 0
\(406\) −15.0000 5.19615i −0.744438 0.257881i
\(407\) −3.00000 5.19615i −0.148704 0.257564i
\(408\) 0 0
\(409\) −14.5000 25.1147i −0.716979 1.24184i −0.962191 0.272374i \(-0.912191\pi\)
0.245212 0.969469i \(-0.421142\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 9.50000 + 16.4545i 0.468031 + 0.810654i
\(413\) −3.00000 15.5885i −0.147620 0.767058i
\(414\) 0 0
\(415\) 0 0
\(416\) 5.00000 0.245145
\(417\) 0 0
\(418\) 24.0000 1.17388
\(419\) −12.0000 + 20.7846i −0.586238 + 1.01539i 0.408481 + 0.912767i \(0.366058\pi\)
−0.994720 + 0.102628i \(0.967275\pi\)
\(420\) 0 0
\(421\) −7.00000 12.1244i −0.341159 0.590905i 0.643489 0.765455i \(-0.277486\pi\)
−0.984648 + 0.174550i \(0.944153\pi\)
\(422\) 6.50000 + 11.2583i 0.316415 + 0.548047i
\(423\) 0 0
\(424\) −3.00000 + 5.19615i −0.145693 + 0.252347i
\(425\) −15.0000 + 25.9808i −0.727607 + 1.26025i
\(426\) 0 0
\(427\) 2.00000 1.73205i 0.0967868 0.0838198i
\(428\) 9.00000 15.5885i 0.435031 0.753497i
\(429\) 0 0
\(430\) 0 0
\(431\) −9.00000 + 15.5885i −0.433515 + 0.750870i −0.997173 0.0751385i \(-0.976060\pi\)
0.563658 + 0.826008i \(0.309393\pi\)
\(432\) 0 0
\(433\) −25.0000 −1.20142 −0.600712 0.799466i \(-0.705116\pi\)
−0.600712 + 0.799466i \(0.705116\pi\)
\(434\) −2.50000 0.866025i −0.120004 0.0415705i
\(435\) 0 0
\(436\) 5.00000 0.239457
\(437\) −12.0000 20.7846i −0.574038 0.994263i
\(438\) 0 0
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −30.0000 −1.42695
\(443\) −12.0000 + 20.7846i −0.570137 + 0.987507i 0.426414 + 0.904528i \(0.359777\pi\)
−0.996551 + 0.0829786i \(0.973557\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 8.00000 0.378811
\(447\) 0 0
\(448\) 2.50000 + 0.866025i 0.118114 + 0.0409159i
\(449\) 24.0000 1.13263 0.566315 0.824189i \(-0.308369\pi\)
0.566315 + 0.824189i \(0.308369\pi\)
\(450\) 0 0
\(451\) 18.0000 31.1769i 0.847587 1.46806i
\(452\) −12.0000 −0.564433
\(453\) 0 0
\(454\) −3.00000 + 5.19615i −0.140797 + 0.243868i
\(455\) 0 0
\(456\) 0 0
\(457\) 9.50000 16.4545i 0.444391 0.769708i −0.553618 0.832771i \(-0.686753\pi\)
0.998010 + 0.0630623i \(0.0200867\pi\)
\(458\) −2.50000 + 4.33013i −0.116817 + 0.202334i
\(459\) 0 0
\(460\) 0 0
\(461\) 9.00000 + 15.5885i 0.419172 + 0.726027i 0.995856 0.0909401i \(-0.0289872\pi\)
−0.576685 + 0.816967i \(0.695654\pi\)
\(462\) 0 0
\(463\) −4.00000 + 6.92820i −0.185896 + 0.321981i −0.943878 0.330294i \(-0.892852\pi\)
0.757982 + 0.652275i \(0.226185\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −24.0000 −1.11178
\(467\) 6.00000 + 10.3923i 0.277647 + 0.480899i 0.970799 0.239892i \(-0.0771121\pi\)
−0.693153 + 0.720791i \(0.743779\pi\)
\(468\) 0 0
\(469\) 0.500000 + 2.59808i 0.0230879 + 0.119968i
\(470\) 0 0
\(471\) 0 0
\(472\) −3.00000 5.19615i −0.138086 0.239172i
\(473\) −3.00000 5.19615i −0.137940 0.238919i
\(474\) 0 0
\(475\) −10.0000 17.3205i −0.458831 0.794719i
\(476\) −15.0000 5.19615i −0.687524 0.238165i
\(477\) 0 0
\(478\) 12.0000 + 20.7846i 0.548867 + 0.950666i
\(479\) −12.0000 −0.548294 −0.274147 0.961688i \(-0.588395\pi\)
−0.274147 + 0.961688i \(0.588395\pi\)
\(480\) 0 0
\(481\) −5.00000 −0.227980
\(482\) −8.50000 + 14.7224i −0.387164 + 0.670588i
\(483\) 0 0
\(484\) −12.5000 21.6506i −0.568182 0.984120i
\(485\) 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 \(-0.194428\pi\)
\(488\) 0.500000 0.866025i 0.0226339 0.0392031i
\(489\) 0 0
\(490\) 0 0
\(491\) −15.0000 + 25.9808i −0.676941 + 1.17250i 0.298957 + 0.954267i \(0.403361\pi\)
−0.975898 + 0.218229i \(0.929972\pi\)
\(492\) 0 0
\(493\) 36.0000 1.62136
\(494\) 10.0000 17.3205i 0.449921 0.779287i
\(495\) 0 0
\(496\) −1.00000 −0.0449013
\(497\) −30.0000 10.3923i −1.34568 0.466159i
\(498\) 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
\(502\) 9.00000 15.5885i 0.401690 0.695747i
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −18.0000 + 31.1769i −0.800198 + 1.38598i
\(507\) 0 0
\(508\) 6.50000 + 11.2583i 0.288391 + 0.499508i
\(509\) −30.0000 −1.32973 −0.664863 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(510\) 0 0
\(511\) −4.00000 + 3.46410i −0.176950 + 0.153243i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −3.00000 + 5.19615i −0.132324 + 0.229192i
\(515\) 0 0
\(516\) 0 0
\(517\) 18.0000 31.1769i 0.791639 1.37116i
\(518\) −2.50000 0.866025i −0.109844 0.0380510i
\(519\) 0 0
\(520\) 0 0
\(521\) 21.0000 36.3731i 0.920027 1.59353i 0.120656 0.992694i \(-0.461500\pi\)
0.799370 0.600839i \(-0.205167\pi\)
\(522\) 0 0
\(523\) −11.5000 19.9186i −0.502860 0.870979i −0.999995 0.00330547i \(-0.998948\pi\)
0.497135 0.867673i \(-0.334385\pi\)
\(524\) −6.00000 10.3923i −0.262111 0.453990i
\(525\) 0 0
\(526\) 3.00000 5.19615i 0.130806 0.226563i
\(527\) 6.00000 0.261364
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) 8.00000 6.92820i 0.346844 0.300376i
\(533\) −15.0000 25.9808i −0.649722 1.12535i
\(534\) 0 0
\(535\) 0 0
\(536\) 0.500000 + 0.866025i 0.0215967 + 0.0374066i
\(537\) 0 0
\(538\) 0 0
\(539\) −33.0000 25.9808i −1.42141 1.11907i
\(540\) 0 0
\(541\) 5.00000 + 8.66025i 0.214967 + 0.372333i 0.953262 0.302144i \(-0.0977023\pi\)
−0.738296 + 0.674477i \(0.764369\pi\)
\(542\) −7.00000 −0.300676
\(543\) 0 0
\(544\) −6.00000 −0.257248
\(545\) 0 0
\(546\) 0 0
\(547\) 18.5000 + 32.0429i 0.791003 + 1.37006i 0.925347 + 0.379122i \(0.123774\pi\)
−0.134344 + 0.990935i \(0.542893\pi\)
\(548\) −3.00000 5.19615i −0.128154 0.221969i
\(549\) 0 0
\(550\) −15.0000 + 25.9808i −0.639602 + 1.10782i
\(551\) −12.0000 + 20.7846i −0.511217 + 0.885454i
\(552\) 0 0
\(553\) 2.00000 1.73205i 0.0850487 0.0736543i
\(554\) −8.50000 + 14.7224i −0.361130 + 0.625496i
\(555\) 0 0
\(556\) −7.00000 −0.296866
\(557\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(558\) 0 0
\(559\) −5.00000 −0.211477
\(560\) 0 0
\(561\) 0 0
\(562\) −12.0000 −0.506189
\(563\) −21.0000 36.3731i −0.885044 1.53294i −0.845663 0.533718i \(-0.820794\pi\)
−0.0393818 0.999224i \(-0.512539\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −13.0000 −0.546431
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) −18.0000 + 31.1769i −0.754599 + 1.30700i 0.190974 + 0.981595i \(0.438835\pi\)
−0.945573 + 0.325409i \(0.894498\pi\)
\(570\) 0 0
\(571\) 8.00000 + 13.8564i 0.334790 + 0.579873i 0.983444 0.181210i \(-0.0580014\pi\)
−0.648655 + 0.761083i \(0.724668\pi\)
\(572\) −30.0000 −1.25436
\(573\) 0 0
\(574\) −3.00000 15.5885i −0.125218 0.650650i
\(575\) 30.0000 1.25109
\(576\) 0 0
\(577\) −11.5000 + 19.9186i −0.478751 + 0.829222i −0.999703 0.0243645i \(-0.992244\pi\)
0.520952 + 0.853586i \(0.325577\pi\)
\(578\) 19.0000 0.790296
\(579\) 0 0
\(580\) 0 0
\(581\) 3.00000 + 15.5885i 0.124461 + 0.646718i
\(582\) 0 0
\(583\) 18.0000 31.1769i 0.745484 1.29122i
\(584\) −1.00000 + 1.73205i −0.0413803 + 0.0716728i
\(585\) 0 0
\(586\) 9.00000 + 15.5885i 0.371787 + 0.643953i
\(587\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(588\) 0 0
\(589\) −2.00000 + 3.46410i −0.0824086 + 0.142736i
\(590\) 0 0
\(591\) 0 0
\(592\) −1.00000 −0.0410997
\(593\) 18.0000 + 31.1769i 0.739171 + 1.28028i 0.952869 + 0.303383i \(0.0981160\pi\)
−0.213697 + 0.976900i \(0.568551\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.00000 10.3923i −0.245770 0.425685i
\(597\) 0 0
\(598\) 15.0000 + 25.9808i 0.613396 + 1.06243i
\(599\) 18.0000 + 31.1769i 0.735460 + 1.27385i 0.954521 + 0.298143i \(0.0963673\pi\)
−0.219061 + 0.975711i \(0.570299\pi\)
\(600\) 0 0
\(601\) −23.5000 40.7032i −0.958585 1.66032i −0.725942 0.687756i \(-0.758596\pi\)
−0.232643 0.972562i \(-0.574737\pi\)
\(602\) −2.50000 0.866025i −0.101892 0.0352966i
\(603\) 0 0
\(604\) −8.50000 14.7224i −0.345860 0.599047i
\(605\) 0 0
\(606\) 0 0
\(607\) −16.0000 −0.649420 −0.324710 0.945814i \(-0.605267\pi\)
−0.324710 + 0.945814i \(0.605267\pi\)
\(608\) 2.00000 3.46410i 0.0811107 0.140488i
\(609\) 0 0
\(610\) 0 0
\(611\) −15.0000 25.9808i −0.606835 1.05107i
\(612\) 0 0
\(613\) −5.50000 + 9.52628i −0.222143 + 0.384763i −0.955458 0.295126i \(-0.904638\pi\)
0.733316 + 0.679888i \(0.237972\pi\)
\(614\) −8.50000 + 14.7224i −0.343032 + 0.594149i
\(615\) 0 0
\(616\) −15.0000 5.19615i −0.604367 0.209359i
\(617\) −15.0000 + 25.9808i −0.603877 + 1.04595i 0.388351 + 0.921512i \(0.373045\pi\)
−0.992228 + 0.124434i \(0.960288\pi\)
\(618\) 0 0
\(619\) −25.0000 −1.00483 −0.502417 0.864625i \(-0.667556\pi\)
−0.502417 + 0.864625i \(0.667556\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 12.0000 0.481156
\(623\) 0 0
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 11.0000 + 19.0526i 0.439648 + 0.761493i
\(627\) 0 0
\(628\) 11.0000 19.0526i 0.438948 0.760280i
\(629\) 6.00000 0.239236
\(630\) 0 0
\(631\) −7.00000 −0.278666 −0.139333 0.990246i \(-0.544496\pi\)
−0.139333 + 0.990246i \(0.544496\pi\)
\(632\) 0.500000 0.866025i 0.0198889 0.0344486i
\(633\) 0 0
\(634\) 9.00000 + 15.5885i 0.357436 + 0.619097i
\(635\) 0 0
\(636\) 0 0
\(637\) −32.5000 + 12.9904i −1.28770 + 0.514698i
\(638\) 36.0000 1.42525
\(639\) 0 0
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 0 0
\(643\) 12.5000 21.6506i 0.492952 0.853818i −0.507015 0.861937i \(-0.669251\pi\)
0.999967 + 0.00811944i \(0.00258453\pi\)
\(644\) 3.00000 + 15.5885i 0.118217 + 0.614271i
\(645\) 0 0
\(646\) −12.0000 + 20.7846i −0.472134 + 0.817760i
\(647\) −6.00000 + 10.3923i −0.235884 + 0.408564i −0.959529 0.281609i \(-0.909132\pi\)
0.723645 + 0.690172i \(0.242465\pi\)
\(648\) 0 0
\(649\) 18.0000 + 31.1769i 0.706562 + 1.22380i
\(650\) 12.5000 + 21.6506i 0.490290 + 0.849208i
\(651\) 0 0
\(652\) −5.50000 + 9.52628i −0.215397 + 0.373078i
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −3.00000 5.19615i −0.117130 0.202876i
\(657\) 0 0
\(658\) −3.00000 15.5885i −0.116952 0.607701i
\(659\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(660\) 0 0
\(661\) −25.0000 43.3013i −0.972387 1.68422i −0.688301 0.725426i \(-0.741643\pi\)
−0.284087 0.958799i \(-0.591690\pi\)
\(662\) −10.0000 17.3205i −0.388661 0.673181i
\(663\) 0 0
\(664\) 3.00000 + 5.19615i 0.116423 + 0.201650i
\(665\) 0 0
\(666\) 0 0
\(667\) −18.0000 31.1769i −0.696963 1.20717i
\(668\) 18.0000 0.696441
\(669\) 0 0
\(670\) 0 0
\(671\) −3.00000 + 5.19615i −0.115814 + 0.200595i
\(672\) 0 0
\(673\) 17.0000 + 29.4449i 0.655302 + 1.13502i 0.981818 + 0.189824i \(0.0607919\pi\)
−0.326516 + 0.945192i \(0.605875\pi\)
\(674\) −1.00000 1.73205i −0.0385186 0.0667161i
\(675\) 0 0
\(676\) −6.00000 + 10.3923i −0.230769 + 0.399704i
\(677\) 6.00000 10.3923i 0.230599 0.399409i −0.727386 0.686229i \(-0.759265\pi\)
0.957984 + 0.286820i \(0.0925982\pi\)
\(678\) 0 0
\(679\) −8.50000 44.1673i −0.326200 1.69499i
\(680\) 0 0
\(681\) 0 0
\(682\) 6.00000 0.229752
\(683\) 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −18.5000 + 0.866025i −0.706333 + 0.0330650i
\(687\) 0 0
\(688\) −1.00000 −0.0381246
\(689\) −15.0000 25.9808i −0.571454 0.989788i
\(690\) 0 0
\(691\) −8.50000 + 14.7224i −0.323355 + 0.560068i −0.981178 0.193105i \(-0.938144\pi\)
0.657823 + 0.753173i \(0.271478\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) 0 0
\(696\) 0 0
\(697\) 18.0000 + 31.1769i 0.681799 + 1.18091i
\(698\) −1.00000 −0.0378506
\(699\) 0 0
\(700\) 2.50000 + 12.9904i 0.0944911 + 0.490990i
\(701\) −48.0000 −1.81293 −0.906467 0.422276i \(-0.861231\pi\)
−0.906467 + 0.422276i \(0.861231\pi\)
\(702\) 0 0
\(703\) −2.00000 + 3.46410i −0.0754314 + 0.130651i
\(704\) −6.00000 −0.226134
\(705\) 0 0
\(706\) −18.0000 + 31.1769i −0.677439 + 1.17336i
\(707\) −30.0000 10.3923i −1.12827 0.390843i
\(708\) 0 0
\(709\) −8.50000 + 14.7224i −0.319224 + 0.552913i −0.980326 0.197383i \(-0.936756\pi\)
0.661102 + 0.750296i \(0.270089\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.00000 5.19615i −0.112351 0.194597i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) −6.00000 −0.223918
\(719\) 6.00000 + 10.3923i 0.223762 + 0.387568i 0.955947 0.293538i \(-0.0948328\pi\)
−0.732185 + 0.681106i \(0.761499\pi\)
\(720\) 0 0
\(721\) −47.5000 16.4545i −1.76899 0.612797i
\(722\) 1.50000 + 2.59808i 0.0558242 + 0.0966904i
\(723\) 0 0
\(724\) 5.00000 + 8.66025i 0.185824 + 0.321856i
\(725\) −15.0000 25.9808i −0.557086 0.964901i
\(726\) 0 0
\(727\) −2.50000 4.33013i −0.0927199 0.160596i 0.815935 0.578144i \(-0.196223\pi\)
−0.908655 + 0.417548i \(0.862889\pi\)
\(728\) −10.0000 + 8.66025i −0.370625 + 0.320970i
\(729\) 0 0
\(730\) 0 0
\(731\) 6.00000 0.221918
\(732\) 0 0
\(733\) 17.0000 0.627909 0.313955 0.949438i \(-0.398346\pi\)
0.313955 + 0.949438i \(0.398346\pi\)
\(734\) 14.0000 24.2487i 0.516749 0.895036i
\(735\) 0 0
\(736\) 3.00000 + 5.19615i 0.110581 + 0.191533i
\(737\) −3.00000 5.19615i −0.110506 0.191403i
\(738\) 0 0
\(739\) 24.5000 42.4352i 0.901247 1.56101i 0.0753699 0.997156i \(-0.475986\pi\)
0.825877 0.563850i \(-0.190680\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −3.00000 15.5885i −0.110133 0.572270i
\(743\) 9.00000 15.5885i 0.330178 0.571885i −0.652369 0.757902i \(-0.726225\pi\)
0.982547 + 0.186017i \(0.0595579\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −13.0000 + 22.5167i −0.475964 + 0.824394i
\(747\) 0 0
\(748\) 36.0000 1.31629
\(749\) 9.00000 + 46.7654i 0.328853 + 1.70877i
\(750\) 0 0
\(751\) −16.0000 −0.583848 −0.291924 0.956441i \(-0.594295\pi\)
−0.291924 + 0.956441i \(0.594295\pi\)
\(752\) −3.00000 5.19615i −0.109399 0.189484i
\(753\) 0 0
\(754\) 15.0000 25.9808i 0.546268 0.946164i
\(755\) 0 0
\(756\) 0 0
\(757\) 29.0000 1.05402 0.527011 0.849858i \(-0.323312\pi\)
0.527011 + 0.849858i \(0.323312\pi\)
\(758\) 0.500000 0.866025i 0.0181608 0.0314555i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) −10.0000 + 8.66025i −0.362024 + 0.313522i
\(764\) 0 0
\(765\) 0 0
\(766\) 3.00000 5.19615i 0.108394 0.187745i
\(767\) 30.0000 1.08324
\(768\) 0 0
\(769\) 5.00000 8.66025i 0.180305 0.312297i −0.761680 0.647954i \(-0.775625\pi\)
0.941984 + 0.335657i \(0.108958\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.500000 0.866025i 0.0179954 0.0311689i
\(773\) −12.0000 + 20.7846i −0.431610 + 0.747570i −0.997012 0.0772449i \(-0.975388\pi\)
0.565402 + 0.824815i \(0.308721\pi\)
\(774\) 0 0
\(775\) −2.50000 4.33013i −0.0898027 0.155543i
\(776\) −8.50000 14.7224i −0.305132 0.528505i
\(777\) 0 0
\(778\) −6.00000 + 10.3923i −0.215110 + 0.372582i
\(779\) −24.0000 −0.859889
\(780\) 0 0
\(781\) 72.0000 2.57636
\(782\) −18.0000 31.1769i −0.643679 1.11488i
\(783\) 0 0
\(784\) −6.50000 + 2.59808i −0.232143 + 0.0927884i
\(785\) 0 0
\(786\) 0 0
\(787\) 15.5000 + 26.8468i 0.552515 + 0.956985i 0.998092 + 0.0617409i \(0.0196653\pi\)
−0.445577 + 0.895244i \(0.647001\pi\)
\(788\) −6.00000 10.3923i −0.213741 0.370211i
\(789\) 0 0
\(790\) 0 0
\(791\) 24.0000 20.7846i 0.853342 0.739016i
\(792\) 0 0
\(793\) 2.50000 + 4.33013i 0.0887776 + 0.153767i
\(794\) −13.0000 −0.461353
\(795\)