Properties

Label 1134.2.f.c.757.1
Level $1134$
Weight $2$
Character 1134.757
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.f (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 757.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.757
Dual form 1134.2.f.c.379.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +1.00000 q^{10} +(-2.50000 - 4.33013i) q^{11} +(0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +2.00000 q^{17} -1.00000 q^{19} +(-0.500000 - 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} +(0.500000 - 0.866025i) q^{23} +(2.00000 + 3.46410i) q^{25} -1.00000 q^{28} +(-2.00000 - 3.46410i) q^{29} +(4.50000 - 7.79423i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{34} -1.00000 q^{35} +5.00000 q^{37} +(0.500000 + 0.866025i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(4.50000 - 7.79423i) q^{41} +(5.00000 + 8.66025i) q^{43} +5.00000 q^{44} -1.00000 q^{46} +(-3.00000 - 5.19615i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(2.00000 - 3.46410i) q^{50} +12.0000 q^{53} +5.00000 q^{55} +(0.500000 + 0.866025i) q^{56} +(-2.00000 + 3.46410i) q^{58} +(7.00000 - 12.1244i) q^{59} -9.00000 q^{62} +1.00000 q^{64} +(4.00000 - 6.92820i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(0.500000 + 0.866025i) q^{70} -13.0000 q^{71} -2.00000 q^{73} +(-2.50000 - 4.33013i) q^{74} +(0.500000 - 0.866025i) q^{76} +(2.50000 - 4.33013i) q^{77} +(-3.00000 - 5.19615i) q^{79} +1.00000 q^{80} -9.00000 q^{82} +(2.00000 + 3.46410i) q^{83} +(-1.00000 + 1.73205i) q^{85} +(5.00000 - 8.66025i) q^{86} +(-2.50000 - 4.33013i) q^{88} -9.00000 q^{89} +(0.500000 + 0.866025i) q^{92} +(-3.00000 + 5.19615i) q^{94} +(0.500000 - 0.866025i) q^{95} +(-8.00000 - 13.8564i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} - q^{5} + q^{7} + 2 q^{8} + O(q^{10}) \) \( 2 q - q^{2} - q^{4} - q^{5} + q^{7} + 2 q^{8} + 2 q^{10} - 5 q^{11} + q^{14} - q^{16} + 4 q^{17} - 2 q^{19} - q^{20} - 5 q^{22} + q^{23} + 4 q^{25} - 2 q^{28} - 4 q^{29} + 9 q^{31} - q^{32} - 2 q^{34} - 2 q^{35} + 10 q^{37} + q^{38} - q^{40} + 9 q^{41} + 10 q^{43} + 10 q^{44} - 2 q^{46} - 6 q^{47} - q^{49} + 4 q^{50} + 24 q^{53} + 10 q^{55} + q^{56} - 4 q^{58} + 14 q^{59} - 18 q^{62} + 2 q^{64} + 8 q^{67} - 2 q^{68} + q^{70} - 26 q^{71} - 4 q^{73} - 5 q^{74} + q^{76} + 5 q^{77} - 6 q^{79} + 2 q^{80} - 18 q^{82} + 4 q^{83} - 2 q^{85} + 10 q^{86} - 5 q^{88} - 18 q^{89} + q^{92} - 6 q^{94} + q^{95} - 16 q^{97} + 2 q^{98} + O(q^{100}) \)

Character values

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

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

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
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i −0.955901 0.293691i \(-0.905116\pi\)
0.732294 + 0.680989i \(0.238450\pi\)
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.00000 0.316228
\(11\) −2.50000 4.33013i −0.753778 1.30558i −0.945979 0.324227i \(-0.894896\pi\)
0.192201 0.981356i \(-0.438437\pi\)
\(12\) 0 0
\(13\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(14\) 0.500000 0.866025i 0.133631 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416 −0.114708 0.993399i \(-0.536593\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) 0 0
\(22\) −2.50000 + 4.33013i −0.533002 + 0.923186i
\(23\) 0.500000 0.866025i 0.104257 0.180579i −0.809177 0.587565i \(-0.800087\pi\)
0.913434 + 0.406986i \(0.133420\pi\)
\(24\) 0 0
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) 0 0
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) −2.00000 3.46410i −0.371391 0.643268i 0.618389 0.785872i \(-0.287786\pi\)
−0.989780 + 0.142605i \(0.954452\pi\)
\(30\) 0 0
\(31\) 4.50000 7.79423i 0.808224 1.39988i −0.105869 0.994380i \(-0.533762\pi\)
0.914093 0.405505i \(-0.132904\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −1.00000 1.73205i −0.171499 0.297044i
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) 5.00000 0.821995 0.410997 0.911636i \(-0.365181\pi\)
0.410997 + 0.911636i \(0.365181\pi\)
\(38\) 0.500000 + 0.866025i 0.0811107 + 0.140488i
\(39\) 0 0
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) 4.50000 7.79423i 0.702782 1.21725i −0.264704 0.964330i \(-0.585274\pi\)
0.967486 0.252924i \(-0.0813924\pi\)
\(42\) 0 0
\(43\) 5.00000 + 8.66025i 0.762493 + 1.32068i 0.941562 + 0.336840i \(0.109358\pi\)
−0.179069 + 0.983836i \(0.557309\pi\)
\(44\) 5.00000 0.753778
\(45\) 0 0
\(46\) −1.00000 −0.147442
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 2.00000 3.46410i 0.282843 0.489898i
\(51\) 0 0
\(52\) 0 0
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 0 0
\(55\) 5.00000 0.674200
\(56\) 0.500000 + 0.866025i 0.0668153 + 0.115728i
\(57\) 0 0
\(58\) −2.00000 + 3.46410i −0.262613 + 0.454859i
\(59\) 7.00000 12.1244i 0.911322 1.57846i 0.0991242 0.995075i \(-0.468396\pi\)
0.812198 0.583382i \(-0.198271\pi\)
\(60\) 0 0
\(61\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(62\) −9.00000 −1.14300
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 4.00000 6.92820i 0.488678 0.846415i −0.511237 0.859440i \(-0.670813\pi\)
0.999915 + 0.0130248i \(0.00414604\pi\)
\(68\) −1.00000 + 1.73205i −0.121268 + 0.210042i
\(69\) 0 0
\(70\) 0.500000 + 0.866025i 0.0597614 + 0.103510i
\(71\) −13.0000 −1.54282 −0.771408 0.636341i \(-0.780447\pi\)
−0.771408 + 0.636341i \(0.780447\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −2.50000 4.33013i −0.290619 0.503367i
\(75\) 0 0
\(76\) 0.500000 0.866025i 0.0573539 0.0993399i
\(77\) 2.50000 4.33013i 0.284901 0.493464i
\(78\) 0 0
\(79\) −3.00000 5.19615i −0.337526 0.584613i 0.646440 0.762964i \(-0.276257\pi\)
−0.983967 + 0.178352i \(0.942924\pi\)
\(80\) 1.00000 0.111803
\(81\) 0 0
\(82\) −9.00000 −0.993884
\(83\) 2.00000 + 3.46410i 0.219529 + 0.380235i 0.954664 0.297686i \(-0.0962148\pi\)
−0.735135 + 0.677920i \(0.762881\pi\)
\(84\) 0 0
\(85\) −1.00000 + 1.73205i −0.108465 + 0.187867i
\(86\) 5.00000 8.66025i 0.539164 0.933859i
\(87\) 0 0
\(88\) −2.50000 4.33013i −0.266501 0.461593i
\(89\) −9.00000 −0.953998 −0.476999 0.878904i \(-0.658275\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.500000 + 0.866025i 0.0521286 + 0.0902894i
\(93\) 0 0
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) 0.500000 0.866025i 0.0512989 0.0888523i
\(96\) 0 0
\(97\) −8.00000 13.8564i −0.812277 1.40690i −0.911267 0.411816i \(-0.864894\pi\)
0.0989899 0.995088i \(-0.468439\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) −4.00000 −0.400000
\(101\) 7.00000 + 12.1244i 0.696526 + 1.20642i 0.969664 + 0.244443i \(0.0786053\pi\)
−0.273138 + 0.961975i \(0.588061\pi\)
\(102\) 0 0
\(103\) 0.500000 0.866025i 0.0492665 0.0853320i −0.840341 0.542059i \(-0.817645\pi\)
0.889607 + 0.456727i \(0.150978\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −6.00000 10.3923i −0.582772 1.00939i
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) 7.00000 0.670478 0.335239 0.942133i \(-0.391183\pi\)
0.335239 + 0.942133i \(0.391183\pi\)
\(110\) −2.50000 4.33013i −0.238366 0.412861i
\(111\) 0 0
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) 1.00000 1.73205i 0.0940721 0.162938i −0.815149 0.579252i \(-0.803345\pi\)
0.909221 + 0.416314i \(0.136678\pi\)
\(114\) 0 0
\(115\) 0.500000 + 0.866025i 0.0466252 + 0.0807573i
\(116\) 4.00000 0.371391
\(117\) 0 0
\(118\) −14.0000 −1.28880
\(119\) 1.00000 + 1.73205i 0.0916698 + 0.158777i
\(120\) 0 0
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) 0 0
\(123\) 0 0
\(124\) 4.50000 + 7.79423i 0.404112 + 0.699942i
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −11.0000 + 19.0526i −0.961074 + 1.66463i −0.241264 + 0.970460i \(0.577562\pi\)
−0.719811 + 0.694170i \(0.755772\pi\)
\(132\) 0 0
\(133\) −0.500000 0.866025i −0.0433555 0.0750939i
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) 2.00000 0.171499
\(137\) −8.00000 13.8564i −0.683486 1.18383i −0.973910 0.226935i \(-0.927130\pi\)
0.290424 0.956898i \(-0.406204\pi\)
\(138\) 0 0
\(139\) 10.0000 17.3205i 0.848189 1.46911i −0.0346338 0.999400i \(-0.511026\pi\)
0.882823 0.469706i \(-0.155640\pi\)
\(140\) 0.500000 0.866025i 0.0422577 0.0731925i
\(141\) 0 0
\(142\) 6.50000 + 11.2583i 0.545468 + 0.944778i
\(143\) 0 0
\(144\) 0 0
\(145\) 4.00000 0.332182
\(146\) 1.00000 + 1.73205i 0.0827606 + 0.143346i
\(147\) 0 0
\(148\) −2.50000 + 4.33013i −0.205499 + 0.355934i
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0 0
\(151\) −5.00000 8.66025i −0.406894 0.704761i 0.587646 0.809118i \(-0.300055\pi\)
−0.994540 + 0.104357i \(0.966722\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 0 0
\(154\) −5.00000 −0.402911
\(155\) 4.50000 + 7.79423i 0.361449 + 0.626048i
\(156\) 0 0
\(157\) −4.00000 + 6.92820i −0.319235 + 0.552931i −0.980329 0.197372i \(-0.936759\pi\)
0.661094 + 0.750303i \(0.270093\pi\)
\(158\) −3.00000 + 5.19615i −0.238667 + 0.413384i
\(159\) 0 0
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 1.00000 0.0788110
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 4.50000 + 7.79423i 0.351391 + 0.608627i
\(165\) 0 0
\(166\) 2.00000 3.46410i 0.155230 0.268866i
\(167\) −5.00000 + 8.66025i −0.386912 + 0.670151i −0.992032 0.125983i \(-0.959791\pi\)
0.605121 + 0.796134i \(0.293125\pi\)
\(168\) 0 0
\(169\) 6.50000 + 11.2583i 0.500000 + 0.866025i
\(170\) 2.00000 0.153393
\(171\) 0 0
\(172\) −10.0000 −0.762493
\(173\) −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
\(175\) −2.00000 + 3.46410i −0.151186 + 0.261861i
\(176\) −2.50000 + 4.33013i −0.188445 + 0.326396i
\(177\) 0 0
\(178\) 4.50000 + 7.79423i 0.337289 + 0.584202i
\(179\) 24.0000 1.79384 0.896922 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) 0 0
\(181\) 18.0000 1.33793 0.668965 0.743294i \(-0.266738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) −2.50000 + 4.33013i −0.183804 + 0.318357i
\(186\) 0 0
\(187\) −5.00000 8.66025i −0.365636 0.633300i
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) −1.00000 −0.0725476
\(191\) 1.50000 + 2.59808i 0.108536 + 0.187990i 0.915177 0.403051i \(-0.132050\pi\)
−0.806641 + 0.591041i \(0.798717\pi\)
\(192\) 0 0
\(193\) 5.00000 8.66025i 0.359908 0.623379i −0.628037 0.778183i \(-0.716141\pi\)
0.987945 + 0.154805i \(0.0494748\pi\)
\(194\) −8.00000 + 13.8564i −0.574367 + 0.994832i
\(195\) 0 0
\(196\) −0.500000 0.866025i −0.0357143 0.0618590i
\(197\) −10.0000 −0.712470 −0.356235 0.934396i \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 0 0
\(199\) −13.0000 −0.921546 −0.460773 0.887518i \(-0.652428\pi\)
−0.460773 + 0.887518i \(0.652428\pi\)
\(200\) 2.00000 + 3.46410i 0.141421 + 0.244949i
\(201\) 0 0
\(202\) 7.00000 12.1244i 0.492518 0.853067i
\(203\) 2.00000 3.46410i 0.140372 0.243132i
\(204\) 0 0
\(205\) 4.50000 + 7.79423i 0.314294 + 0.544373i
\(206\) −1.00000 −0.0696733
\(207\) 0 0
\(208\) 0 0
\(209\) 2.50000 + 4.33013i 0.172929 + 0.299521i
\(210\) 0 0
\(211\) 11.0000 19.0526i 0.757271 1.31163i −0.186966 0.982366i \(-0.559865\pi\)
0.944237 0.329266i \(-0.106801\pi\)
\(212\) −6.00000 + 10.3923i −0.412082 + 0.713746i
\(213\) 0 0
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) −10.0000 −0.681994
\(216\) 0 0
\(217\) 9.00000 0.610960
\(218\) −3.50000 6.06218i −0.237050 0.410582i
\(219\) 0 0
\(220\) −2.50000 + 4.33013i −0.168550 + 0.291937i
\(221\) 0 0
\(222\) 0 0
\(223\) −2.50000 4.33013i −0.167412 0.289967i 0.770097 0.637927i \(-0.220208\pi\)
−0.937509 + 0.347960i \(0.886874\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) −2.00000 −0.133038
\(227\) −3.00000 5.19615i −0.199117 0.344881i 0.749125 0.662428i \(-0.230474\pi\)
−0.948242 + 0.317547i \(0.897141\pi\)
\(228\) 0 0
\(229\) −14.0000 + 24.2487i −0.925146 + 1.60240i −0.133820 + 0.991006i \(0.542724\pi\)
−0.791326 + 0.611394i \(0.790609\pi\)
\(230\) 0.500000 0.866025i 0.0329690 0.0571040i
\(231\) 0 0
\(232\) −2.00000 3.46410i −0.131306 0.227429i
\(233\) 14.0000 0.917170 0.458585 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) 0 0
\(235\) 6.00000 0.391397
\(236\) 7.00000 + 12.1244i 0.455661 + 0.789228i
\(237\) 0 0
\(238\) 1.00000 1.73205i 0.0648204 0.112272i
\(239\) −12.0000 + 20.7846i −0.776215 + 1.34444i 0.157893 + 0.987456i \(0.449530\pi\)
−0.934109 + 0.356988i \(0.883804\pi\)
\(240\) 0 0
\(241\) −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i \(-0.315567\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) 14.0000 0.899954
\(243\) 0 0
\(244\) 0 0
\(245\) −0.500000 0.866025i −0.0319438 0.0553283i
\(246\) 0 0
\(247\) 0 0
\(248\) 4.50000 7.79423i 0.285750 0.494934i
\(249\) 0 0
\(250\) 4.50000 + 7.79423i 0.284605 + 0.492950i
\(251\) −24.0000 −1.51487 −0.757433 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) 0 0
\(253\) −5.00000 −0.314347
\(254\) 0 0
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −13.5000 + 23.3827i −0.842107 + 1.45857i 0.0460033 + 0.998941i \(0.485352\pi\)
−0.888110 + 0.459631i \(0.847982\pi\)
\(258\) 0 0
\(259\) 2.50000 + 4.33013i 0.155342 + 0.269061i
\(260\) 0 0
\(261\) 0 0
\(262\) 22.0000 1.35916
\(263\) 10.5000 + 18.1865i 0.647458 + 1.12143i 0.983728 + 0.179664i \(0.0575011\pi\)
−0.336270 + 0.941766i \(0.609166\pi\)
\(264\) 0 0
\(265\) −6.00000 + 10.3923i −0.368577 + 0.638394i
\(266\) −0.500000 + 0.866025i −0.0306570 + 0.0530994i
\(267\) 0 0
\(268\) 4.00000 + 6.92820i 0.244339 + 0.423207i
\(269\) 13.0000 0.792624 0.396312 0.918116i \(-0.370290\pi\)
0.396312 + 0.918116i \(0.370290\pi\)
\(270\) 0 0
\(271\) 24.0000 1.45790 0.728948 0.684569i \(-0.240010\pi\)
0.728948 + 0.684569i \(0.240010\pi\)
\(272\) −1.00000 1.73205i −0.0606339 0.105021i
\(273\) 0 0
\(274\) −8.00000 + 13.8564i −0.483298 + 0.837096i
\(275\) 10.0000 17.3205i 0.603023 1.04447i
\(276\) 0 0
\(277\) 9.50000 + 16.4545i 0.570800 + 0.988654i 0.996484 + 0.0837823i \(0.0267000\pi\)
−0.425684 + 0.904872i \(0.639967\pi\)
\(278\) −20.0000 −1.19952
\(279\) 0 0
\(280\) −1.00000 −0.0597614
\(281\) 5.00000 + 8.66025i 0.298275 + 0.516627i 0.975741 0.218926i \(-0.0702554\pi\)
−0.677466 + 0.735554i \(0.736922\pi\)
\(282\) 0 0
\(283\) 10.0000 17.3205i 0.594438 1.02960i −0.399188 0.916869i \(-0.630708\pi\)
0.993626 0.112728i \(-0.0359589\pi\)
\(284\) 6.50000 11.2583i 0.385704 0.668059i
\(285\) 0 0
\(286\) 0 0
\(287\) 9.00000 0.531253
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) −2.00000 3.46410i −0.117444 0.203419i
\(291\) 0 0
\(292\) 1.00000 1.73205i 0.0585206 0.101361i
\(293\) −9.00000 + 15.5885i −0.525786 + 0.910687i 0.473763 + 0.880652i \(0.342895\pi\)
−0.999549 + 0.0300351i \(0.990438\pi\)
\(294\) 0 0
\(295\) 7.00000 + 12.1244i 0.407556 + 0.705907i
\(296\) 5.00000 0.290619
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) 0 0
\(301\) −5.00000 + 8.66025i −0.288195 + 0.499169i
\(302\) −5.00000 + 8.66025i −0.287718 + 0.498342i
\(303\) 0 0
\(304\) 0.500000 + 0.866025i 0.0286770 + 0.0496700i
\(305\) 0 0
\(306\) 0 0
\(307\) −5.00000 −0.285365 −0.142683 0.989769i \(-0.545573\pi\)
−0.142683 + 0.989769i \(0.545573\pi\)
\(308\) 2.50000 + 4.33013i 0.142451 + 0.246732i
\(309\) 0 0
\(310\) 4.50000 7.79423i 0.255583 0.442682i
\(311\) 4.00000 6.92820i 0.226819 0.392862i −0.730044 0.683400i \(-0.760501\pi\)
0.956864 + 0.290537i \(0.0938340\pi\)
\(312\) 0 0
\(313\) 4.00000 + 6.92820i 0.226093 + 0.391605i 0.956647 0.291250i \(-0.0940712\pi\)
−0.730554 + 0.682855i \(0.760738\pi\)
\(314\) 8.00000 0.451466
\(315\) 0 0
\(316\) 6.00000 0.337526
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 0 0
\(319\) −10.0000 + 17.3205i −0.559893 + 0.969762i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) −0.500000 0.866025i −0.0278639 0.0482617i
\(323\) −2.00000 −0.111283
\(324\) 0 0
\(325\) 0 0
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) 0 0
\(328\) 4.50000 7.79423i 0.248471 0.430364i
\(329\) 3.00000 5.19615i 0.165395 0.286473i
\(330\) 0 0
\(331\) 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i \(-0.131604\pi\)
−0.805812 + 0.592172i \(0.798271\pi\)
\(332\) −4.00000 −0.219529
\(333\) 0 0
\(334\) 10.0000 0.547176
\(335\) 4.00000 + 6.92820i 0.218543 + 0.378528i
\(336\) 0 0
\(337\) −13.5000 + 23.3827i −0.735392 + 1.27374i 0.219159 + 0.975689i \(0.429669\pi\)
−0.954551 + 0.298047i \(0.903665\pi\)
\(338\) 6.50000 11.2583i 0.353553 0.612372i
\(339\) 0 0
\(340\) −1.00000 1.73205i −0.0542326 0.0939336i
\(341\) −45.0000 −2.43689
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 5.00000 + 8.66025i 0.269582 + 0.466930i
\(345\) 0 0
\(346\) −3.50000 + 6.06218i −0.188161 + 0.325905i
\(347\) 1.50000 2.59808i 0.0805242 0.139472i −0.822951 0.568112i \(-0.807674\pi\)
0.903475 + 0.428640i \(0.141007\pi\)
\(348\) 0 0
\(349\) 13.0000 + 22.5167i 0.695874 + 1.20529i 0.969885 + 0.243563i \(0.0783162\pi\)
−0.274011 + 0.961727i \(0.588351\pi\)
\(350\) 4.00000 0.213809
\(351\) 0 0
\(352\) 5.00000 0.266501
\(353\) 1.50000 + 2.59808i 0.0798369 + 0.138282i 0.903179 0.429263i \(-0.141227\pi\)
−0.823343 + 0.567545i \(0.807893\pi\)
\(354\) 0 0
\(355\) 6.50000 11.2583i 0.344984 0.597530i
\(356\) 4.50000 7.79423i 0.238500 0.413093i
\(357\) 0 0
\(358\) −12.0000 20.7846i −0.634220 1.09850i
\(359\) 4.00000 0.211112 0.105556 0.994413i \(-0.466338\pi\)
0.105556 + 0.994413i \(0.466338\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) −9.00000 15.5885i −0.473029 0.819311i
\(363\) 0 0
\(364\) 0 0
\(365\) 1.00000 1.73205i 0.0523424 0.0906597i
\(366\) 0 0
\(367\) −17.5000 30.3109i −0.913493 1.58222i −0.809093 0.587680i \(-0.800041\pi\)
−0.104399 0.994535i \(-0.533292\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 0 0
\(370\) 5.00000 0.259938
\(371\) 6.00000 + 10.3923i 0.311504 + 0.539542i
\(372\) 0 0
\(373\) 8.50000 14.7224i 0.440113 0.762299i −0.557584 0.830120i \(-0.688272\pi\)
0.997697 + 0.0678218i \(0.0216049\pi\)
\(374\) −5.00000 + 8.66025i −0.258544 + 0.447811i
\(375\) 0 0
\(376\) −3.00000 5.19615i −0.154713 0.267971i
\(377\) 0 0
\(378\) 0 0
\(379\) −14.0000 −0.719132 −0.359566 0.933120i \(-0.617075\pi\)
−0.359566 + 0.933120i \(0.617075\pi\)
\(380\) 0.500000 + 0.866025i 0.0256495 + 0.0444262i
\(381\) 0 0
\(382\) 1.50000 2.59808i 0.0767467 0.132929i
\(383\) 5.00000 8.66025i 0.255488 0.442518i −0.709540 0.704665i \(-0.751097\pi\)
0.965028 + 0.262147i \(0.0844305\pi\)
\(384\) 0 0
\(385\) 2.50000 + 4.33013i 0.127412 + 0.220684i
\(386\) −10.0000 −0.508987
\(387\) 0 0
\(388\) 16.0000 0.812277
\(389\) 10.0000 + 17.3205i 0.507020 + 0.878185i 0.999967 + 0.00812520i \(0.00258636\pi\)
−0.492947 + 0.870059i \(0.664080\pi\)
\(390\) 0 0
\(391\) 1.00000 1.73205i 0.0505722 0.0875936i
\(392\) −0.500000 + 0.866025i −0.0252538 + 0.0437409i
\(393\) 0 0
\(394\) 5.00000 + 8.66025i 0.251896 + 0.436297i
\(395\) 6.00000 0.301893
\(396\) 0 0
\(397\) −30.0000 −1.50566 −0.752828 0.658217i \(-0.771311\pi\)
−0.752828 + 0.658217i \(0.771311\pi\)
\(398\) 6.50000 + 11.2583i 0.325816 + 0.564329i
\(399\) 0 0
\(400\) 2.00000 3.46410i 0.100000 0.173205i
\(401\) 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i \(-0.736472\pi\)
0.976050 + 0.217545i \(0.0698049\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −14.0000 −0.696526
\(405\) 0 0
\(406\) −4.00000 −0.198517
\(407\) −12.5000 21.6506i −0.619602 1.07318i
\(408\) 0 0
\(409\) 5.00000 8.66025i 0.247234 0.428222i −0.715523 0.698589i \(-0.753812\pi\)
0.962757 + 0.270367i \(0.0871450\pi\)
\(410\) 4.50000 7.79423i 0.222239 0.384930i
\(411\) 0 0
\(412\) 0.500000 + 0.866025i 0.0246332 + 0.0426660i
\(413\) 14.0000 0.688895
\(414\) 0 0
\(415\) −4.00000 −0.196352
\(416\) 0 0
\(417\) 0 0
\(418\) 2.50000 4.33013i 0.122279 0.211793i
\(419\) −3.00000 + 5.19615i −0.146560 + 0.253849i −0.929954 0.367677i \(-0.880153\pi\)
0.783394 + 0.621525i \(0.213487\pi\)
\(420\) 0 0
\(421\) 13.5000 + 23.3827i 0.657950 + 1.13960i 0.981146 + 0.193270i \(0.0619094\pi\)
−0.323196 + 0.946332i \(0.604757\pi\)
\(422\) −22.0000 −1.07094
\(423\) 0 0
\(424\) 12.0000 0.582772
\(425\) 4.00000 + 6.92820i 0.194029 + 0.336067i
\(426\) 0 0
\(427\) 0 0
\(428\) −6.00000 + 10.3923i −0.290021 + 0.502331i
\(429\) 0 0
\(430\) 5.00000 + 8.66025i 0.241121 + 0.417635i
\(431\) −15.0000 −0.722525 −0.361262 0.932464i \(-0.617654\pi\)
−0.361262 + 0.932464i \(0.617654\pi\)
\(432\) 0 0
\(433\) −4.00000 −0.192228 −0.0961139 0.995370i \(-0.530641\pi\)
−0.0961139 + 0.995370i \(0.530641\pi\)
\(434\) −4.50000 7.79423i −0.216007 0.374135i
\(435\) 0 0
\(436\) −3.50000 + 6.06218i −0.167620 + 0.290326i
\(437\) −0.500000 + 0.866025i −0.0239182 + 0.0414276i
\(438\) 0 0
\(439\) −12.0000 20.7846i −0.572729 0.991995i −0.996284 0.0861252i \(-0.972552\pi\)
0.423556 0.905870i \(-0.360782\pi\)
\(440\) 5.00000 0.238366
\(441\) 0 0
\(442\) 0 0
\(443\) −5.50000 9.52628i −0.261313 0.452607i 0.705278 0.708931i \(-0.250822\pi\)
−0.966591 + 0.256323i \(0.917489\pi\)
\(444\) 0 0
\(445\) 4.50000 7.79423i 0.213320 0.369482i
\(446\) −2.50000 + 4.33013i −0.118378 + 0.205037i
\(447\) 0 0
\(448\) 0.500000 + 0.866025i 0.0236228 + 0.0409159i
\(449\) 10.0000 0.471929 0.235965 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) 0 0
\(451\) −45.0000 −2.11897
\(452\) 1.00000 + 1.73205i 0.0470360 + 0.0814688i
\(453\) 0 0
\(454\) −3.00000 + 5.19615i −0.140797 + 0.243868i
\(455\) 0 0
\(456\) 0 0
\(457\) −6.50000 11.2583i −0.304057 0.526642i 0.672994 0.739648i \(-0.265008\pi\)
−0.977051 + 0.213006i \(0.931675\pi\)
\(458\) 28.0000 1.30835
\(459\) 0 0
\(460\) −1.00000 −0.0466252
\(461\) −15.5000 26.8468i −0.721907 1.25038i −0.960235 0.279195i \(-0.909933\pi\)
0.238328 0.971185i \(-0.423401\pi\)
\(462\) 0 0
\(463\) 7.00000 12.1244i 0.325318 0.563467i −0.656259 0.754536i \(-0.727862\pi\)
0.981577 + 0.191069i \(0.0611955\pi\)
\(464\) −2.00000 + 3.46410i −0.0928477 + 0.160817i
\(465\) 0 0
\(466\) −7.00000 12.1244i −0.324269 0.561650i
\(467\) −26.0000 −1.20314 −0.601568 0.798821i \(-0.705457\pi\)
−0.601568 + 0.798821i \(0.705457\pi\)
\(468\) 0 0
\(469\) 8.00000 0.369406
\(470\) −3.00000 5.19615i −0.138380 0.239681i
\(471\) 0 0
\(472\) 7.00000 12.1244i 0.322201 0.558069i
\(473\) 25.0000 43.3013i 1.14950 1.99099i
\(474\) 0 0
\(475\) −2.00000 3.46410i −0.0917663 0.158944i
\(476\) −2.00000 −0.0916698
\(477\) 0 0
\(478\) 24.0000 1.09773
\(479\) −16.0000 27.7128i −0.731059 1.26623i −0.956431 0.291958i \(-0.905693\pi\)
0.225372 0.974273i \(-0.427640\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −7.00000 + 12.1244i −0.318841 + 0.552249i
\(483\) 0 0
\(484\) −7.00000 12.1244i −0.318182 0.551107i
\(485\) 16.0000 0.726523
\(486\) 0 0
\(487\) 26.0000 1.17817 0.589086 0.808070i \(-0.299488\pi\)
0.589086 + 0.808070i \(0.299488\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −0.500000 + 0.866025i −0.0225877 + 0.0391230i
\(491\) −4.50000 + 7.79423i −0.203082 + 0.351749i −0.949520 0.313707i \(-0.898429\pi\)
0.746438 + 0.665455i \(0.231763\pi\)
\(492\) 0 0
\(493\) −4.00000 6.92820i −0.180151 0.312031i
\(494\) 0 0
\(495\) 0 0
\(496\) −9.00000 −0.404112
\(497\) −6.50000 11.2583i −0.291565 0.505005i
\(498\) 0 0
\(499\) −5.00000 + 8.66025i −0.223831 + 0.387686i −0.955968 0.293471i \(-0.905190\pi\)
0.732137 + 0.681157i \(0.238523\pi\)
\(500\) 4.50000 7.79423i 0.201246 0.348569i
\(501\) 0 0
\(502\) 12.0000 + 20.7846i 0.535586 + 0.927663i
\(503\) 36.0000 1.60516 0.802580 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) 0 0
\(505\) −14.0000 −0.622992
\(506\) 2.50000 + 4.33013i 0.111139 + 0.192498i
\(507\) 0 0
\(508\) 0 0
\(509\) −9.00000 + 15.5885i −0.398918 + 0.690946i −0.993593 0.113020i \(-0.963948\pi\)
0.594675 + 0.803966i \(0.297281\pi\)
\(510\) 0 0
\(511\) −1.00000 1.73205i −0.0442374 0.0766214i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 27.0000 1.19092
\(515\) 0.500000 + 0.866025i 0.0220326 + 0.0381616i
\(516\) 0 0
\(517\) −15.0000 + 25.9808i −0.659699 + 1.14263i
\(518\) 2.50000 4.33013i 0.109844 0.190255i
\(519\) 0 0
\(520\) 0 0
\(521\) −15.0000 −0.657162 −0.328581 0.944476i \(-0.606570\pi\)
−0.328581 + 0.944476i \(0.606570\pi\)
\(522\) 0 0
\(523\) 11.0000 0.480996 0.240498 0.970650i \(-0.422689\pi\)
0.240498 + 0.970650i \(0.422689\pi\)
\(524\) −11.0000 19.0526i −0.480537 0.832315i
\(525\) 0 0
\(526\) 10.5000 18.1865i 0.457822 0.792971i
\(527\) 9.00000 15.5885i 0.392046 0.679044i
\(528\) 0 0
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 12.0000 0.521247
\(531\) 0 0
\(532\) 1.00000 0.0433555
\(533\) 0 0
\(534\) 0 0
\(535\) −6.00000 + 10.3923i −0.259403 + 0.449299i
\(536\) 4.00000 6.92820i 0.172774 0.299253i
\(537\) 0 0
\(538\) −6.50000 11.2583i −0.280235 0.485381i
\(539\) 5.00000 0.215365
\(540\) 0 0
\(541\) −3.00000 −0.128980 −0.0644900 0.997918i \(-0.520542\pi\)
−0.0644900 + 0.997918i \(0.520542\pi\)
\(542\) −12.0000 20.7846i −0.515444 0.892775i
\(543\) 0 0
\(544\) −1.00000 + 1.73205i −0.0428746 + 0.0742611i
\(545\) −3.50000 + 6.06218i −0.149924 + 0.259675i
\(546\) 0 0
\(547\) −6.00000 10.3923i −0.256541 0.444343i 0.708772 0.705438i \(-0.249250\pi\)
−0.965313 + 0.261095i \(0.915916\pi\)
\(548\) 16.0000 0.683486
\(549\) 0 0
\(550\) −20.0000 −0.852803
\(551\) 2.00000 + 3.46410i 0.0852029 + 0.147576i
\(552\) 0 0
\(553\) 3.00000 5.19615i 0.127573 0.220963i
\(554\) 9.50000 16.4545i 0.403616 0.699084i
\(555\) 0 0
\(556\) 10.0000 + 17.3205i 0.424094 + 0.734553i
\(557\) 22.0000 0.932170 0.466085 0.884740i \(-0.345664\pi\)
0.466085 + 0.884740i \(0.345664\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0.500000 + 0.866025i 0.0211289 + 0.0365963i
\(561\) 0 0
\(562\) 5.00000 8.66025i 0.210912 0.365311i
\(563\) 2.00000 3.46410i 0.0842900 0.145994i −0.820798 0.571218i \(-0.806471\pi\)
0.905088 + 0.425223i \(0.139804\pi\)
\(564\) 0 0
\(565\) 1.00000 + 1.73205i 0.0420703 + 0.0728679i
\(566\) −20.0000 −0.840663
\(567\) 0 0
\(568\) −13.0000 −0.545468
\(569\) −15.0000 25.9808i −0.628833 1.08917i −0.987786 0.155815i \(-0.950200\pi\)
0.358954 0.933355i \(-0.383134\pi\)
\(570\) 0 0
\(571\) −9.00000 + 15.5885i −0.376638 + 0.652357i −0.990571 0.137002i \(-0.956253\pi\)
0.613933 + 0.789359i \(0.289587\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −4.50000 7.79423i −0.187826 0.325325i
\(575\) 4.00000 0.166812
\(576\) 0 0
\(577\) −14.0000 −0.582828 −0.291414 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) 6.50000 + 11.2583i 0.270364 + 0.468285i
\(579\) 0 0
\(580\) −2.00000 + 3.46410i −0.0830455 + 0.143839i
\(581\) −2.00000 + 3.46410i −0.0829740 + 0.143715i
\(582\) 0 0
\(583\) −30.0000 51.9615i −1.24247 2.15203i
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) 18.0000 0.743573
\(587\) −7.00000 12.1244i −0.288921 0.500426i 0.684632 0.728889i \(-0.259963\pi\)
−0.973552 + 0.228464i \(0.926630\pi\)
\(588\) 0 0
\(589\) −4.50000 + 7.79423i −0.185419 + 0.321156i
\(590\) 7.00000 12.1244i 0.288185 0.499152i
\(591\) 0 0
\(592\) −2.50000 4.33013i −0.102749 0.177967i
\(593\) 9.00000 0.369586 0.184793 0.982777i \(-0.440839\pi\)
0.184793 + 0.982777i \(0.440839\pi\)
\(594\) 0 0
\(595\) −2.00000 −0.0819920
\(596\) −3.00000 5.19615i −0.122885 0.212843i
\(597\) 0 0
\(598\) 0 0
\(599\) 13.5000 23.3827i 0.551595 0.955391i −0.446565 0.894751i \(-0.647353\pi\)
0.998160 0.0606393i \(-0.0193139\pi\)
\(600\) 0 0
\(601\) −4.00000 6.92820i −0.163163 0.282607i 0.772838 0.634603i \(-0.218836\pi\)
−0.936002 + 0.351996i \(0.885503\pi\)
\(602\) 10.0000 0.407570
\(603\) 0 0
\(604\) 10.0000 0.406894
\(605\) −7.00000 12.1244i −0.284590 0.492925i
\(606\) 0 0
\(607\) −6.00000 + 10.3923i −0.243532 + 0.421811i −0.961718 0.274041i \(-0.911640\pi\)
0.718186 + 0.695852i \(0.244973\pi\)
\(608\) 0.500000 0.866025i 0.0202777 0.0351220i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −15.0000 −0.605844 −0.302922 0.953015i \(-0.597962\pi\)
−0.302922 + 0.953015i \(0.597962\pi\)
\(614\) 2.50000 + 4.33013i 0.100892 + 0.174750i
\(615\) 0 0
\(616\) 2.50000 4.33013i 0.100728 0.174466i
\(617\) −7.00000 + 12.1244i −0.281809 + 0.488108i −0.971830 0.235681i \(-0.924268\pi\)
0.690021 + 0.723789i \(0.257601\pi\)
\(618\) 0 0
\(619\) 5.50000 + 9.52628i 0.221064 + 0.382893i 0.955131 0.296183i \(-0.0957138\pi\)
−0.734068 + 0.679076i \(0.762380\pi\)
\(620\) −9.00000 −0.361449
\(621\) 0 0
\(622\) −8.00000 −0.320771
\(623\) −4.50000 7.79423i −0.180289 0.312269i
\(624\) 0 0
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) 4.00000 6.92820i 0.159872 0.276907i
\(627\) 0 0
\(628\) −4.00000 6.92820i −0.159617 0.276465i
\(629\) 10.0000 0.398726
\(630\) 0 0
\(631\) 38.0000 1.51276 0.756378 0.654135i \(-0.226967\pi\)
0.756378 + 0.654135i \(0.226967\pi\)
\(632\) −3.00000 5.19615i −0.119334 0.206692i
\(633\) 0 0
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 20.0000 0.791808
\(639\) 0 0
\(640\) 1.00000 0.0395285
\(641\) 11.0000 + 19.0526i 0.434474 + 0.752531i 0.997253 0.0740768i \(-0.0236010\pi\)
−0.562779 + 0.826608i \(0.690268\pi\)
\(642\) 0 0
\(643\) 6.50000 11.2583i 0.256335 0.443985i −0.708922 0.705287i \(-0.750818\pi\)
0.965257 + 0.261301i \(0.0841516\pi\)
\(644\) −0.500000 + 0.866025i −0.0197028 + 0.0341262i
\(645\) 0 0
\(646\) 1.00000 + 1.73205i 0.0393445 + 0.0681466i
\(647\) 42.0000 1.65119 0.825595 0.564263i \(-0.190840\pi\)
0.825595 + 0.564263i \(0.190840\pi\)
\(648\) 0 0
\(649\) −70.0000 −2.74774
\(650\) 0 0
\(651\) 0 0
\(652\) 2.00000 3.46410i 0.0783260 0.135665i
\(653\) 15.0000 25.9808i 0.586995 1.01671i −0.407628 0.913148i \(-0.633644\pi\)
0.994623 0.103558i \(-0.0330227\pi\)
\(654\) 0 0
\(655\) −11.0000 19.0526i −0.429806 0.744445i
\(656\) −9.00000 −0.351391
\(657\) 0 0
\(658\) −6.00000 −0.233904
\(659\) −8.50000 14.7224i −0.331113 0.573505i 0.651617 0.758548i \(-0.274091\pi\)
−0.982730 + 0.185043i \(0.940757\pi\)
\(660\) 0 0
\(661\) −14.0000 + 24.2487i −0.544537 + 0.943166i 0.454099 + 0.890951i \(0.349961\pi\)
−0.998636 + 0.0522143i \(0.983372\pi\)
\(662\) 2.00000 3.46410i 0.0777322 0.134636i
\(663\) 0 0
\(664\) 2.00000 + 3.46410i 0.0776151 + 0.134433i
\(665\) 1.00000 0.0387783
\(666\) 0 0
\(667\) −4.00000 −0.154881
\(668\) −5.00000 8.66025i −0.193456 0.335075i
\(669\) 0 0
\(670\) 4.00000 6.92820i 0.154533 0.267660i
\(671\) 0 0
\(672\) 0 0
\(673\) −13.0000 22.5167i −0.501113 0.867953i −0.999999 0.00128586i \(-0.999591\pi\)
0.498886 0.866668i \(-0.333743\pi\)
\(674\) 27.0000 1.04000
\(675\) 0 0
\(676\) −13.0000 −0.500000
\(677\) −13.5000 23.3827i −0.518847 0.898670i −0.999760 0.0219013i \(-0.993028\pi\)
0.480913 0.876768i \(-0.340305\pi\)
\(678\) 0 0
\(679\) 8.00000 13.8564i 0.307012 0.531760i
\(680\) −1.00000 + 1.73205i −0.0383482 + 0.0664211i
\(681\) 0 0
\(682\) 22.5000 + 38.9711i 0.861570 + 1.49228i
\(683\) −9.00000 −0.344375 −0.172188 0.985064i \(-0.555084\pi\)
−0.172188 + 0.985064i \(0.555084\pi\)
\(684\) 0 0
\(685\) 16.0000 0.611329
\(686\) 0.500000 + 0.866025i 0.0190901 + 0.0330650i
\(687\) 0 0
\(688\) 5.00000 8.66025i 0.190623 0.330169i
\(689\) 0 0
\(690\) 0 0
\(691\) 2.00000 + 3.46410i 0.0760836 + 0.131781i 0.901557 0.432660i \(-0.142425\pi\)
−0.825473 + 0.564441i \(0.809092\pi\)
\(692\) 7.00000 0.266100
\(693\) 0 0
\(694\) −3.00000 −0.113878
\(695\) 10.0000 + 17.3205i 0.379322 + 0.657004i
\(696\) 0 0
\(697\) 9.00000 15.5885i 0.340899 0.590455i
\(698\) 13.0000 22.5167i 0.492057 0.852268i
\(699\) 0 0
\(700\) −2.00000 3.46410i −0.0755929 0.130931i
\(701\) −20.0000 −0.755390 −0.377695 0.925930i \(-0.623283\pi\)
−0.377695 + 0.925930i \(0.623283\pi\)
\(702\) 0 0
\(703\) −5.00000 −0.188579
\(704\) −2.50000 4.33013i −0.0942223 0.163198i
\(705\) 0 0
\(706\) 1.50000 2.59808i 0.0564532 0.0977799i
\(707\) −7.00000 + 12.1244i −0.263262 + 0.455983i
\(708\) 0 0
\(709\) 12.5000 + 21.6506i 0.469447 + 0.813107i 0.999390 0.0349269i \(-0.0111198\pi\)
−0.529943 + 0.848034i \(0.677787\pi\)
\(710\) −13.0000 −0.487881
\(711\) 0 0
\(712\) −9.00000 −0.337289
\(713\) −4.50000 7.79423i −0.168526 0.291896i
\(714\) 0 0
\(715\) 0 0
\(716\) −12.0000 + 20.7846i −0.448461 + 0.776757i
\(717\) 0 0
\(718\) −2.00000 3.46410i −0.0746393 0.129279i
\(719\) −30.0000 −1.11881 −0.559406 0.828894i \(-0.688971\pi\)
−0.559406 + 0.828894i \(0.688971\pi\)
\(720\) 0 0
\(721\) 1.00000 0.0372419
\(722\) 9.00000 + 15.5885i 0.334945 + 0.580142i
\(723\) 0 0
\(724\) −9.00000 + 15.5885i −0.334482 + 0.579340i
\(725\) 8.00000 13.8564i 0.297113 0.514614i
\(726\) 0 0
\(727\) 16.0000 + 27.7128i 0.593407 + 1.02781i 0.993770 + 0.111454i \(0.0355509\pi\)
−0.400362 + 0.916357i \(0.631116\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −2.00000 −0.0740233
\(731\) 10.0000 + 17.3205i 0.369863 + 0.640622i
\(732\) 0 0
\(733\) 9.00000 15.5885i 0.332423 0.575773i −0.650564 0.759452i \(-0.725467\pi\)
0.982986 + 0.183679i \(0.0588007\pi\)
\(734\) −17.5000 + 30.3109i −0.645937 + 1.11880i
\(735\) 0 0
\(736\) 0.500000 + 0.866025i 0.0184302 + 0.0319221i
\(737\) −40.0000 −1.47342
\(738\) 0 0
\(739\) 18.0000 0.662141 0.331070 0.943606i \(-0.392590\pi\)
0.331070 + 0.943606i \(0.392590\pi\)
\(740\) −2.50000 4.33013i −0.0919018 0.159179i
\(741\) 0 0
\(742\) 6.00000 10.3923i 0.220267 0.381514i
\(743\) 10.5000 18.1865i 0.385208 0.667199i −0.606590 0.795015i \(-0.707463\pi\)
0.991798 + 0.127815i \(0.0407965\pi\)
\(744\) 0 0
\(745\) −3.00000 5.19615i −0.109911 0.190372i
\(746\) −17.0000 −0.622414
\(747\) 0 0
\(748\) 10.0000 0.365636
\(749\) 6.00000 + 10.3923i 0.219235 + 0.379727i
\(750\) 0 0
\(751\) −9.00000 + 15.5885i −0.328415 + 0.568831i −0.982197 0.187851i \(-0.939848\pi\)
0.653783 + 0.756682i \(0.273181\pi\)
\(752\) −3.00000 + 5.19615i −0.109399 + 0.189484i
\(753\) 0 0
\(754\) 0 0
\(755\) 10.0000 0.363937
\(756\) 0 0
\(757\) 42.0000 1.52652 0.763258 0.646094i \(-0.223599\pi\)
0.763258 + 0.646094i \(0.223599\pi\)
\(758\) 7.00000 + 12.1244i 0.254251 + 0.440376i
\(759\) 0 0
\(760\) 0.500000 0.866025i 0.0181369 0.0314140i
\(761\) 11.0000 19.0526i 0.398750 0.690655i −0.594822 0.803857i \(-0.702778\pi\)
0.993572 + 0.113203i \(0.0361109\pi\)
\(762\) 0 0
\(763\) 3.50000 + 6.06218i 0.126709 + 0.219466i
\(764\) −3.00000 −0.108536
\(765\) 0 0
\(766\) −10.0000 −0.361315
\(767\) 0 0
\(768\) 0 0
\(769\) −20.0000 + 34.6410i −0.721218 + 1.24919i 0.239293 + 0.970947i \(0.423084\pi\)
−0.960512 + 0.278240i \(0.910249\pi\)
\(770\) 2.50000 4.33013i 0.0900937 0.156047i
\(771\) 0 0
\(772\) 5.00000 + 8.66025i 0.179954 + 0.311689i
\(773\) 19.0000 0.683383 0.341691 0.939812i \(-0.389000\pi\)
0.341691 + 0.939812i \(0.389000\pi\)
\(774\) 0 0
\(775\) 36.0000 1.29316
\(776\) −8.00000 13.8564i −0.287183 0.497416i
\(777\) 0 0
\(778\) 10.0000 17.3205i 0.358517 0.620970i
\(779\) −4.50000 + 7.79423i −0.161229 + 0.279257i
\(780\) 0 0
\(781\) 32.5000 + 56.2917i 1.16294 + 2.01427i
\(782\) −2.00000 −0.0715199
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) −4.00000 6.92820i −0.142766 0.247278i
\(786\) 0 0
\(787\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(788\) 5.00000 8.66025i 0.178118 0.308509i
\(789\) 0 0
\(790\) −3.00000 5.19615i −0.106735 0.184871i
\(791\) 2.00000 0.0711118
\(792\) 0 0
\(793\) 0 0 </