Properties

Label 1134.2.f.n.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.n.379.1

$q$-expansion

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

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 −0.732294 0.680989i \(-0.761550\pi\)
0.955901 + 0.293691i \(0.0948835\pi\)
\(6\) 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 \(0.105104\pi\)
−0.192201 + 0.981356i \(0.561563\pi\)
\(12\) 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 \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 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 −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) 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 0.989780 0.142605i \(-0.0455477\pi\)
−0.618389 + 0.785872i \(0.712214\pi\)
\(30\) 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 \(0.414726\pi\)
−0.967486 + 0.252924i \(0.918608\pi\)
\(42\) 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 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) 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 \(-0.808354\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(54\) 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 \(0.531604\pi\)
−0.812198 + 0.583382i \(0.801729\pi\)
\(60\) 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 \(-0.219553\pi\)
0.771408 + 0.636341i \(0.219553\pi\)
\(72\) 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 0.735135 0.677920i \(-0.237119\pi\)
−0.954664 + 0.297686i \(0.903785\pi\)
\(84\) 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 \(-0.341725\pi\)
0.476999 + 0.878904i \(0.341725\pi\)
\(90\) 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 \(-0.921395\pi\)
0.273138 0.961975i \(-0.411939\pi\)
\(102\) 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 \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 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 −0.909221 0.416314i \(-0.863322\pi\)
0.815149 + 0.579252i \(0.196655\pi\)
\(114\) 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 \(-0.422438\pi\)
0.719811 0.694170i \(-0.244228\pi\)
\(132\) 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 \(0.0728704\pi\)
−0.290424 + 0.956898i \(0.593796\pi\)
\(138\) 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 −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 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 −0.605121 0.796134i \(-0.706875\pi\)
0.992032 + 0.125983i \(0.0402085\pi\)
\(168\) 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 0.967851 0.251523i \(-0.0809315\pi\)
−0.701751 + 0.712422i \(0.747598\pi\)
\(174\) 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 \(-0.854202\pi\)
−0.896922 + 0.442189i \(0.854202\pi\)
\(180\) 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 0.806641 0.591041i \(-0.201283\pi\)
−0.915177 + 0.403051i \(0.867950\pi\)
\(192\) 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 \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(198\) 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 0.948242 0.317547i \(-0.102859\pi\)
−0.749125 + 0.662428i \(0.769526\pi\)
\(228\) 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 \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) 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 \(-0.550470\pi\)
0.934109 0.356988i \(-0.116196\pi\)
\(240\) 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 \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 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 \(-0.514648\pi\)
0.888110 0.459631i \(-0.152018\pi\)
\(258\) 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 \(-0.942499\pi\)
0.336270 0.941766i \(-0.390834\pi\)
\(264\) 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 \(-0.629710\pi\)
−0.396312 + 0.918116i \(0.629710\pi\)
\(270\) 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 0.677466 0.735554i \(-0.263078\pi\)
−0.975741 + 0.218926i \(0.929745\pi\)
\(282\) 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 \(-0.657105\pi\)
0.999549 0.0300351i \(-0.00956192\pi\)
\(294\) 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 −0.956864 0.290537i \(-0.906166\pi\)
0.730044 + 0.683400i \(0.239499\pi\)
\(312\) 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 \(-0.997978\pi\)
0.494489 0.869184i \(-0.335355\pi\)
\(318\) 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 −0.903475 0.428640i \(-0.858993\pi\)
0.822951 + 0.568112i \(0.192326\pi\)
\(348\) 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 0.823343 0.567545i \(-0.192107\pi\)
−0.903179 + 0.429263i \(0.858773\pi\)
\(354\) 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 \(-0.533662\pi\)
−0.105556 + 0.994413i \(0.533662\pi\)
\(360\) 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 −0.965028 0.262147i \(-0.915569\pi\)
0.709540 + 0.704665i \(0.248903\pi\)
\(384\) 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 \(-0.997414\pi\)
0.492947 0.870059i \(-0.335920\pi\)
\(390\) 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 −0.976050 0.217545i \(-0.930195\pi\)
0.676425 + 0.736512i \(0.263528\pi\)
\(402\) 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 −0.783394 0.621525i \(-0.786513\pi\)
0.929954 + 0.367677i \(0.119847\pi\)
\(420\) 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 \(-0.382346\pi\)
0.361262 + 0.932464i \(0.382346\pi\)
\(432\) 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 0.966591 0.256323i \(-0.0825112\pi\)
−0.705278 + 0.708931i \(0.749178\pi\)
\(444\) 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 \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 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 \(0.0900675\pi\)
−0.238328 + 0.971185i \(0.576599\pi\)
\(462\) 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 \(-0.294543\pi\)
0.601568 + 0.798821i \(0.294543\pi\)
\(468\) 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 \(0.0943068\pi\)
−0.225372 + 0.974273i \(0.572360\pi\)
\(480\) 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 −0.746438 0.665455i \(-0.768237\pi\)
0.949520 + 0.313707i \(0.101571\pi\)
\(492\) 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 \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 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 −0.594675 0.803966i \(-0.702719\pi\)
0.993593 + 0.113020i \(0.0360525\pi\)
\(510\) 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 \(-0.393430\pi\)
0.328581 + 0.944476i \(0.393430\pi\)
\(522\) 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 \(-0.654336\pi\)
−0.466085 + 0.884740i \(0.654336\pi\)
\(558\) 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 −0.905088 0.425223i \(-0.860196\pi\)
0.820798 + 0.571218i \(0.193529\pi\)
\(564\) 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 \(0.0498003\pi\)
−0.358954 + 0.933355i \(0.616866\pi\)
\(570\) 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 0.973552 0.228464i \(-0.0733702\pi\)
−0.684632 + 0.728889i \(0.740037\pi\)
\(588\) 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 \(-0.559161\pi\)
−0.184793 + 0.982777i \(0.559161\pi\)
\(594\) 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 \(0.352647\pi\)
−0.998160 + 0.0606393i \(0.980686\pi\)
\(600\) 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 −0.690021 0.723789i \(-0.742399\pi\)
0.971830 + 0.235681i \(0.0757321\pi\)
\(618\) 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 0.562779 0.826608i \(-0.309732\pi\)
−0.997253 + 0.0740768i \(0.976399\pi\)
\(642\) 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 \(-0.809160\pi\)
−0.825595 + 0.564263i \(0.809160\pi\)
\(648\) 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 \(0.366356\pi\)
−0.994623 + 0.103558i \(0.966977\pi\)
\(654\) 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 0.982730 0.185043i \(-0.0592425\pi\)
−0.651617 + 0.758548i \(0.725909\pi\)
\(660\) 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 \(0.00697196\pi\)
−0.480913 + 0.876768i \(0.659695\pi\)
\(678\) 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 \(-0.444916\pi\)
0.172188 + 0.985064i \(0.444916\pi\)
\(684\) 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 \(-0.376717\pi\)
0.377695 + 0.925930i \(0.376717\pi\)
\(702\) 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 \(-0.311029\pi\)
0.559406 + 0.828894i \(0.311029\pi\)
\(720\) 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 −0.991798 0.127815i \(-0.959204\pi\)
0.606590 + 0.795015i \(0.292537\pi\)
\(744\) 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 −0.993572 0.113203i \(-0.963889\pi\)
0.594822 + 0.803857i \(0.297222\pi\)
\(762\) 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 \(-0.611000\pi\)
−0.341691 + 0.939812i \(0.611000\pi\)
\(774\) 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