Properties

Label 1134.2.f.c.379.1
Level $1134$
Weight $2$
Character 1134.379
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 379.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1134.379
Dual form 1134.2.f.c.757.1

$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

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

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 \(-0.238450\pi\)
−0.955901 + 0.293691i \(0.905116\pi\)
\(6\) 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 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0 0
\(13\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(14\) 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 0.913434 0.406986i \(-0.133420\pi\)
−0.809177 + 0.587565i \(0.800087\pi\)
\(24\) 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 \(-0.954452\pi\)
0.618389 + 0.785872i \(0.287786\pi\)
\(30\) 0 0
\(31\) 4.50000 + 7.79423i 0.808224 + 1.39988i 0.914093 + 0.405505i \(0.132904\pi\)
−0.105869 + 0.994380i \(0.533762\pi\)
\(32\) −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 0.967486 + 0.252924i \(0.0813924\pi\)
−0.264704 + 0.964330i \(0.585274\pi\)
\(42\) 0 0
\(43\) 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i \(-0.557309\pi\)
0.941562 0.336840i \(-0.109358\pi\)
\(44\) 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 \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) 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 0.812198 + 0.583382i \(0.198271\pi\)
0.0991242 + 0.995075i \(0.468396\pi\)
\(60\) 0 0
\(61\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) −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 0.999915 0.0130248i \(-0.00414604\pi\)
−0.511237 + 0.859440i \(0.670813\pi\)
\(68\) −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 −0.983967 0.178352i \(-0.942924\pi\)
0.646440 + 0.762964i \(0.276257\pi\)
\(80\) 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 \(-0.762881\pi\)
0.954664 + 0.297686i \(0.0962148\pi\)
\(84\) 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 0.0989899 + 0.995088i \(0.468439\pi\)
−0.911267 + 0.411816i \(0.864894\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) −4.00000 −0.400000
\(101\) 7.00000 12.1244i 0.696526 1.20642i −0.273138 0.961975i \(-0.588061\pi\)
0.969664 0.244443i \(-0.0786053\pi\)
\(102\) 0 0
\(103\) 0.500000 + 0.866025i 0.0492665 + 0.0853320i 0.889607 0.456727i \(-0.150978\pi\)
−0.840341 + 0.542059i \(0.817645\pi\)
\(104\) 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 0.909221 0.416314i \(-0.136678\pi\)
−0.815149 + 0.579252i \(0.803345\pi\)
\(114\) 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 −0.719811 0.694170i \(-0.755772\pi\)
−0.241264 0.970460i \(-0.577562\pi\)
\(132\) 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 0.290424 + 0.956898i \(0.406204\pi\)
−0.973910 + 0.226935i \(0.927130\pi\)
\(138\) 0 0
\(139\) 10.0000 + 17.3205i 0.848189 + 1.46911i 0.882823 + 0.469706i \(0.155640\pi\)
−0.0346338 + 0.999400i \(0.511026\pi\)
\(140\) 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 \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) −5.00000 + 8.66025i −0.406894 + 0.704761i −0.994540 0.104357i \(-0.966722\pi\)
0.587646 + 0.809118i \(0.300055\pi\)
\(152\) −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 0.661094 0.750303i \(-0.270093\pi\)
−0.980329 + 0.197372i \(0.936759\pi\)
\(158\) −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 \(-0.293125\pi\)
−0.992032 + 0.125983i \(0.959791\pi\)
\(168\) 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 \(-0.919068\pi\)
0.701751 + 0.712422i \(0.252402\pi\)
\(174\) 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 −0.806641 0.591041i \(-0.798717\pi\)
0.915177 + 0.403051i \(0.132050\pi\)
\(192\) 0 0
\(193\) 5.00000 + 8.66025i 0.359908 + 0.623379i 0.987945 0.154805i \(-0.0494748\pi\)
−0.628037 + 0.778183i \(0.716141\pi\)
\(194\) −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 0.944237 + 0.329266i \(0.106801\pi\)
−0.186966 + 0.982366i \(0.559865\pi\)
\(212\) −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 −0.937509 0.347960i \(-0.886874\pi\)
0.770097 + 0.637927i \(0.220208\pi\)
\(224\) −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 \(-0.897141\pi\)
0.749125 + 0.662428i \(0.230474\pi\)
\(228\) 0 0
\(229\) −14.0000 24.2487i −0.925146 1.60240i −0.791326 0.611394i \(-0.790609\pi\)
−0.133820 0.991006i \(-0.542724\pi\)
\(230\) 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 −0.934109 0.356988i \(-0.883804\pi\)
0.157893 0.987456i \(-0.449530\pi\)
\(240\) 0 0
\(241\) −7.00000 + 12.1244i −0.450910 + 0.780998i −0.998443 0.0557856i \(-0.982234\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) 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 −0.888110 0.459631i \(-0.847982\pi\)
0.0460033 0.998941i \(-0.485352\pi\)
\(258\) 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 −0.336270 0.941766i \(-0.609166\pi\)
0.983728 0.179664i \(-0.0575011\pi\)
\(264\) 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 −0.425684 0.904872i \(-0.639967\pi\)
0.996484 0.0837823i \(-0.0267000\pi\)
\(278\) −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 \(-0.736922\pi\)
0.975741 + 0.218926i \(0.0702554\pi\)
\(282\) 0 0
\(283\) 10.0000 + 17.3205i 0.594438 + 1.02960i 0.993626 + 0.112728i \(0.0359589\pi\)
−0.399188 + 0.916869i \(0.630708\pi\)
\(284\) 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 −0.999549 0.0300351i \(-0.990438\pi\)
0.473763 0.880652i \(-0.342895\pi\)
\(294\) 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 \(-0.0938340\pi\)
−0.730044 + 0.683400i \(0.760501\pi\)
\(312\) 0 0
\(313\) 4.00000 6.92820i 0.226093 0.391605i −0.730554 0.682855i \(-0.760738\pi\)
0.956647 + 0.291250i \(0.0940712\pi\)
\(314\) 8.00000 0.451466
\(315\) 0 0
\(316\) 6.00000 0.337526
\(317\) 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
\(319\) −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 −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) −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 −0.954551 0.298047i \(-0.903665\pi\)
0.219159 0.975689i \(-0.429669\pi\)
\(338\) 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 \(-0.141007\pi\)
−0.822951 + 0.568112i \(0.807674\pi\)
\(348\) 0 0
\(349\) 13.0000 22.5167i 0.695874 1.20529i −0.274011 0.961727i \(-0.588351\pi\)
0.969885 0.243563i \(-0.0783162\pi\)
\(350\) 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 \(-0.807893\pi\)
0.903179 + 0.429263i \(0.141227\pi\)
\(354\) 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 −0.104399 + 0.994535i \(0.533292\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) −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 0.997697 0.0678218i \(-0.0216049\pi\)
−0.557584 + 0.830120i \(0.688272\pi\)
\(374\) −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 \(-0.0844305\pi\)
−0.709540 + 0.704665i \(0.751097\pi\)
\(384\) 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 −0.492947 0.870059i \(-0.664080\pi\)
0.999967 0.00812520i \(-0.00258636\pi\)
\(390\) 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 \(-0.0698049\pi\)
−0.676425 + 0.736512i \(0.736472\pi\)
\(402\) 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 0.962757 0.270367i \(-0.0871450\pi\)
−0.715523 + 0.698589i \(0.753812\pi\)
\(410\) 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 \(-0.213487\pi\)
−0.929954 + 0.367677i \(0.880153\pi\)
\(420\) 0 0
\(421\) 13.5000 23.3827i 0.657950 1.13960i −0.323196 0.946332i \(-0.604757\pi\)
0.981146 0.193270i \(-0.0619094\pi\)
\(422\) −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 0.423556 + 0.905870i \(0.360782\pi\)
−0.996284 + 0.0861252i \(0.972552\pi\)
\(440\) 5.00000 0.238366
\(441\) 0 0
\(442\) 0 0
\(443\) −5.50000 + 9.52628i −0.261313 + 0.452607i −0.966591 0.256323i \(-0.917489\pi\)
0.705278 + 0.708931i \(0.250822\pi\)
\(444\) 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 −0.977051 0.213006i \(-0.931675\pi\)
0.672994 + 0.739648i \(0.265008\pi\)
\(458\) 28.0000 1.30835
\(459\) 0 0
\(460\) −1.00000 −0.0466252
\(461\) −15.5000 + 26.8468i −0.721907 + 1.25038i 0.238328 + 0.971185i \(0.423401\pi\)
−0.960235 + 0.279195i \(0.909933\pi\)
\(462\) 0 0
\(463\) 7.00000 + 12.1244i 0.325318 + 0.563467i 0.981577 0.191069i \(-0.0611955\pi\)
−0.656259 + 0.754536i \(0.727862\pi\)
\(464\) −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 0.225372 + 0.974273i \(0.427640\pi\)
−0.956431 + 0.291958i \(0.905693\pi\)
\(480\) 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 \(-0.231763\pi\)
−0.949520 + 0.313707i \(0.898429\pi\)
\(492\) 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 0.732137 0.681157i \(-0.238523\pi\)
−0.955968 + 0.293471i \(0.905190\pi\)
\(500\) 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 0.594675 0.803966i \(-0.297281\pi\)
−0.993593 + 0.113020i \(0.963948\pi\)
\(510\) 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 −0.965313 0.261095i \(-0.915916\pi\)
0.708772 + 0.705438i \(0.249250\pi\)
\(548\) 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 0.905088 0.425223i \(-0.139804\pi\)
−0.820798 + 0.571218i \(0.806471\pi\)
\(564\) 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 0.358954 + 0.933355i \(0.383134\pi\)
−0.987786 + 0.155815i \(0.950200\pi\)
\(570\) 0 0
\(571\) −9.00000 15.5885i −0.376638 0.652357i 0.613933 0.789359i \(-0.289587\pi\)
−0.990571 + 0.137002i \(0.956253\pi\)
\(572\) 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 \(-0.926630\pi\)
0.684632 + 0.728889i \(0.259963\pi\)
\(588\) 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 0.998160 + 0.0606393i \(0.0193139\pi\)
−0.446565 + 0.894751i \(0.647353\pi\)
\(600\) 0 0
\(601\) −4.00000 + 6.92820i −0.163163 + 0.282607i −0.936002 0.351996i \(-0.885503\pi\)
0.772838 + 0.634603i \(0.218836\pi\)
\(602\) 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 0.718186 0.695852i \(-0.244973\pi\)
−0.961718 + 0.274041i \(0.911640\pi\)
\(608\) 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 \(-0.257601\pi\)
−0.971830 + 0.235681i \(0.924268\pi\)
\(618\) 0 0
\(619\) 5.50000 9.52628i 0.221064 0.382893i −0.734068 0.679076i \(-0.762380\pi\)
0.955131 + 0.296183i \(0.0957138\pi\)
\(620\) −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 \(-0.690268\pi\)
0.997253 + 0.0740768i \(0.0236010\pi\)
\(642\) 0 0
\(643\) 6.50000 + 11.2583i 0.256335 + 0.443985i 0.965257 0.261301i \(-0.0841516\pi\)
−0.708922 + 0.705287i \(0.750818\pi\)
\(644\) −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 0.994623 + 0.103558i \(0.0330227\pi\)
−0.407628 + 0.913148i \(0.633644\pi\)
\(654\) 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 \(-0.940757\pi\)
0.651617 + 0.758548i \(0.274091\pi\)
\(660\) 0 0
\(661\) −14.0000 24.2487i −0.544537 0.943166i −0.998636 0.0522143i \(-0.983372\pi\)
0.454099 0.890951i \(-0.349961\pi\)
\(662\) 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 0.498886 + 0.866668i \(0.333743\pi\)
−0.999999 + 0.00128586i \(0.999591\pi\)
\(674\) 27.0000 1.04000
\(675\) 0 0
\(676\) −13.0000 −0.500000
\(677\) −13.5000 + 23.3827i −0.518847 + 0.898670i 0.480913 + 0.876768i \(0.340305\pi\)
−0.999760 + 0.0219013i \(0.993028\pi\)
\(678\) 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 −0.825473 0.564441i \(-0.809092\pi\)
0.901557 + 0.432660i \(0.142425\pi\)
\(692\) 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 −0.529943 0.848034i \(-0.677787\pi\)
0.999390 + 0.0349269i \(0.0111198\pi\)
\(710\) −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 −0.400362 0.916357i \(-0.631116\pi\)
0.993770 0.111454i \(-0.0355509\pi\)
\(728\) 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 0.982986 0.183679i \(-0.0588007\pi\)
−0.650564 + 0.759452i \(0.725467\pi\)
\(734\) −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 \(-0.0407965\pi\)
−0.606590 + 0.795015i \(0.707463\pi\)
\(744\) 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 0.653783 0.756682i \(-0.273181\pi\)
−0.982197 + 0.187851i \(0.939848\pi\)
\(752\) −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 \(-0.0361109\pi\)
−0.594822 + 0.803857i \(0.702778\pi\)
\(762\) 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 −0.960512 0.278240i \(-0.910249\pi\)
0.239293 0.970947i \(-0.423084\pi\)
\(770\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(788\) 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