Properties

Label 1134.2.t.c.1025.1
Level $1134$
Weight $2$
Character 1134.1025
Analytic conductor $9.055$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.t (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 378)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1025.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1134.1025
Dual form 1134.2.t.c.593.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +(0.500000 - 2.59808i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +(0.500000 - 2.59808i) q^{7} -1.00000i q^{8} +(1.50000 + 0.866025i) q^{10} +(-1.73205 + 2.00000i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 3.00000i) q^{17} +(6.00000 - 3.46410i) q^{19} +(-0.866025 - 1.50000i) q^{20} -6.00000i q^{23} -2.00000 q^{25} +(2.50000 - 0.866025i) q^{28} +(-7.79423 + 4.50000i) q^{29} +(-3.00000 + 1.73205i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.00000 - 1.73205i) q^{34} +(-0.866025 + 4.50000i) q^{35} +(-2.00000 - 3.46410i) q^{37} -6.92820 q^{38} +1.73205i q^{40} +(1.73205 - 3.00000i) q^{41} +(4.00000 + 6.92820i) q^{43} +(-3.00000 + 5.19615i) q^{46} +(-1.73205 + 3.00000i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(1.73205 + 1.00000i) q^{50} +(-2.59808 - 1.50000i) q^{53} +(-2.59808 - 0.500000i) q^{56} +9.00000 q^{58} +(-6.06218 - 10.5000i) q^{59} +(-3.00000 - 1.73205i) q^{61} +3.46410 q^{62} -1.00000 q^{64} +(-7.00000 - 12.1244i) q^{67} -3.46410 q^{68} +(3.00000 - 3.46410i) q^{70} +6.00000i q^{71} +(-10.5000 - 6.06218i) q^{73} +4.00000i q^{74} +(6.00000 + 3.46410i) q^{76} +(-5.50000 + 9.52628i) q^{79} +(0.866025 - 1.50000i) q^{80} +(-3.00000 + 1.73205i) q^{82} +(-8.66025 - 15.0000i) q^{83} +(3.00000 - 5.19615i) q^{85} -8.00000i q^{86} +(-5.19615 - 9.00000i) q^{89} +(5.19615 - 3.00000i) q^{92} +(3.00000 - 1.73205i) q^{94} +(-10.3923 + 6.00000i) q^{95} +(6.00000 - 3.46410i) q^{97} +(4.33013 + 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} + 2 q^{7} + O(q^{10}) \) \( 4 q + 2 q^{4} + 2 q^{7} + 6 q^{10} - 2 q^{16} + 24 q^{19} - 8 q^{25} + 10 q^{28} - 12 q^{31} + 12 q^{34} - 8 q^{37} + 16 q^{43} - 12 q^{46} - 26 q^{49} + 36 q^{58} - 12 q^{61} - 4 q^{64} - 28 q^{67} + 12 q^{70} - 42 q^{73} + 24 q^{76} - 22 q^{79} - 12 q^{82} + 12 q^{85} + 12 q^{94} + 24 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −1.73205 −0.774597 −0.387298 0.921954i \(-0.626592\pi\)
−0.387298 + 0.921954i \(0.626592\pi\)
\(6\) 0 0
\(7\) 0.500000 2.59808i 0.188982 0.981981i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.50000 + 0.866025i 0.474342 + 0.273861i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(14\) −1.73205 + 2.00000i −0.462910 + 0.534522i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.73205 + 3.00000i −0.420084 + 0.727607i −0.995947 0.0899392i \(-0.971333\pi\)
0.575863 + 0.817546i \(0.304666\pi\)
\(18\) 0 0
\(19\) 6.00000 3.46410i 1.37649 0.794719i 0.384759 0.923017i \(-0.374285\pi\)
0.991736 + 0.128298i \(0.0409513\pi\)
\(20\) −0.866025 1.50000i −0.193649 0.335410i
\(21\) 0 0
\(22\) 0 0
\(23\) 6.00000i 1.25109i −0.780189 0.625543i \(-0.784877\pi\)
0.780189 0.625543i \(-0.215123\pi\)
\(24\) 0 0
\(25\) −2.00000 −0.400000
\(26\) 0 0
\(27\) 0 0
\(28\) 2.50000 0.866025i 0.472456 0.163663i
\(29\) −7.79423 + 4.50000i −1.44735 + 0.835629i −0.998323 0.0578882i \(-0.981563\pi\)
−0.449029 + 0.893517i \(0.648230\pi\)
\(30\) 0 0
\(31\) −3.00000 + 1.73205i −0.538816 + 0.311086i −0.744599 0.667512i \(-0.767359\pi\)
0.205783 + 0.978598i \(0.434026\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 3.00000 1.73205i 0.514496 0.297044i
\(35\) −0.866025 + 4.50000i −0.146385 + 0.760639i
\(36\) 0 0
\(37\) −2.00000 3.46410i −0.328798 0.569495i 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) −6.92820 −1.12390
\(39\) 0 0
\(40\) 1.73205i 0.273861i
\(41\) 1.73205 3.00000i 0.270501 0.468521i −0.698489 0.715621i \(-0.746144\pi\)
0.968990 + 0.247099i \(0.0794774\pi\)
\(42\) 0 0
\(43\) 4.00000 + 6.92820i 0.609994 + 1.05654i 0.991241 + 0.132068i \(0.0421616\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) −1.73205 + 3.00000i −0.252646 + 0.437595i −0.964253 0.264982i \(-0.914634\pi\)
0.711608 + 0.702577i \(0.247967\pi\)
\(48\) 0 0
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) 1.73205 + 1.00000i 0.244949 + 0.141421i
\(51\) 0 0
\(52\) 0 0
\(53\) −2.59808 1.50000i −0.356873 0.206041i 0.310835 0.950464i \(-0.399391\pi\)
−0.667708 + 0.744423i \(0.732725\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.59808 0.500000i −0.347183 0.0668153i
\(57\) 0 0
\(58\) 9.00000 1.18176
\(59\) −6.06218 10.5000i −0.789228 1.36698i −0.926440 0.376442i \(-0.877147\pi\)
0.137212 0.990542i \(-0.456186\pi\)
\(60\) 0 0
\(61\) −3.00000 1.73205i −0.384111 0.221766i 0.295495 0.955344i \(-0.404516\pi\)
−0.679605 + 0.733578i \(0.737849\pi\)
\(62\) 3.46410 0.439941
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −7.00000 12.1244i −0.855186 1.48123i −0.876472 0.481452i \(-0.840109\pi\)
0.0212861 0.999773i \(-0.493224\pi\)
\(68\) −3.46410 −0.420084
\(69\) 0 0
\(70\) 3.00000 3.46410i 0.358569 0.414039i
\(71\) 6.00000i 0.712069i 0.934473 + 0.356034i \(0.115871\pi\)
−0.934473 + 0.356034i \(0.884129\pi\)
\(72\) 0 0
\(73\) −10.5000 6.06218i −1.22893 0.709524i −0.262126 0.965034i \(-0.584423\pi\)
−0.966807 + 0.255510i \(0.917757\pi\)
\(74\) 4.00000i 0.464991i
\(75\) 0 0
\(76\) 6.00000 + 3.46410i 0.688247 + 0.397360i
\(77\) 0 0
\(78\) 0 0
\(79\) −5.50000 + 9.52628i −0.618798 + 1.07179i 0.370907 + 0.928670i \(0.379047\pi\)
−0.989705 + 0.143120i \(0.954286\pi\)
\(80\) 0.866025 1.50000i 0.0968246 0.167705i
\(81\) 0 0
\(82\) −3.00000 + 1.73205i −0.331295 + 0.191273i
\(83\) −8.66025 15.0000i −0.950586 1.64646i −0.744160 0.668002i \(-0.767150\pi\)
−0.206427 0.978462i \(-0.566184\pi\)
\(84\) 0 0
\(85\) 3.00000 5.19615i 0.325396 0.563602i
\(86\) 8.00000i 0.862662i
\(87\) 0 0
\(88\) 0 0
\(89\) −5.19615 9.00000i −0.550791 0.953998i −0.998218 0.0596775i \(-0.980993\pi\)
0.447427 0.894321i \(-0.352341\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 5.19615 3.00000i 0.541736 0.312772i
\(93\) 0 0
\(94\) 3.00000 1.73205i 0.309426 0.178647i
\(95\) −10.3923 + 6.00000i −1.06623 + 0.615587i
\(96\) 0 0
\(97\) 6.00000 3.46410i 0.609208 0.351726i −0.163448 0.986552i \(-0.552261\pi\)
0.772655 + 0.634826i \(0.218928\pi\)
\(98\) 4.33013 + 5.50000i 0.437409 + 0.555584i
\(99\) 0 0
\(100\) −1.00000 1.73205i −0.100000 0.173205i
\(101\) −5.19615 −0.517036 −0.258518 0.966006i \(-0.583234\pi\)
−0.258518 + 0.966006i \(0.583234\pi\)
\(102\) 0 0
\(103\) 10.3923i 1.02398i 0.858990 + 0.511992i \(0.171092\pi\)
−0.858990 + 0.511992i \(0.828908\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 1.50000 + 2.59808i 0.145693 + 0.252347i
\(107\) 2.59808 1.50000i 0.251166 0.145010i −0.369132 0.929377i \(-0.620345\pi\)
0.620298 + 0.784366i \(0.287012\pi\)
\(108\) 0 0
\(109\) −8.00000 + 13.8564i −0.766261 + 1.32720i 0.173316 + 0.984866i \(0.444552\pi\)
−0.939577 + 0.342337i \(0.888782\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.00000 + 1.73205i 0.188982 + 0.163663i
\(113\) 15.5885 + 9.00000i 1.46644 + 0.846649i 0.999295 0.0375328i \(-0.0119499\pi\)
0.467143 + 0.884182i \(0.345283\pi\)
\(114\) 0 0
\(115\) 10.3923i 0.969087i
\(116\) −7.79423 4.50000i −0.723676 0.417815i
\(117\) 0 0
\(118\) 12.1244i 1.11614i
\(119\) 6.92820 + 6.00000i 0.635107 + 0.550019i
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) 1.73205 + 3.00000i 0.156813 + 0.271607i
\(123\) 0 0
\(124\) −3.00000 1.73205i −0.269408 0.155543i
\(125\) 12.1244 1.08444
\(126\) 0 0
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) −10.3923 −0.907980 −0.453990 0.891007i \(-0.650000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(132\) 0 0
\(133\) −6.00000 17.3205i −0.520266 1.50188i
\(134\) 14.0000i 1.20942i
\(135\) 0 0
\(136\) 3.00000 + 1.73205i 0.257248 + 0.148522i
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) −9.00000 5.19615i −0.763370 0.440732i 0.0671344 0.997744i \(-0.478614\pi\)
−0.830504 + 0.557012i \(0.811948\pi\)
\(140\) −4.33013 + 1.50000i −0.365963 + 0.126773i
\(141\) 0 0
\(142\) 3.00000 5.19615i 0.251754 0.436051i
\(143\) 0 0
\(144\) 0 0
\(145\) 13.5000 7.79423i 1.12111 0.647275i
\(146\) 6.06218 + 10.5000i 0.501709 + 0.868986i
\(147\) 0 0
\(148\) 2.00000 3.46410i 0.164399 0.284747i
\(149\) 15.0000i 1.22885i 0.788976 + 0.614424i \(0.210612\pi\)
−0.788976 + 0.614424i \(0.789388\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) −3.46410 6.00000i −0.280976 0.486664i
\(153\) 0 0
\(154\) 0 0
\(155\) 5.19615 3.00000i 0.417365 0.240966i
\(156\) 0 0
\(157\) −9.00000 + 5.19615i −0.718278 + 0.414698i −0.814119 0.580699i \(-0.802779\pi\)
0.0958404 + 0.995397i \(0.469446\pi\)
\(158\) 9.52628 5.50000i 0.757870 0.437557i
\(159\) 0 0
\(160\) −1.50000 + 0.866025i −0.118585 + 0.0684653i
\(161\) −15.5885 3.00000i −1.22854 0.236433i
\(162\) 0 0
\(163\) −1.00000 1.73205i −0.0783260 0.135665i 0.824202 0.566296i \(-0.191624\pi\)
−0.902528 + 0.430632i \(0.858291\pi\)
\(164\) 3.46410 0.270501
\(165\) 0 0
\(166\) 17.3205i 1.34433i
\(167\) 8.66025 15.0000i 0.670151 1.16073i −0.307711 0.951480i \(-0.599563\pi\)
0.977861 0.209255i \(-0.0671038\pi\)
\(168\) 0 0
\(169\) −6.50000 11.2583i −0.500000 0.866025i
\(170\) −5.19615 + 3.00000i −0.398527 + 0.230089i
\(171\) 0 0
\(172\) −4.00000 + 6.92820i −0.304997 + 0.528271i
\(173\) −2.59808 + 4.50000i −0.197528 + 0.342129i −0.947726 0.319084i \(-0.896625\pi\)
0.750198 + 0.661213i \(0.229958\pi\)
\(174\) 0 0
\(175\) −1.00000 + 5.19615i −0.0755929 + 0.392792i
\(176\) 0 0
\(177\) 0 0
\(178\) 10.3923i 0.778936i
\(179\) 12.9904 + 7.50000i 0.970947 + 0.560576i 0.899525 0.436870i \(-0.143913\pi\)
0.0714220 + 0.997446i \(0.477246\pi\)
\(180\) 0 0
\(181\) 17.3205i 1.28742i −0.765268 0.643712i \(-0.777394\pi\)
0.765268 0.643712i \(-0.222606\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −6.00000 −0.442326
\(185\) 3.46410 + 6.00000i 0.254686 + 0.441129i
\(186\) 0 0
\(187\) 0 0
\(188\) −3.46410 −0.252646
\(189\) 0 0
\(190\) 12.0000 0.870572
\(191\) 5.19615 + 3.00000i 0.375980 + 0.217072i 0.676068 0.736839i \(-0.263683\pi\)
−0.300088 + 0.953912i \(0.597016\pi\)
\(192\) 0 0
\(193\) −5.00000 8.66025i −0.359908 0.623379i 0.628037 0.778183i \(-0.283859\pi\)
−0.987945 + 0.154805i \(0.950525\pi\)
\(194\) −6.92820 −0.497416
\(195\) 0 0
\(196\) −1.00000 6.92820i −0.0714286 0.494872i
\(197\) 3.00000i 0.213741i −0.994273 0.106871i \(-0.965917\pi\)
0.994273 0.106871i \(-0.0340831\pi\)
\(198\) 0 0
\(199\) 7.50000 + 4.33013i 0.531661 + 0.306955i 0.741693 0.670740i \(-0.234023\pi\)
−0.210032 + 0.977695i \(0.567357\pi\)
\(200\) 2.00000i 0.141421i
\(201\) 0 0
\(202\) 4.50000 + 2.59808i 0.316619 + 0.182800i
\(203\) 7.79423 + 22.5000i 0.547048 + 1.57919i
\(204\) 0 0
\(205\) −3.00000 + 5.19615i −0.209529 + 0.362915i
\(206\) 5.19615 9.00000i 0.362033 0.627060i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −8.00000 + 13.8564i −0.550743 + 0.953914i 0.447478 + 0.894295i \(0.352322\pi\)
−0.998221 + 0.0596196i \(0.981011\pi\)
\(212\) 3.00000i 0.206041i
\(213\) 0 0
\(214\) −3.00000 −0.205076
\(215\) −6.92820 12.0000i −0.472500 0.818393i
\(216\) 0 0
\(217\) 3.00000 + 8.66025i 0.203653 + 0.587896i
\(218\) 13.8564 8.00000i 0.938474 0.541828i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 13.5000 7.79423i 0.904027 0.521940i 0.0255224 0.999674i \(-0.491875\pi\)
0.878504 + 0.477734i \(0.158542\pi\)
\(224\) −0.866025 2.50000i −0.0578638 0.167038i
\(225\) 0 0
\(226\) −9.00000 15.5885i −0.598671 1.03693i
\(227\) 25.9808 1.72440 0.862202 0.506565i \(-0.169085\pi\)
0.862202 + 0.506565i \(0.169085\pi\)
\(228\) 0 0
\(229\) 3.46410i 0.228914i −0.993428 0.114457i \(-0.963487\pi\)
0.993428 0.114457i \(-0.0365129\pi\)
\(230\) 5.19615 9.00000i 0.342624 0.593442i
\(231\) 0 0
\(232\) 4.50000 + 7.79423i 0.295439 + 0.511716i
\(233\) 25.9808 15.0000i 1.70206 0.982683i 0.758380 0.651813i \(-0.225991\pi\)
0.943676 0.330870i \(-0.107342\pi\)
\(234\) 0 0
\(235\) 3.00000 5.19615i 0.195698 0.338960i
\(236\) 6.06218 10.5000i 0.394614 0.683492i
\(237\) 0 0
\(238\) −3.00000 8.66025i −0.194461 0.561361i
\(239\) 20.7846 + 12.0000i 1.34444 + 0.776215i 0.987456 0.157893i \(-0.0504702\pi\)
0.356988 + 0.934109i \(0.383804\pi\)
\(240\) 0 0
\(241\) 1.73205i 0.111571i −0.998443 0.0557856i \(-0.982234\pi\)
0.998443 0.0557856i \(-0.0177663\pi\)
\(242\) −9.52628 5.50000i −0.612372 0.353553i
\(243\) 0 0
\(244\) 3.46410i 0.221766i
\(245\) 11.2583 + 4.50000i 0.719268 + 0.287494i
\(246\) 0 0
\(247\) 0 0
\(248\) 1.73205 + 3.00000i 0.109985 + 0.190500i
\(249\) 0 0
\(250\) −10.5000 6.06218i −0.664078 0.383406i
\(251\) 8.66025 0.546630 0.273315 0.961925i \(-0.411880\pi\)
0.273315 + 0.961925i \(0.411880\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 6.06218 + 3.50000i 0.380375 + 0.219610i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −20.7846 −1.29651 −0.648254 0.761424i \(-0.724501\pi\)
−0.648254 + 0.761424i \(0.724501\pi\)
\(258\) 0 0
\(259\) −10.0000 + 3.46410i −0.621370 + 0.215249i
\(260\) 0 0
\(261\) 0 0
\(262\) 9.00000 + 5.19615i 0.556022 + 0.321019i
\(263\) 18.0000i 1.10993i −0.831875 0.554964i \(-0.812732\pi\)
0.831875 0.554964i \(-0.187268\pi\)
\(264\) 0 0
\(265\) 4.50000 + 2.59808i 0.276433 + 0.159599i
\(266\) −3.46410 + 18.0000i −0.212398 + 1.10365i
\(267\) 0 0
\(268\) 7.00000 12.1244i 0.427593 0.740613i
\(269\) −0.866025 + 1.50000i −0.0528025 + 0.0914566i −0.891219 0.453574i \(-0.850149\pi\)
0.838416 + 0.545031i \(0.183482\pi\)
\(270\) 0 0
\(271\) 10.5000 6.06218i 0.637830 0.368251i −0.145948 0.989292i \(-0.546623\pi\)
0.783778 + 0.621041i \(0.213290\pi\)
\(272\) −1.73205 3.00000i −0.105021 0.181902i
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 5.19615 + 9.00000i 0.311645 + 0.539784i
\(279\) 0 0
\(280\) 4.50000 + 0.866025i 0.268926 + 0.0517549i
\(281\) 15.5885 9.00000i 0.929929 0.536895i 0.0431402 0.999069i \(-0.486264\pi\)
0.886789 + 0.462174i \(0.152930\pi\)
\(282\) 0 0
\(283\) −6.00000 + 3.46410i −0.356663 + 0.205919i −0.667616 0.744506i \(-0.732685\pi\)
0.310953 + 0.950425i \(0.399352\pi\)
\(284\) −5.19615 + 3.00000i −0.308335 + 0.178017i
\(285\) 0 0
\(286\) 0 0
\(287\) −6.92820 6.00000i −0.408959 0.354169i
\(288\) 0 0
\(289\) 2.50000 + 4.33013i 0.147059 + 0.254713i
\(290\) −15.5885 −0.915386
\(291\) 0 0
\(292\) 12.1244i 0.709524i
\(293\) 14.7224 25.5000i 0.860094 1.48973i −0.0117441 0.999931i \(-0.503738\pi\)
0.871838 0.489795i \(-0.162928\pi\)
\(294\) 0 0
\(295\) 10.5000 + 18.1865i 0.611334 + 1.05886i
\(296\) −3.46410 + 2.00000i −0.201347 + 0.116248i
\(297\) 0 0
\(298\) 7.50000 12.9904i 0.434463 0.752513i
\(299\) 0 0
\(300\) 0 0
\(301\) 20.0000 6.92820i 1.15278 0.399335i
\(302\) 6.92820 + 4.00000i 0.398673 + 0.230174i
\(303\) 0 0
\(304\) 6.92820i 0.397360i
\(305\) 5.19615 + 3.00000i 0.297531 + 0.171780i
\(306\) 0 0
\(307\) 6.92820i 0.395413i 0.980261 + 0.197707i \(0.0633494\pi\)
−0.980261 + 0.197707i \(0.936651\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −6.00000 −0.340777
\(311\) −6.92820 12.0000i −0.392862 0.680458i 0.599963 0.800027i \(-0.295182\pi\)
−0.992826 + 0.119570i \(0.961848\pi\)
\(312\) 0 0
\(313\) 19.5000 + 11.2583i 1.10221 + 0.636358i 0.936799 0.349867i \(-0.113773\pi\)
0.165406 + 0.986226i \(0.447107\pi\)
\(314\) 10.3923 0.586472
\(315\) 0 0
\(316\) −11.0000 −0.618798
\(317\) −5.19615 3.00000i −0.291845 0.168497i 0.346929 0.937892i \(-0.387225\pi\)
−0.638774 + 0.769395i \(0.720558\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.73205 0.0968246
\(321\) 0 0
\(322\) 12.0000 + 10.3923i 0.668734 + 0.579141i
\(323\) 24.0000i 1.33540i
\(324\) 0 0
\(325\) 0 0
\(326\) 2.00000i 0.110770i
\(327\) 0 0
\(328\) −3.00000 1.73205i −0.165647 0.0956365i
\(329\) 6.92820 + 6.00000i 0.381964 + 0.330791i
\(330\) 0 0
\(331\) −5.00000 + 8.66025i −0.274825 + 0.476011i −0.970091 0.242742i \(-0.921953\pi\)
0.695266 + 0.718752i \(0.255287\pi\)
\(332\) 8.66025 15.0000i 0.475293 0.823232i
\(333\) 0 0
\(334\) −15.0000 + 8.66025i −0.820763 + 0.473868i
\(335\) 12.1244 + 21.0000i 0.662424 + 1.14735i
\(336\) 0 0
\(337\) 11.5000 19.9186i 0.626445 1.08503i −0.361815 0.932250i \(-0.617843\pi\)
0.988260 0.152784i \(-0.0488240\pi\)
\(338\) 13.0000i 0.707107i
\(339\) 0 0
\(340\) 6.00000 0.325396
\(341\) 0 0
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 6.92820 4.00000i 0.373544 0.215666i
\(345\) 0 0
\(346\) 4.50000 2.59808i 0.241921 0.139673i
\(347\) −28.5788 + 16.5000i −1.53419 + 0.885766i −0.535031 + 0.844833i \(0.679700\pi\)
−0.999162 + 0.0409337i \(0.986967\pi\)
\(348\) 0 0
\(349\) 3.00000 1.73205i 0.160586 0.0927146i −0.417553 0.908652i \(-0.637112\pi\)
0.578140 + 0.815938i \(0.303779\pi\)
\(350\) 3.46410 4.00000i 0.185164 0.213809i
\(351\) 0 0
\(352\) 0 0
\(353\) 3.46410 0.184376 0.0921878 0.995742i \(-0.470614\pi\)
0.0921878 + 0.995742i \(0.470614\pi\)
\(354\) 0 0
\(355\) 10.3923i 0.551566i
\(356\) 5.19615 9.00000i 0.275396 0.476999i
\(357\) 0 0
\(358\) −7.50000 12.9904i −0.396387 0.686563i
\(359\) −20.7846 + 12.0000i −1.09697 + 0.633336i −0.935423 0.353529i \(-0.884981\pi\)
−0.161546 + 0.986865i \(0.551648\pi\)
\(360\) 0 0
\(361\) 14.5000 25.1147i 0.763158 1.32183i
\(362\) −8.66025 + 15.0000i −0.455173 + 0.788382i
\(363\) 0 0
\(364\) 0 0
\(365\) 18.1865 + 10.5000i 0.951927 + 0.549595i
\(366\) 0 0
\(367\) 8.66025i 0.452062i 0.974120 + 0.226031i \(0.0725750\pi\)
−0.974120 + 0.226031i \(0.927425\pi\)
\(368\) 5.19615 + 3.00000i 0.270868 + 0.156386i
\(369\) 0 0
\(370\) 6.92820i 0.360180i
\(371\) −5.19615 + 6.00000i −0.269771 + 0.311504i
\(372\) 0 0
\(373\) 14.0000 0.724893 0.362446 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 3.00000 + 1.73205i 0.154713 + 0.0893237i
\(377\) 0 0
\(378\) 0 0
\(379\) −14.0000 −0.719132 −0.359566 0.933120i \(-0.617075\pi\)
−0.359566 + 0.933120i \(0.617075\pi\)
\(380\) −10.3923 6.00000i −0.533114 0.307794i
\(381\) 0 0
\(382\) −3.00000 5.19615i −0.153493 0.265858i
\(383\) 17.3205 0.885037 0.442518 0.896759i \(-0.354085\pi\)
0.442518 + 0.896759i \(0.354085\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10.0000i 0.508987i
\(387\) 0 0
\(388\) 6.00000 + 3.46410i 0.304604 + 0.175863i
\(389\) 21.0000i 1.06474i 0.846511 + 0.532371i \(0.178699\pi\)
−0.846511 + 0.532371i \(0.821301\pi\)
\(390\) 0 0
\(391\) 18.0000 + 10.3923i 0.910299 + 0.525561i
\(392\) −2.59808 + 6.50000i −0.131223 + 0.328300i
\(393\) 0 0
\(394\) −1.50000 + 2.59808i −0.0755689 + 0.130889i
\(395\) 9.52628 16.5000i 0.479319 0.830205i
\(396\) 0 0
\(397\) −24.0000 + 13.8564i −1.20453 + 0.695433i −0.961558 0.274601i \(-0.911454\pi\)
−0.242967 + 0.970034i \(0.578121\pi\)
\(398\) −4.33013 7.50000i −0.217050 0.375941i
\(399\) 0 0
\(400\) 1.00000 1.73205i 0.0500000 0.0866025i
\(401\) 6.00000i 0.299626i −0.988714 0.149813i \(-0.952133\pi\)
0.988714 0.149813i \(-0.0478671\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −2.59808 4.50000i −0.129259 0.223883i
\(405\) 0 0
\(406\) 4.50000 23.3827i 0.223331 1.16046i
\(407\) 0 0
\(408\) 0 0
\(409\) 13.5000 7.79423i 0.667532 0.385400i −0.127609 0.991825i \(-0.540730\pi\)
0.795141 + 0.606425i \(0.207397\pi\)
\(410\) 5.19615 3.00000i 0.256620 0.148159i
\(411\) 0 0
\(412\) −9.00000 + 5.19615i −0.443398 + 0.255996i
\(413\) −30.3109 + 10.5000i −1.49150 + 0.516671i
\(414\) 0 0
\(415\) 15.0000 + 25.9808i 0.736321 + 1.27535i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.73205 + 3.00000i −0.0846162 + 0.146560i −0.905228 0.424927i \(-0.860300\pi\)
0.820611 + 0.571487i \(0.193633\pi\)
\(420\) 0 0
\(421\) −16.0000 27.7128i −0.779792 1.35064i −0.932061 0.362301i \(-0.881991\pi\)
0.152269 0.988339i \(-0.451342\pi\)
\(422\) 13.8564 8.00000i 0.674519 0.389434i
\(423\) 0 0
\(424\) −1.50000 + 2.59808i −0.0728464 + 0.126174i
\(425\) 3.46410 6.00000i 0.168034 0.291043i
\(426\) 0 0
\(427\) −6.00000 + 6.92820i −0.290360 + 0.335279i
\(428\) 2.59808 + 1.50000i 0.125583 + 0.0725052i
\(429\) 0 0
\(430\) 13.8564i 0.668215i
\(431\) −31.1769 18.0000i −1.50174 0.867029i −0.999998 0.00201168i \(-0.999360\pi\)
−0.501741 0.865018i \(-0.667307\pi\)
\(432\) 0 0
\(433\) 1.73205i 0.0832370i −0.999134 0.0416185i \(-0.986749\pi\)
0.999134 0.0416185i \(-0.0132514\pi\)
\(434\) 1.73205 9.00000i 0.0831411 0.432014i
\(435\) 0 0
\(436\) −16.0000 −0.766261
\(437\) −20.7846 36.0000i −0.994263 1.72211i
\(438\) 0 0
\(439\) 27.0000 + 15.5885i 1.28864 + 0.743996i 0.978412 0.206666i \(-0.0662612\pi\)
0.310228 + 0.950662i \(0.399595\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −7.79423 4.50000i −0.370315 0.213801i 0.303281 0.952901i \(-0.401918\pi\)
−0.673596 + 0.739100i \(0.735251\pi\)
\(444\) 0 0
\(445\) 9.00000 + 15.5885i 0.426641 + 0.738964i
\(446\) −15.5885 −0.738135
\(447\) 0 0
\(448\) −0.500000 + 2.59808i −0.0236228 + 0.122748i
\(449\) 6.00000i 0.283158i 0.989927 + 0.141579i \(0.0452178\pi\)
−0.989927 + 0.141579i \(0.954782\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 18.0000i 0.846649i
\(453\) 0 0
\(454\) −22.5000 12.9904i −1.05598 0.609669i
\(455\) 0 0
\(456\) 0 0
\(457\) 20.5000 35.5070i 0.958950 1.66095i 0.233890 0.972263i \(-0.424854\pi\)
0.725059 0.688686i \(-0.241812\pi\)
\(458\) −1.73205 + 3.00000i −0.0809334 + 0.140181i
\(459\) 0 0
\(460\) −9.00000 + 5.19615i −0.419627 + 0.242272i
\(461\) −11.2583 19.5000i −0.524353 0.908206i −0.999598 0.0283522i \(-0.990974\pi\)
0.475245 0.879853i \(-0.342359\pi\)
\(462\) 0 0
\(463\) −11.5000 + 19.9186i −0.534450 + 0.925695i 0.464739 + 0.885448i \(0.346148\pi\)
−0.999190 + 0.0402476i \(0.987185\pi\)
\(464\) 9.00000i 0.417815i
\(465\) 0 0
\(466\) −30.0000 −1.38972
\(467\) −2.59808 4.50000i −0.120225 0.208235i 0.799632 0.600491i \(-0.205028\pi\)
−0.919856 + 0.392256i \(0.871695\pi\)
\(468\) 0 0
\(469\) −35.0000 + 12.1244i −1.61615 + 0.559851i
\(470\) −5.19615 + 3.00000i −0.239681 + 0.138380i
\(471\) 0 0
\(472\) −10.5000 + 6.06218i −0.483302 + 0.279034i
\(473\) 0 0
\(474\) 0 0
\(475\) −12.0000 + 6.92820i −0.550598 + 0.317888i
\(476\) −1.73205 + 9.00000i −0.0793884 + 0.412514i
\(477\) 0 0
\(478\) −12.0000 20.7846i −0.548867 0.950666i
\(479\) −13.8564 −0.633115 −0.316558 0.948573i \(-0.602527\pi\)
−0.316558 + 0.948573i \(0.602527\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.866025 + 1.50000i −0.0394464 + 0.0683231i
\(483\) 0 0
\(484\) 5.50000 + 9.52628i 0.250000 + 0.433013i
\(485\) −10.3923 + 6.00000i −0.471890 + 0.272446i
\(486\) 0 0
\(487\) −0.500000 + 0.866025i −0.0226572 + 0.0392434i −0.877132 0.480250i \(-0.840546\pi\)
0.854475 + 0.519493i \(0.173879\pi\)
\(488\) −1.73205 + 3.00000i −0.0784063 + 0.135804i
\(489\) 0 0
\(490\) −7.50000 9.52628i −0.338815 0.430353i
\(491\) −2.59808 1.50000i −0.117250 0.0676941i 0.440228 0.897886i \(-0.354898\pi\)
−0.557478 + 0.830192i \(0.688231\pi\)
\(492\) 0 0
\(493\) 31.1769i 1.40414i
\(494\) 0 0
\(495\) 0 0
\(496\) 3.46410i 0.155543i
\(497\) 15.5885 + 3.00000i 0.699238 + 0.134568i
\(498\) 0 0
\(499\) −14.0000 −0.626726 −0.313363 0.949633i \(-0.601456\pi\)
−0.313363 + 0.949633i \(0.601456\pi\)
\(500\) 6.06218 + 10.5000i 0.271109 + 0.469574i
\(501\) 0 0
\(502\) −7.50000 4.33013i −0.334741 0.193263i
\(503\) 27.7128 1.23565 0.617827 0.786314i \(-0.288013\pi\)
0.617827 + 0.786314i \(0.288013\pi\)
\(504\) 0 0
\(505\) 9.00000 0.400495
\(506\) 0 0
\(507\) 0 0
\(508\) −3.50000 6.06218i −0.155287 0.268966i
\(509\) −34.6410 −1.53544 −0.767718 0.640788i \(-0.778608\pi\)
−0.767718 + 0.640788i \(0.778608\pi\)
\(510\) 0 0
\(511\) −21.0000 + 24.2487i −0.928985 + 1.07270i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 18.0000 + 10.3923i 0.793946 + 0.458385i
\(515\) 18.0000i 0.793175i
\(516\) 0 0
\(517\) 0 0
\(518\) 10.3923 + 2.00000i 0.456612 + 0.0878750i
\(519\) 0 0
\(520\) 0 0
\(521\) 1.73205 3.00000i 0.0758825 0.131432i −0.825587 0.564275i \(-0.809156\pi\)
0.901470 + 0.432842i \(0.142489\pi\)
\(522\) 0 0
\(523\) 18.0000 10.3923i 0.787085 0.454424i −0.0518503 0.998655i \(-0.516512\pi\)
0.838935 + 0.544231i \(0.183179\pi\)
\(524\) −5.19615 9.00000i −0.226995 0.393167i
\(525\) 0 0
\(526\) −9.00000 + 15.5885i −0.392419 + 0.679689i
\(527\) 12.0000i 0.522728i
\(528\) 0 0
\(529\) −13.0000 −0.565217
\(530\) −2.59808 4.50000i −0.112853 0.195468i
\(531\) 0 0
\(532\) 12.0000 13.8564i 0.520266 0.600751i
\(533\) 0 0
\(534\) 0 0
\(535\) −4.50000 + 2.59808i −0.194552 + 0.112325i
\(536\) −12.1244 + 7.00000i −0.523692 + 0.302354i
\(537\) 0 0
\(538\) 1.50000 0.866025i 0.0646696 0.0373370i
\(539\) 0 0
\(540\) 0 0
\(541\) 17.0000 + 29.4449i 0.730887 + 1.26593i 0.956504 + 0.291718i \(0.0942267\pi\)
−0.225617 + 0.974216i \(0.572440\pi\)
\(542\) −12.1244 −0.520786
\(543\) 0 0
\(544\) 3.46410i 0.148522i
\(545\) 13.8564 24.0000i 0.593543 1.02805i
\(546\) 0 0
\(547\) −4.00000 6.92820i −0.171028 0.296229i 0.767752 0.640747i \(-0.221375\pi\)
−0.938779 + 0.344519i \(0.888042\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −31.1769 + 54.0000i −1.32818 + 2.30048i
\(552\) 0 0
\(553\) 22.0000 + 19.0526i 0.935535 + 0.810197i
\(554\) −6.92820 4.00000i −0.294351 0.169944i
\(555\) 0 0
\(556\) 10.3923i 0.440732i
\(557\) 15.5885 + 9.00000i 0.660504 + 0.381342i 0.792469 0.609912i \(-0.208795\pi\)
−0.131965 + 0.991254i \(0.542129\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −3.46410 3.00000i −0.146385 0.126773i
\(561\) 0 0
\(562\) −18.0000 −0.759284
\(563\) 2.59808 + 4.50000i 0.109496 + 0.189652i 0.915566 0.402167i \(-0.131743\pi\)
−0.806070 + 0.591820i \(0.798410\pi\)
\(564\) 0 0
\(565\) −27.0000 15.5885i −1.13590 0.655811i
\(566\) 6.92820 0.291214
\(567\) 0 0
\(568\) 6.00000 0.251754
\(569\) −36.3731 21.0000i −1.52484 0.880366i −0.999567 0.0294311i \(-0.990630\pi\)
−0.525271 0.850935i \(-0.676036\pi\)
\(570\) 0 0
\(571\) 20.0000 + 34.6410i 0.836974 + 1.44968i 0.892413 + 0.451219i \(0.149011\pi\)
−0.0554391 + 0.998462i \(0.517656\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 3.00000 + 8.66025i 0.125218 + 0.361472i
\(575\) 12.0000i 0.500435i
\(576\) 0 0
\(577\) −13.5000 7.79423i −0.562012 0.324478i 0.191940 0.981407i \(-0.438522\pi\)
−0.753953 + 0.656929i \(0.771855\pi\)
\(578\) 5.00000i 0.207973i
\(579\) 0 0
\(580\) 13.5000 + 7.79423i 0.560557 + 0.323638i
\(581\) −43.3013 + 15.0000i −1.79644 + 0.622305i
\(582\) 0 0
\(583\) 0 0
\(584\) −6.06218 + 10.5000i −0.250855 + 0.434493i
\(585\) 0 0
\(586\) −25.5000 + 14.7224i −1.05340 + 0.608178i
\(587\) −18.1865 31.5000i −0.750639 1.30014i −0.947514 0.319716i \(-0.896413\pi\)
0.196875 0.980429i \(-0.436921\pi\)
\(588\) 0 0
\(589\) −12.0000 + 20.7846i −0.494451 + 0.856415i
\(590\) 21.0000i 0.864556i
\(591\) 0 0
\(592\) 4.00000 0.164399
\(593\) 12.1244 + 21.0000i 0.497888 + 0.862367i 0.999997 0.00243746i \(-0.000775869\pi\)
−0.502109 + 0.864804i \(0.667443\pi\)
\(594\) 0 0
\(595\) −12.0000 10.3923i −0.491952 0.426043i
\(596\) −12.9904 + 7.50000i −0.532107 + 0.307212i
\(597\) 0 0
\(598\) 0 0
\(599\) 20.7846 12.0000i 0.849236 0.490307i −0.0111569 0.999938i \(-0.503551\pi\)
0.860393 + 0.509631i \(0.170218\pi\)
\(600\) 0 0
\(601\) 1.50000 0.866025i 0.0611863 0.0353259i −0.469095 0.883148i \(-0.655420\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) −20.7846 4.00000i −0.847117 0.163028i
\(603\) 0 0
\(604\) −4.00000 6.92820i −0.162758 0.281905i
\(605\) −19.0526 −0.774597
\(606\) 0 0
\(607\) 32.9090i 1.33573i −0.744281 0.667867i \(-0.767208\pi\)
0.744281 0.667867i \(-0.232792\pi\)
\(608\) 3.46410 6.00000i 0.140488 0.243332i
\(609\) 0 0
\(610\) −3.00000 5.19615i −0.121466 0.210386i
\(611\) 0 0
\(612\) 0 0
\(613\) −4.00000 + 6.92820i −0.161558 + 0.279827i −0.935428 0.353518i \(-0.884985\pi\)
0.773869 + 0.633345i \(0.218319\pi\)
\(614\) 3.46410 6.00000i 0.139800 0.242140i
\(615\) 0 0
\(616\) 0 0
\(617\) 5.19615 + 3.00000i 0.209189 + 0.120775i 0.600935 0.799298i \(-0.294795\pi\)
−0.391745 + 0.920074i \(0.628129\pi\)
\(618\) 0 0
\(619\) 20.7846i 0.835404i −0.908584 0.417702i \(-0.862836\pi\)
0.908584 0.417702i \(-0.137164\pi\)
\(620\) 5.19615 + 3.00000i 0.208683 + 0.120483i
\(621\) 0 0
\(622\) 13.8564i 0.555591i
\(623\) −25.9808 + 9.00000i −1.04090 + 0.360577i
\(624\) 0 0
\(625\) −11.0000 −0.440000
\(626\) −11.2583 19.5000i −0.449973 0.779377i
\(627\) 0 0
\(628\) −9.00000 5.19615i −0.359139 0.207349i
\(629\) 13.8564 0.552491
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 9.52628 + 5.50000i 0.378935 + 0.218778i
\(633\) 0 0
\(634\) 3.00000 + 5.19615i 0.119145 + 0.206366i
\(635\) 12.1244 0.481140
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −1.50000 0.866025i −0.0592927 0.0342327i
\(641\) 12.0000i 0.473972i 0.971513 + 0.236986i \(0.0761595\pi\)
−0.971513 + 0.236986i \(0.923841\pi\)
\(642\) 0 0
\(643\) 24.0000 + 13.8564i 0.946468 + 0.546443i 0.891982 0.452071i \(-0.149315\pi\)
0.0544858 + 0.998515i \(0.482648\pi\)
\(644\) −5.19615 15.0000i −0.204757 0.591083i
\(645\) 0 0
\(646\) 12.0000 20.7846i 0.472134 0.817760i
\(647\) −5.19615 + 9.00000i −0.204282 + 0.353827i −0.949904 0.312543i \(-0.898819\pi\)
0.745622 + 0.666369i \(0.232153\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 1.00000 1.73205i 0.0391630 0.0678323i
\(653\) 15.0000i 0.586995i −0.955960 0.293498i \(-0.905181\pi\)
0.955960 0.293498i \(-0.0948193\pi\)
\(654\) 0 0
\(655\) 18.0000 0.703318
\(656\) 1.73205 + 3.00000i 0.0676252 + 0.117130i
\(657\) 0 0
\(658\) −3.00000 8.66025i −0.116952 0.337612i
\(659\) −23.3827 + 13.5000i −0.910860 + 0.525885i −0.880708 0.473660i \(-0.842933\pi\)
−0.0301523 + 0.999545i \(0.509599\pi\)
\(660\) 0 0
\(661\) 12.0000 6.92820i 0.466746 0.269476i −0.248131 0.968727i \(-0.579816\pi\)
0.714877 + 0.699251i \(0.246483\pi\)
\(662\) 8.66025 5.00000i 0.336590 0.194331i
\(663\) 0 0
\(664\) −15.0000 + 8.66025i −0.582113 + 0.336083i
\(665\) 10.3923 + 30.0000i 0.402996 + 1.16335i
\(666\) 0 0
\(667\) 27.0000 + 46.7654i 1.04544 + 1.81076i
\(668\) 17.3205 0.670151
\(669\) 0 0
\(670\) 24.2487i 0.936809i
\(671\) 0 0
\(672\) 0 0
\(673\) 2.50000 + 4.33013i 0.0963679 + 0.166914i 0.910179 0.414216i \(-0.135944\pi\)
−0.813811 + 0.581130i \(0.802611\pi\)
\(674\) −19.9186 + 11.5000i −0.767235 + 0.442963i
\(675\) 0 0
\(676\) 6.50000 11.2583i 0.250000 0.433013i
\(677\) 12.9904 22.5000i 0.499261 0.864745i −0.500739 0.865598i \(-0.666938\pi\)
1.00000 0.000853228i \(0.000271591\pi\)
\(678\) 0 0
\(679\) −6.00000 17.3205i −0.230259 0.664700i
\(680\) −5.19615 3.00000i −0.199263 0.115045i
\(681\) 0 0
\(682\) 0 0
\(683\) 7.79423 + 4.50000i 0.298238 + 0.172188i 0.641651 0.766997i \(-0.278250\pi\)
−0.343413 + 0.939184i \(0.611583\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 16.4545 8.50000i 0.628235 0.324532i
\(687\) 0 0
\(688\) −8.00000 −0.304997
\(689\) 0 0
\(690\) 0 0
\(691\) 24.0000 + 13.8564i 0.913003 + 0.527123i 0.881396 0.472378i \(-0.156604\pi\)
0.0316069 + 0.999500i \(0.489938\pi\)
\(692\) −5.19615 −0.197528
\(693\) 0 0
\(694\) 33.0000 1.25266
\(695\) 15.5885 + 9.00000i 0.591304 + 0.341389i
\(696\) 0 0
\(697\) 6.00000 + 10.3923i 0.227266 + 0.393637i
\(698\) −3.46410 −0.131118
\(699\) 0 0
\(700\) −5.00000 + 1.73205i −0.188982 + 0.0654654i
\(701\) 27.0000i 1.01978i −0.860241 0.509888i \(-0.829687\pi\)
0.860241 0.509888i \(-0.170313\pi\)
\(702\) 0 0
\(703\) −24.0000 13.8564i −0.905177 0.522604i
\(704\) 0 0
\(705\) 0 0
\(706\) −3.00000 1.73205i −0.112906 0.0651866i
\(707\) −2.59808 + 13.5000i −0.0977107 + 0.507720i
\(708\) 0 0
\(709\) −14.0000 + 24.2487i −0.525781 + 0.910679i 0.473768 + 0.880650i \(0.342894\pi\)
−0.999549 + 0.0300298i \(0.990440\pi\)
\(710\) −5.19615 + 9.00000i −0.195008 + 0.337764i
\(711\) 0 0
\(712\) −9.00000 + 5.19615i −0.337289 + 0.194734i
\(713\) 10.3923 + 18.0000i 0.389195 + 0.674105i
\(714\) 0 0
\(715\) 0 0
\(716\) 15.0000i 0.560576i
\(717\) 0 0
\(718\) 24.0000 0.895672
\(719\) −24.2487 42.0000i −0.904324 1.56634i −0.821822 0.569745i \(-0.807042\pi\)
−0.0825027 0.996591i \(-0.526291\pi\)
\(720\) 0 0
\(721\) 27.0000 + 5.19615i 1.00553 + 0.193515i
\(722\) −25.1147 + 14.5000i −0.934674 + 0.539634i
\(723\) 0 0
\(724\) 15.0000 8.66025i 0.557471 0.321856i
\(725\) 15.5885 9.00000i 0.578941 0.334252i
\(726\) 0 0
\(727\) −10.5000 + 6.06218i −0.389423 + 0.224834i −0.681910 0.731436i \(-0.738851\pi\)
0.292487 + 0.956270i \(0.405517\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −10.5000 18.1865i −0.388622 0.673114i
\(731\) −27.7128 −1.02500
\(732\) 0 0
\(733\) 6.92820i 0.255899i −0.991781 0.127950i \(-0.959160\pi\)
0.991781 0.127950i \(-0.0408395\pi\)
\(734\) 4.33013 7.50000i 0.159828 0.276830i
\(735\) 0 0
\(736\) −3.00000 5.19615i −0.110581 0.191533i
\(737\) 0 0
\(738\) 0 0
\(739\) 5.00000 8.66025i 0.183928 0.318573i −0.759287 0.650756i \(-0.774452\pi\)
0.943215 + 0.332184i \(0.107785\pi\)
\(740\) −3.46410 + 6.00000i −0.127343 + 0.220564i
\(741\) 0 0
\(742\) 7.50000 2.59808i 0.275334 0.0953784i
\(743\) 31.1769 + 18.0000i 1.14377 + 0.660356i 0.947361 0.320166i \(-0.103739\pi\)
0.196409 + 0.980522i \(0.437072\pi\)
\(744\) 0 0
\(745\) 25.9808i 0.951861i
\(746\) −12.1244 7.00000i −0.443904 0.256288i
\(747\) 0 0
\(748\) 0 0
\(749\) −2.59808 7.50000i −0.0949316 0.274044i
\(750\) 0 0
\(751\) 7.00000 0.255434 0.127717 0.991811i \(-0.459235\pi\)
0.127717 + 0.991811i \(0.459235\pi\)
\(752\) −1.73205 3.00000i −0.0631614 0.109399i
\(753\) 0 0
\(754\) 0 0
\(755\) 13.8564 0.504286
\(756\) 0 0
\(757\) −38.0000 −1.38113 −0.690567 0.723269i \(-0.742639\pi\)
−0.690567 + 0.723269i \(0.742639\pi\)
\(758\) 12.1244 + 7.00000i 0.440376 + 0.254251i
\(759\) 0 0
\(760\) 6.00000 + 10.3923i 0.217643 + 0.376969i
\(761\) −34.6410 −1.25574 −0.627868 0.778320i \(-0.716072\pi\)
−0.627868 + 0.778320i \(0.716072\pi\)
\(762\) 0 0
\(763\) 32.0000 + 27.7128i 1.15848 + 1.00327i
\(764\) 6.00000i 0.217072i
\(765\) 0 0
\(766\) −15.0000 8.66025i −0.541972 0.312908i
\(767\) 0 0
\(768\) 0 0
\(769\) −42.0000 24.2487i −1.51456 0.874431i −0.999854 0.0170631i \(-0.994568\pi\)
−0.514704 0.857368i \(-0.672098\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 5.00000 8.66025i 0.179954 0.311689i
\(773\) −6.92820 + 12.0000i −0.249190 + 0.431610i −0.963301 0.268422i \(-0.913498\pi\)
0.714111 + 0.700032i \(0.246831\pi\)
\(774\) 0 0
\(775\) 6.00000 3.46410i 0.215526 0.124434i
\(776\) −3.46410 6.00000i −0.124354 0.215387i
\(777\) 0 0
\(778\) 10.5000 18.1865i 0.376443 0.652019i
\(779\) 24.0000i 0.859889i
\(780\) 0 0
\(781\) 0 0
\(782\) −10.3923 18.0000i −0.371628 0.643679i
\(783\) 0 0
\(784\) 5.50000 4.33013i 0.196429 0.154647i
\(785\) 15.5885 9.00000i 0.556376 0.321224i
\(786\) 0 0
\(787\) −3.00000 + 1.73205i −0.106938 + 0.0617409i −0.552515 0.833503i \(-0.686332\pi\)
0.445577 + 0.895244i \(0.352999\pi\)
\(788\) 2.59808 1.50000i 0.0925526 0.0534353i
\(789\) 0 0
\(790\) −16.5000 + 9.52628i −0.587044 + 0.338930i
\(791\) 31.1769 36.0000i 1.10852 1.28001i
\(792\) 0 0