Properties

Label 1134.2.t.c.1025.2
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 1025.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1134.1025
Dual form 1134.2.t.c.593.2

$q$-expansion

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

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 \(-0.373408\pi\)
0.387298 + 0.921954i \(0.373408\pi\)
\(6\) 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 −0.575863 0.817546i \(-0.695334\pi\)
0.995947 + 0.0899392i \(0.0286673\pi\)
\(18\) 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 \(0.215123\pi\)
−0.780189 + 0.625543i \(0.784877\pi\)
\(24\) 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 0.449029 0.893517i \(-0.351770\pi\)
0.998323 + 0.0578882i \(0.0184367\pi\)
\(30\) 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 −0.968990 0.247099i \(-0.920523\pi\)
0.698489 + 0.715621i \(0.253856\pi\)
\(42\) 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 −0.711608 0.702577i \(-0.752033\pi\)
0.964253 + 0.264982i \(0.0853660\pi\)
\(48\) 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 0.667708 0.744423i \(-0.267275\pi\)
−0.310835 + 0.950464i \(0.600609\pi\)
\(54\) 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 \(0.122853\pi\)
−0.137212 + 0.990542i \(0.543814\pi\)
\(60\) 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 \(-0.884129\pi\)
0.934473 0.356034i \(-0.115871\pi\)
\(72\) 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 \(0.232850\pi\)
0.206427 + 0.978462i \(0.433816\pi\)
\(84\) 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 \(0.0190072\pi\)
−0.447427 + 0.894321i \(0.647659\pi\)
\(90\) 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 \(-0.416766\pi\)
0.258518 + 0.966006i \(0.416766\pi\)
\(102\) 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 −0.620298 0.784366i \(-0.712988\pi\)
0.369132 + 0.929377i \(0.379655\pi\)
\(108\) 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 −0.467143 0.884182i \(-0.654717\pi\)
−0.999295 + 0.0375328i \(0.988050\pi\)
\(114\) 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 \(-0.350000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(132\) 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 \(-0.789388\pi\)
0.788976 0.614424i \(-0.210612\pi\)
\(150\) 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 \(0.400437\pi\)
−0.977861 + 0.209255i \(0.932896\pi\)
\(168\) 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 −0.750198 0.661213i \(-0.770042\pi\)
0.947726 + 0.319084i \(0.103375\pi\)
\(174\) 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 −0.0714220 0.997446i \(-0.522754\pi\)
−0.899525 + 0.436870i \(0.856087\pi\)
\(180\) 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 0.300088 0.953912i \(-0.402984\pi\)
−0.676068 + 0.736839i \(0.736317\pi\)
\(192\) 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 \(0.0340831\pi\)
−0.994273 + 0.106871i \(0.965917\pi\)
\(198\) 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 \(-0.830915\pi\)
−0.862202 + 0.506565i \(0.830915\pi\)
\(228\) 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 \(0.774009\pi\)
−0.943676 + 0.330870i \(0.892658\pi\)
\(234\) 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 −0.356988 0.934109i \(-0.616196\pi\)
−0.987456 + 0.157893i \(0.949530\pi\)
\(240\) 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 \(-0.588120\pi\)
−0.273315 + 0.961925i \(0.588120\pi\)
\(252\) 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 \(-0.275499\pi\)
0.648254 + 0.761424i \(0.275499\pi\)
\(258\) 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 \(0.187268\pi\)
−0.831875 + 0.554964i \(0.812732\pi\)
\(264\) 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 −0.838416 0.545031i \(-0.816518\pi\)
0.891219 + 0.453574i \(0.149851\pi\)
\(270\) 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 −0.886789 0.462174i \(-0.847070\pi\)
−0.0431402 + 0.999069i \(0.513736\pi\)
\(282\) 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 \(0.496262\pi\)
−0.871838 + 0.489795i \(0.837072\pi\)
\(294\) 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 0.992826 0.119570i \(-0.0381515\pi\)
−0.599963 + 0.800027i \(0.704818\pi\)
\(312\) 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 0.638774 0.769395i \(-0.279442\pi\)
−0.346929 + 0.937892i \(0.612775\pi\)
\(318\) 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 \(-0.320300\pi\)
0.999162 0.0409337i \(-0.0130332\pi\)
\(348\) 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 \(-0.529386\pi\)
−0.0921878 + 0.995742i \(0.529386\pi\)
\(354\) 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 0.161546 0.986865i \(-0.448352\pi\)
0.935423 + 0.353529i \(0.115019\pi\)
\(360\) 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 \(-0.645915\pi\)
−0.442518 + 0.896759i \(0.645915\pi\)
\(384\) 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 \(-0.821301\pi\)
0.846511 0.532371i \(-0.178699\pi\)
\(390\) 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 \(0.0478671\pi\)
−0.988714 + 0.149813i \(0.952133\pi\)
\(402\) 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 −0.820611 0.571487i \(-0.806367\pi\)
0.905228 + 0.424927i \(0.139700\pi\)
\(420\) 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 \(0.000640338\pi\)
0.501741 + 0.865018i \(0.332693\pi\)
\(432\) 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 0.673596 0.739100i \(-0.264749\pi\)
−0.303281 + 0.952901i \(0.598082\pi\)
\(444\) 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 \(-0.954782\pi\)
0.989927 0.141579i \(-0.0452178\pi\)
\(450\) 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 \(0.00902599\pi\)
−0.475245 + 0.879853i \(0.657641\pi\)
\(462\) 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 0.919856 0.392256i \(-0.128305\pi\)
−0.799632 + 0.600491i \(0.794972\pi\)
\(468\) 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 \(-0.397473\pi\)
0.316558 + 0.948573i \(0.397473\pi\)
\(480\) 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 0.557478 0.830192i \(-0.311769\pi\)
−0.440228 + 0.897886i \(0.645102\pi\)
\(492\) 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 \(-0.711987\pi\)
−0.617827 + 0.786314i \(0.711987\pi\)
\(504\) 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 \(-0.221392\pi\)
0.767718 + 0.640788i \(0.221392\pi\)
\(510\) 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 −0.901470 0.432842i \(-0.857511\pi\)
0.825587 + 0.564275i \(0.190844\pi\)
\(522\) 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 0.131965 0.991254i \(-0.457871\pi\)
−0.792469 + 0.609912i \(0.791205\pi\)
\(558\) 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 0.806070 0.591820i \(-0.201590\pi\)
−0.915566 + 0.402167i \(0.868257\pi\)
\(564\) 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 \(0.00936956\pi\)
0.525271 + 0.850935i \(0.323964\pi\)
\(570\) 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 \(0.103587\pi\)
−0.196875 + 0.980429i \(0.563079\pi\)
\(588\) 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 0.502109 0.864804i \(-0.332557\pi\)
−0.999997 + 0.00243746i \(0.999224\pi\)
\(594\) 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 −0.860393 0.509631i \(-0.829782\pi\)
0.0111569 + 0.999938i \(0.496449\pi\)
\(600\) 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 0.391745 0.920074i \(-0.371871\pi\)
−0.600935 + 0.799298i \(0.705205\pi\)
\(618\) 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 \(-0.923841\pi\)
0.971513 0.236986i \(-0.0761595\pi\)
\(642\) 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 −0.745622 0.666369i \(-0.767847\pi\)
0.949904 + 0.312543i \(0.101181\pi\)
\(648\) 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 \(0.0948193\pi\)
−0.955960 + 0.293498i \(0.905181\pi\)
\(654\) 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 0.0301523 0.999545i \(-0.490401\pi\)
0.880708 + 0.473660i \(0.157067\pi\)
\(660\) 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 −1.00000 0.000853228i \(-0.999728\pi\)
0.500739 + 0.865598i \(0.333062\pi\)
\(678\) 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 0.343413 0.939184i \(-0.388417\pi\)
−0.641651 + 0.766997i \(0.721750\pi\)
\(684\) 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 \(0.170313\pi\)
−0.860241 + 0.509888i \(0.829687\pi\)
\(702\) 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 \(0.192958\pi\)
0.0825027 + 0.996591i \(0.473709\pi\)
\(720\) 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 −0.196409 0.980522i \(-0.562928\pi\)
−0.947361 + 0.320166i \(0.896261\pi\)
\(744\) 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 \(-0.283928\pi\)
0.627868 + 0.778320i \(0.283928\pi\)
\(762\) 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 −0.714111 0.700032i \(-0.753169\pi\)
0.963301 + 0.268422i \(0.0865023\pi\)
\(774\) 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
\(793\) 0