Properties

Label 1386.2.k.t.991.1
Level $1386$
Weight $2$
Character 1386.991
Analytic conductor $11.067$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1386.991
Dual form 1386.2.k.t.793.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} +(-2.62132 + 0.358719i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} +(-2.62132 + 0.358719i) q^{7} -1.00000 q^{8} +(1.70711 - 2.95680i) q^{10} +(0.500000 - 0.866025i) q^{11} +1.82843 q^{13} +(-1.62132 - 2.09077i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.82843 + 6.63103i) q^{17} +(1.70711 + 2.95680i) q^{19} +3.41421 q^{20} +1.00000 q^{22} +(1.12132 + 1.94218i) q^{23} +(-3.32843 + 5.76500i) q^{25} +(0.914214 + 1.58346i) q^{26} +(1.00000 - 2.44949i) q^{28} +8.65685 q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} -7.65685 q^{34} +(5.53553 + 7.13834i) q^{35} +(3.29289 + 5.70346i) q^{37} +(-1.70711 + 2.95680i) q^{38} +(1.70711 + 2.95680i) q^{40} +2.58579 q^{41} +5.65685 q^{43} +(0.500000 + 0.866025i) q^{44} +(-1.12132 + 1.94218i) q^{46} +(3.24264 + 5.61642i) q^{47} +(6.74264 - 1.88064i) q^{49} -6.65685 q^{50} +(-0.914214 + 1.58346i) q^{52} +(-5.94975 + 10.3053i) q^{53} -3.41421 q^{55} +(2.62132 - 0.358719i) q^{56} +(4.32843 + 7.49706i) q^{58} +(-4.20711 + 7.28692i) q^{59} +(-3.08579 - 5.34474i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-3.12132 - 5.40629i) q^{65} +(-5.62132 + 9.73641i) q^{67} +(-3.82843 - 6.63103i) q^{68} +(-3.41421 + 8.36308i) q^{70} -3.07107 q^{71} +(3.29289 - 5.70346i) q^{73} +(-3.29289 + 5.70346i) q^{74} -3.41421 q^{76} +(-1.00000 + 2.44949i) q^{77} +(2.37868 + 4.11999i) q^{79} +(-1.70711 + 2.95680i) q^{80} +(1.29289 + 2.23936i) q^{82} -16.1421 q^{83} +26.1421 q^{85} +(2.82843 + 4.89898i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-2.24264 - 3.88437i) q^{89} +(-4.79289 + 0.655892i) q^{91} -2.24264 q^{92} +(-3.24264 + 5.61642i) q^{94} +(5.82843 - 10.0951i) q^{95} +1.82843 q^{97} +(5.00000 + 4.89898i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 2q^{4} - 4q^{5} - 2q^{7} - 4q^{8} + O(q^{10}) \) \( 4q + 2q^{2} - 2q^{4} - 4q^{5} - 2q^{7} - 4q^{8} + 4q^{10} + 2q^{11} - 4q^{13} + 2q^{14} - 2q^{16} - 4q^{17} + 4q^{19} + 8q^{20} + 4q^{22} - 4q^{23} - 2q^{25} - 2q^{26} + 4q^{28} + 12q^{29} + 8q^{31} + 2q^{32} - 8q^{34} + 8q^{35} + 16q^{37} - 4q^{38} + 4q^{40} + 16q^{41} + 2q^{44} + 4q^{46} - 4q^{47} + 10q^{49} - 4q^{50} + 2q^{52} - 4q^{53} - 8q^{55} + 2q^{56} + 6q^{58} - 14q^{59} - 18q^{61} + 16q^{62} + 4q^{64} - 4q^{65} - 14q^{67} - 4q^{68} - 8q^{70} + 16q^{71} + 16q^{73} - 16q^{74} - 8q^{76} - 4q^{77} + 18q^{79} - 4q^{80} + 8q^{82} - 8q^{83} + 48q^{85} - 2q^{88} + 8q^{89} - 22q^{91} + 8q^{92} + 4q^{94} + 12q^{95} - 4q^{97} + 20q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) −1.70711 2.95680i −0.763441 1.32232i −0.941067 0.338221i \(-0.890175\pi\)
0.177625 0.984098i \(-0.443158\pi\)
\(6\) 0 0
\(7\) −2.62132 + 0.358719i −0.990766 + 0.135583i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.70711 2.95680i 0.539835 0.935021i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 0 0
\(13\) 1.82843 0.507114 0.253557 0.967320i \(-0.418399\pi\)
0.253557 + 0.967320i \(0.418399\pi\)
\(14\) −1.62132 2.09077i −0.433316 0.558782i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.82843 + 6.63103i −0.928530 + 1.60826i −0.142747 + 0.989759i \(0.545593\pi\)
−0.785783 + 0.618502i \(0.787740\pi\)
\(18\) 0 0
\(19\) 1.70711 + 2.95680i 0.391637 + 0.678335i 0.992666 0.120892i \(-0.0385755\pi\)
−0.601028 + 0.799228i \(0.705242\pi\)
\(20\) 3.41421 0.763441
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 1.12132 + 1.94218i 0.233811 + 0.404973i 0.958927 0.283654i \(-0.0915468\pi\)
−0.725115 + 0.688628i \(0.758213\pi\)
\(24\) 0 0
\(25\) −3.32843 + 5.76500i −0.665685 + 1.15300i
\(26\) 0.914214 + 1.58346i 0.179292 + 0.310543i
\(27\) 0 0
\(28\) 1.00000 2.44949i 0.188982 0.462910i
\(29\) 8.65685 1.60754 0.803769 0.594942i \(-0.202825\pi\)
0.803769 + 0.594942i \(0.202825\pi\)
\(30\) 0 0
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −7.65685 −1.31314
\(35\) 5.53553 + 7.13834i 0.935676 + 1.20660i
\(36\) 0 0
\(37\) 3.29289 + 5.70346i 0.541348 + 0.937643i 0.998827 + 0.0484222i \(0.0154193\pi\)
−0.457479 + 0.889221i \(0.651247\pi\)
\(38\) −1.70711 + 2.95680i −0.276929 + 0.479656i
\(39\) 0 0
\(40\) 1.70711 + 2.95680i 0.269917 + 0.467510i
\(41\) 2.58579 0.403832 0.201916 0.979403i \(-0.435283\pi\)
0.201916 + 0.979403i \(0.435283\pi\)
\(42\) 0 0
\(43\) 5.65685 0.862662 0.431331 0.902194i \(-0.358044\pi\)
0.431331 + 0.902194i \(0.358044\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −1.12132 + 1.94218i −0.165330 + 0.286359i
\(47\) 3.24264 + 5.61642i 0.472988 + 0.819239i 0.999522 0.0309151i \(-0.00984215\pi\)
−0.526534 + 0.850154i \(0.676509\pi\)
\(48\) 0 0
\(49\) 6.74264 1.88064i 0.963234 0.268662i
\(50\) −6.65685 −0.941421
\(51\) 0 0
\(52\) −0.914214 + 1.58346i −0.126779 + 0.219587i
\(53\) −5.94975 + 10.3053i −0.817261 + 1.41554i 0.0904325 + 0.995903i \(0.471175\pi\)
−0.907693 + 0.419634i \(0.862158\pi\)
\(54\) 0 0
\(55\) −3.41421 −0.460372
\(56\) 2.62132 0.358719i 0.350289 0.0479359i
\(57\) 0 0
\(58\) 4.32843 + 7.49706i 0.568350 + 0.984412i
\(59\) −4.20711 + 7.28692i −0.547719 + 0.948677i 0.450712 + 0.892670i \(0.351170\pi\)
−0.998430 + 0.0560070i \(0.982163\pi\)
\(60\) 0 0
\(61\) −3.08579 5.34474i −0.395094 0.684324i 0.598019 0.801482i \(-0.295955\pi\)
−0.993113 + 0.117158i \(0.962621\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −3.12132 5.40629i −0.387152 0.670567i
\(66\) 0 0
\(67\) −5.62132 + 9.73641i −0.686754 + 1.18949i 0.286129 + 0.958191i \(0.407632\pi\)
−0.972882 + 0.231301i \(0.925702\pi\)
\(68\) −3.82843 6.63103i −0.464265 0.804131i
\(69\) 0 0
\(70\) −3.41421 + 8.36308i −0.408077 + 0.999579i
\(71\) −3.07107 −0.364469 −0.182234 0.983255i \(-0.558333\pi\)
−0.182234 + 0.983255i \(0.558333\pi\)
\(72\) 0 0
\(73\) 3.29289 5.70346i 0.385404 0.667539i −0.606421 0.795144i \(-0.707395\pi\)
0.991825 + 0.127604i \(0.0407288\pi\)
\(74\) −3.29289 + 5.70346i −0.382791 + 0.663014i
\(75\) 0 0
\(76\) −3.41421 −0.391637
\(77\) −1.00000 + 2.44949i −0.113961 + 0.279145i
\(78\) 0 0
\(79\) 2.37868 + 4.11999i 0.267622 + 0.463536i 0.968247 0.249994i \(-0.0804287\pi\)
−0.700625 + 0.713530i \(0.747095\pi\)
\(80\) −1.70711 + 2.95680i −0.190860 + 0.330580i
\(81\) 0 0
\(82\) 1.29289 + 2.23936i 0.142776 + 0.247296i
\(83\) −16.1421 −1.77183 −0.885915 0.463848i \(-0.846468\pi\)
−0.885915 + 0.463848i \(0.846468\pi\)
\(84\) 0 0
\(85\) 26.1421 2.83551
\(86\) 2.82843 + 4.89898i 0.304997 + 0.528271i
\(87\) 0 0
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) −2.24264 3.88437i −0.237719 0.411742i 0.722340 0.691538i \(-0.243067\pi\)
−0.960060 + 0.279796i \(0.909733\pi\)
\(90\) 0 0
\(91\) −4.79289 + 0.655892i −0.502432 + 0.0687562i
\(92\) −2.24264 −0.233811
\(93\) 0 0
\(94\) −3.24264 + 5.61642i −0.334453 + 0.579289i
\(95\) 5.82843 10.0951i 0.597984 1.03574i
\(96\) 0 0
\(97\) 1.82843 0.185649 0.0928243 0.995683i \(-0.470411\pi\)
0.0928243 + 0.995683i \(0.470411\pi\)
\(98\) 5.00000 + 4.89898i 0.505076 + 0.494872i
\(99\) 0 0
\(100\) −3.32843 5.76500i −0.332843 0.576500i
\(101\) 5.91421 10.2437i 0.588486 1.01929i −0.405945 0.913898i \(-0.633057\pi\)
0.994431 0.105390i \(-0.0336092\pi\)
\(102\) 0 0
\(103\) −5.29289 9.16756i −0.521524 0.903307i −0.999687 0.0250350i \(-0.992030\pi\)
0.478162 0.878271i \(-0.341303\pi\)
\(104\) −1.82843 −0.179292
\(105\) 0 0
\(106\) −11.8995 −1.15578
\(107\) 5.53553 + 9.58783i 0.535140 + 0.926890i 0.999157 + 0.0410635i \(0.0130746\pi\)
−0.464016 + 0.885827i \(0.653592\pi\)
\(108\) 0 0
\(109\) 0.242641 0.420266i 0.0232408 0.0402542i −0.854171 0.519992i \(-0.825935\pi\)
0.877412 + 0.479738i \(0.159268\pi\)
\(110\) −1.70711 2.95680i −0.162766 0.281919i
\(111\) 0 0
\(112\) 1.62132 + 2.09077i 0.153200 + 0.197559i
\(113\) 13.8284 1.30087 0.650434 0.759562i \(-0.274587\pi\)
0.650434 + 0.759562i \(0.274587\pi\)
\(114\) 0 0
\(115\) 3.82843 6.63103i 0.357003 0.618347i
\(116\) −4.32843 + 7.49706i −0.401884 + 0.696084i
\(117\) 0 0
\(118\) −8.41421 −0.774591
\(119\) 7.65685 18.7554i 0.701903 1.71930i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 3.08579 5.34474i 0.279374 0.483890i
\(123\) 0 0
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) 5.65685 0.505964
\(126\) 0 0
\(127\) −9.72792 −0.863213 −0.431607 0.902062i \(-0.642053\pi\)
−0.431607 + 0.902062i \(0.642053\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 3.12132 5.40629i 0.273758 0.474163i
\(131\) −1.70711 2.95680i −0.149151 0.258336i 0.781763 0.623575i \(-0.214321\pi\)
−0.930914 + 0.365239i \(0.880987\pi\)
\(132\) 0 0
\(133\) −5.53553 7.13834i −0.479992 0.618972i
\(134\) −11.2426 −0.971216
\(135\) 0 0
\(136\) 3.82843 6.63103i 0.328285 0.568606i
\(137\) −2.67157 + 4.62730i −0.228248 + 0.395337i −0.957289 0.289133i \(-0.906633\pi\)
0.729041 + 0.684470i \(0.239966\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) −8.94975 + 1.22474i −0.756392 + 0.103510i
\(141\) 0 0
\(142\) −1.53553 2.65962i −0.128859 0.223191i
\(143\) 0.914214 1.58346i 0.0764504 0.132416i
\(144\) 0 0
\(145\) −14.7782 25.5965i −1.22726 2.12568i
\(146\) 6.58579 0.545044
\(147\) 0 0
\(148\) −6.58579 −0.541348
\(149\) 3.17157 + 5.49333i 0.259825 + 0.450031i 0.966195 0.257812i \(-0.0830017\pi\)
−0.706370 + 0.707843i \(0.749668\pi\)
\(150\) 0 0
\(151\) −4.86396 + 8.42463i −0.395824 + 0.685586i −0.993206 0.116370i \(-0.962874\pi\)
0.597382 + 0.801957i \(0.296207\pi\)
\(152\) −1.70711 2.95680i −0.138465 0.239828i
\(153\) 0 0
\(154\) −2.62132 + 0.358719i −0.211232 + 0.0289064i
\(155\) −13.6569 −1.09694
\(156\) 0 0
\(157\) −3.17157 + 5.49333i −0.253119 + 0.438415i −0.964383 0.264510i \(-0.914790\pi\)
0.711264 + 0.702925i \(0.248123\pi\)
\(158\) −2.37868 + 4.11999i −0.189238 + 0.327769i
\(159\) 0 0
\(160\) −3.41421 −0.269917
\(161\) −3.63604 4.68885i −0.286560 0.369533i
\(162\) 0 0
\(163\) 7.86396 + 13.6208i 0.615953 + 1.06686i 0.990217 + 0.139539i \(0.0445622\pi\)
−0.374264 + 0.927322i \(0.622104\pi\)
\(164\) −1.29289 + 2.23936i −0.100958 + 0.174864i
\(165\) 0 0
\(166\) −8.07107 13.9795i −0.626436 1.08502i
\(167\) 11.7279 0.907534 0.453767 0.891120i \(-0.350080\pi\)
0.453767 + 0.891120i \(0.350080\pi\)
\(168\) 0 0
\(169\) −9.65685 −0.742835
\(170\) 13.0711 + 22.6398i 1.00251 + 1.73639i
\(171\) 0 0
\(172\) −2.82843 + 4.89898i −0.215666 + 0.373544i
\(173\) −2.08579 3.61269i −0.158579 0.274668i 0.775777 0.631007i \(-0.217358\pi\)
−0.934357 + 0.356339i \(0.884025\pi\)
\(174\) 0 0
\(175\) 6.65685 16.3059i 0.503211 1.23261i
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) 2.24264 3.88437i 0.168093 0.291146i
\(179\) −9.44975 + 16.3674i −0.706307 + 1.22336i 0.259910 + 0.965633i \(0.416307\pi\)
−0.966218 + 0.257727i \(0.917026\pi\)
\(180\) 0 0
\(181\) 3.65685 0.271812 0.135906 0.990722i \(-0.456606\pi\)
0.135906 + 0.990722i \(0.456606\pi\)
\(182\) −2.96447 3.82282i −0.219741 0.283366i
\(183\) 0 0
\(184\) −1.12132 1.94218i −0.0826648 0.143180i
\(185\) 11.2426 19.4728i 0.826575 1.43167i
\(186\) 0 0
\(187\) 3.82843 + 6.63103i 0.279962 + 0.484909i
\(188\) −6.48528 −0.472988
\(189\) 0 0
\(190\) 11.6569 0.845677
\(191\) −6.41421 11.1097i −0.464116 0.803873i 0.535045 0.844824i \(-0.320295\pi\)
−0.999161 + 0.0409507i \(0.986961\pi\)
\(192\) 0 0
\(193\) −1.05025 + 1.81909i −0.0755988 + 0.130941i −0.901347 0.433099i \(-0.857420\pi\)
0.825748 + 0.564040i \(0.190754\pi\)
\(194\) 0.914214 + 1.58346i 0.0656367 + 0.113686i
\(195\) 0 0
\(196\) −1.74264 + 6.77962i −0.124474 + 0.484258i
\(197\) 17.4853 1.24577 0.622887 0.782312i \(-0.285959\pi\)
0.622887 + 0.782312i \(0.285959\pi\)
\(198\) 0 0
\(199\) −9.94975 + 17.2335i −0.705319 + 1.22165i 0.261257 + 0.965269i \(0.415863\pi\)
−0.966576 + 0.256379i \(0.917470\pi\)
\(200\) 3.32843 5.76500i 0.235355 0.407647i
\(201\) 0 0
\(202\) 11.8284 0.832245
\(203\) −22.6924 + 3.10538i −1.59269 + 0.217955i
\(204\) 0 0
\(205\) −4.41421 7.64564i −0.308302 0.533995i
\(206\) 5.29289 9.16756i 0.368773 0.638734i
\(207\) 0 0
\(208\) −0.914214 1.58346i −0.0633893 0.109793i
\(209\) 3.41421 0.236166
\(210\) 0 0
\(211\) 4.58579 0.315699 0.157849 0.987463i \(-0.449544\pi\)
0.157849 + 0.987463i \(0.449544\pi\)
\(212\) −5.94975 10.3053i −0.408630 0.707768i
\(213\) 0 0
\(214\) −5.53553 + 9.58783i −0.378401 + 0.655410i
\(215\) −9.65685 16.7262i −0.658592 1.14071i
\(216\) 0 0
\(217\) −4.00000 + 9.79796i −0.271538 + 0.665129i
\(218\) 0.485281 0.0328674
\(219\) 0 0
\(220\) 1.70711 2.95680i 0.115093 0.199347i
\(221\) −7.00000 + 12.1244i −0.470871 + 0.815572i
\(222\) 0 0
\(223\) 11.4142 0.764352 0.382176 0.924089i \(-0.375175\pi\)
0.382176 + 0.924089i \(0.375175\pi\)
\(224\) −1.00000 + 2.44949i −0.0668153 + 0.163663i
\(225\) 0 0
\(226\) 6.91421 + 11.9758i 0.459927 + 0.796616i
\(227\) −11.5858 + 20.0672i −0.768976 + 1.33190i 0.169143 + 0.985591i \(0.445900\pi\)
−0.938119 + 0.346313i \(0.887433\pi\)
\(228\) 0 0
\(229\) −0.343146 0.594346i −0.0226757 0.0392755i 0.854465 0.519509i \(-0.173885\pi\)
−0.877141 + 0.480234i \(0.840552\pi\)
\(230\) 7.65685 0.504878
\(231\) 0 0
\(232\) −8.65685 −0.568350
\(233\) −0.707107 1.22474i −0.0463241 0.0802357i 0.841934 0.539581i \(-0.181417\pi\)
−0.888258 + 0.459345i \(0.848084\pi\)
\(234\) 0 0
\(235\) 11.0711 19.1757i 0.722197 1.25088i
\(236\) −4.20711 7.28692i −0.273859 0.474338i
\(237\) 0 0
\(238\) 20.0711 2.74666i 1.30101 0.178040i
\(239\) 22.2132 1.43685 0.718426 0.695603i \(-0.244863\pi\)
0.718426 + 0.695603i \(0.244863\pi\)
\(240\) 0 0
\(241\) −1.87868 + 3.25397i −0.121016 + 0.209607i −0.920169 0.391522i \(-0.871949\pi\)
0.799152 + 0.601129i \(0.205282\pi\)
\(242\) 0.500000 0.866025i 0.0321412 0.0556702i
\(243\) 0 0
\(244\) 6.17157 0.395094
\(245\) −17.0711 16.7262i −1.09063 1.06860i
\(246\) 0 0
\(247\) 3.12132 + 5.40629i 0.198605 + 0.343994i
\(248\) −2.00000 + 3.46410i −0.127000 + 0.219971i
\(249\) 0 0
\(250\) 2.82843 + 4.89898i 0.178885 + 0.309839i
\(251\) −2.14214 −0.135210 −0.0676052 0.997712i \(-0.521536\pi\)
−0.0676052 + 0.997712i \(0.521536\pi\)
\(252\) 0 0
\(253\) 2.24264 0.140994
\(254\) −4.86396 8.42463i −0.305192 0.528608i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 1.57107 + 2.72117i 0.0980005 + 0.169742i 0.910857 0.412722i \(-0.135422\pi\)
−0.812856 + 0.582464i \(0.802089\pi\)
\(258\) 0 0
\(259\) −10.6777 13.7694i −0.663478 0.855587i
\(260\) 6.24264 0.387152
\(261\) 0 0
\(262\) 1.70711 2.95680i 0.105465 0.182671i
\(263\) 15.5208 26.8828i 0.957054 1.65767i 0.227459 0.973788i \(-0.426958\pi\)
0.729595 0.683879i \(-0.239709\pi\)
\(264\) 0 0
\(265\) 40.6274 2.49572
\(266\) 3.41421 8.36308i 0.209339 0.512773i
\(267\) 0 0
\(268\) −5.62132 9.73641i −0.343377 0.594746i
\(269\) 6.82843 11.8272i 0.416337 0.721116i −0.579231 0.815163i \(-0.696647\pi\)
0.995568 + 0.0940473i \(0.0299805\pi\)
\(270\) 0 0
\(271\) 13.2782 + 22.9985i 0.806592 + 1.39706i 0.915211 + 0.402974i \(0.132024\pi\)
−0.108620 + 0.994083i \(0.534643\pi\)
\(272\) 7.65685 0.464265
\(273\) 0 0
\(274\) −5.34315 −0.322791
\(275\) 3.32843 + 5.76500i 0.200712 + 0.347643i
\(276\) 0 0
\(277\) 1.91421 3.31552i 0.115014 0.199210i −0.802771 0.596287i \(-0.796642\pi\)
0.917785 + 0.397077i \(0.129975\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) −5.53553 7.13834i −0.330811 0.426597i
\(281\) 16.7279 0.997904 0.498952 0.866630i \(-0.333718\pi\)
0.498952 + 0.866630i \(0.333718\pi\)
\(282\) 0 0
\(283\) 10.2929 17.8278i 0.611849 1.05975i −0.379080 0.925364i \(-0.623759\pi\)
0.990929 0.134389i \(-0.0429073\pi\)
\(284\) 1.53553 2.65962i 0.0911172 0.157820i
\(285\) 0 0
\(286\) 1.82843 0.108117
\(287\) −6.77817 + 0.927572i −0.400103 + 0.0547528i
\(288\) 0 0
\(289\) −20.8137 36.0504i −1.22434 2.12061i
\(290\) 14.7782 25.5965i 0.867804 1.50308i
\(291\) 0 0
\(292\) 3.29289 + 5.70346i 0.192702 + 0.333770i
\(293\) 5.17157 0.302127 0.151063 0.988524i \(-0.451730\pi\)
0.151063 + 0.988524i \(0.451730\pi\)
\(294\) 0 0
\(295\) 28.7279 1.67260
\(296\) −3.29289 5.70346i −0.191396 0.331507i
\(297\) 0 0
\(298\) −3.17157 + 5.49333i −0.183724 + 0.318220i
\(299\) 2.05025 + 3.55114i 0.118569 + 0.205368i
\(300\) 0 0
\(301\) −14.8284 + 2.02922i −0.854696 + 0.116963i
\(302\) −9.72792 −0.559779
\(303\) 0 0
\(304\) 1.70711 2.95680i 0.0979093 0.169584i
\(305\) −10.5355 + 18.2481i −0.603263 + 1.04488i
\(306\) 0 0
\(307\) −9.89949 −0.564994 −0.282497 0.959268i \(-0.591163\pi\)
−0.282497 + 0.959268i \(0.591163\pi\)
\(308\) −1.62132 2.09077i −0.0923833 0.119133i
\(309\) 0 0
\(310\) −6.82843 11.8272i −0.387829 0.671739i
\(311\) −4.36396 + 7.55860i −0.247458 + 0.428609i −0.962820 0.270145i \(-0.912928\pi\)
0.715362 + 0.698754i \(0.246262\pi\)
\(312\) 0 0
\(313\) 4.67157 + 8.09140i 0.264053 + 0.457353i 0.967315 0.253578i \(-0.0816073\pi\)
−0.703262 + 0.710931i \(0.748274\pi\)
\(314\) −6.34315 −0.357964
\(315\) 0 0
\(316\) −4.75736 −0.267622
\(317\) 15.6569 + 27.1185i 0.879377 + 1.52312i 0.852026 + 0.523499i \(0.175374\pi\)
0.0273502 + 0.999626i \(0.491293\pi\)
\(318\) 0 0
\(319\) 4.32843 7.49706i 0.242345 0.419755i
\(320\) −1.70711 2.95680i −0.0954302 0.165290i
\(321\) 0 0
\(322\) 2.24264 5.49333i 0.124977 0.306131i
\(323\) −26.1421 −1.45459
\(324\) 0 0
\(325\) −6.08579 + 10.5409i −0.337579 + 0.584703i
\(326\) −7.86396 + 13.6208i −0.435545 + 0.754385i
\(327\) 0 0
\(328\) −2.58579 −0.142776
\(329\) −10.5147 13.5592i −0.579695 0.747545i
\(330\) 0 0
\(331\) 4.96447 + 8.59871i 0.272872 + 0.472628i 0.969596 0.244711i \(-0.0786932\pi\)
−0.696724 + 0.717339i \(0.745360\pi\)
\(332\) 8.07107 13.9795i 0.442957 0.767225i
\(333\) 0 0
\(334\) 5.86396 + 10.1567i 0.320862 + 0.555749i
\(335\) 38.3848 2.09718
\(336\) 0 0
\(337\) −19.7574 −1.07625 −0.538126 0.842864i \(-0.680868\pi\)
−0.538126 + 0.842864i \(0.680868\pi\)
\(338\) −4.82843 8.36308i −0.262632 0.454892i
\(339\) 0 0
\(340\) −13.0711 + 22.6398i −0.708878 + 1.22781i
\(341\) −2.00000 3.46410i −0.108306 0.187592i
\(342\) 0 0
\(343\) −17.0000 + 7.34847i −0.917914 + 0.396780i
\(344\) −5.65685 −0.304997
\(345\) 0 0
\(346\) 2.08579 3.61269i 0.112133 0.194219i
\(347\) 7.29289 12.6317i 0.391503 0.678103i −0.601145 0.799140i \(-0.705289\pi\)
0.992648 + 0.121037i \(0.0386219\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 17.4497 2.38794i 0.932728 0.127641i
\(351\) 0 0
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) −12.6569 + 21.9223i −0.673656 + 1.16681i 0.303203 + 0.952926i \(0.401944\pi\)
−0.976860 + 0.213881i \(0.931389\pi\)
\(354\) 0 0
\(355\) 5.24264 + 9.08052i 0.278250 + 0.481944i
\(356\) 4.48528 0.237719
\(357\) 0 0
\(358\) −18.8995 −0.998869
\(359\) 5.37868 + 9.31615i 0.283876 + 0.491687i 0.972336 0.233587i \(-0.0750463\pi\)
−0.688460 + 0.725274i \(0.741713\pi\)
\(360\) 0 0
\(361\) 3.67157 6.35935i 0.193241 0.334703i
\(362\) 1.82843 + 3.16693i 0.0961000 + 0.166450i
\(363\) 0 0
\(364\) 1.82843 4.47871i 0.0958356 0.234748i
\(365\) −22.4853 −1.17693
\(366\) 0 0
\(367\) −7.36396 + 12.7548i −0.384396 + 0.665793i −0.991685 0.128688i \(-0.958923\pi\)
0.607290 + 0.794481i \(0.292257\pi\)
\(368\) 1.12132 1.94218i 0.0584529 0.101243i
\(369\) 0 0
\(370\) 22.4853 1.16895
\(371\) 11.8995 29.1477i 0.617791 1.51327i
\(372\) 0 0
\(373\) −6.98528 12.0989i −0.361684 0.626455i 0.626554 0.779378i \(-0.284465\pi\)
−0.988238 + 0.152923i \(0.951131\pi\)
\(374\) −3.82843 + 6.63103i −0.197963 + 0.342882i
\(375\) 0 0
\(376\) −3.24264 5.61642i −0.167226 0.289645i
\(377\) 15.8284 0.815205
\(378\) 0 0
\(379\) −25.8701 −1.32886 −0.664428 0.747352i \(-0.731325\pi\)
−0.664428 + 0.747352i \(0.731325\pi\)
\(380\) 5.82843 + 10.0951i 0.298992 + 0.517869i
\(381\) 0 0
\(382\) 6.41421 11.1097i 0.328180 0.568424i
\(383\) 15.1924 + 26.3140i 0.776295 + 1.34458i 0.934064 + 0.357106i \(0.116236\pi\)
−0.157769 + 0.987476i \(0.550430\pi\)
\(384\) 0 0
\(385\) 8.94975 1.22474i 0.456121 0.0624188i
\(386\) −2.10051 −0.106913
\(387\) 0 0
\(388\) −0.914214 + 1.58346i −0.0464122 + 0.0803882i
\(389\) 1.36396 2.36245i 0.0691556 0.119781i −0.829374 0.558693i \(-0.811303\pi\)
0.898530 + 0.438912i \(0.144636\pi\)
\(390\) 0 0
\(391\) −17.1716 −0.868404
\(392\) −6.74264 + 1.88064i −0.340555 + 0.0949865i
\(393\) 0 0
\(394\) 8.74264 + 15.1427i 0.440448 + 0.762878i
\(395\) 8.12132 14.0665i 0.408628 0.707764i
\(396\) 0 0
\(397\) −11.0000 19.0526i −0.552074 0.956221i −0.998125 0.0612128i \(-0.980503\pi\)
0.446051 0.895008i \(-0.352830\pi\)
\(398\) −19.8995 −0.997472
\(399\) 0 0
\(400\) 6.65685 0.332843
\(401\) −2.15685 3.73578i −0.107708 0.186556i 0.807133 0.590369i \(-0.201018\pi\)
−0.914841 + 0.403813i \(0.867685\pi\)
\(402\) 0 0
\(403\) 3.65685 6.33386i 0.182161 0.315512i
\(404\) 5.91421 + 10.2437i 0.294243 + 0.509644i
\(405\) 0 0
\(406\) −14.0355 18.0995i −0.696572 0.898263i
\(407\) 6.58579 0.326445
\(408\) 0 0
\(409\) 11.3640 19.6830i 0.561912 0.973260i −0.435418 0.900228i \(-0.643399\pi\)
0.997330 0.0730312i \(-0.0232673\pi\)
\(410\) 4.41421 7.64564i 0.218002 0.377591i
\(411\) 0 0
\(412\) 10.5858 0.521524
\(413\) 8.41421 20.6105i 0.414036 1.01418i
\(414\) 0 0
\(415\) 27.5563 + 47.7290i 1.35269 + 2.34292i
\(416\) 0.914214 1.58346i 0.0448230 0.0776357i
\(417\) 0 0
\(418\) 1.70711 + 2.95680i 0.0834973 + 0.144622i
\(419\) −2.14214 −0.104650 −0.0523251 0.998630i \(-0.516663\pi\)
−0.0523251 + 0.998630i \(0.516663\pi\)
\(420\) 0 0
\(421\) 23.3137 1.13624 0.568120 0.822946i \(-0.307671\pi\)
0.568120 + 0.822946i \(0.307671\pi\)
\(422\) 2.29289 + 3.97141i 0.111616 + 0.193325i
\(423\) 0 0
\(424\) 5.94975 10.3053i 0.288945 0.500468i
\(425\) −25.4853 44.1418i −1.23622 2.14119i
\(426\) 0 0
\(427\) 10.0061 + 12.9033i 0.484229 + 0.624436i
\(428\) −11.0711 −0.535140
\(429\) 0 0
\(430\) 9.65685 16.7262i 0.465695 0.806607i
\(431\) −10.2071 + 17.6792i −0.491659 + 0.851578i −0.999954 0.00960469i \(-0.996943\pi\)
0.508295 + 0.861183i \(0.330276\pi\)
\(432\) 0 0
\(433\) −2.14214 −0.102944 −0.0514722 0.998674i \(-0.516391\pi\)
−0.0514722 + 0.998674i \(0.516391\pi\)
\(434\) −10.4853 + 1.43488i −0.503310 + 0.0688763i
\(435\) 0 0
\(436\) 0.242641 + 0.420266i 0.0116204 + 0.0201271i
\(437\) −3.82843 + 6.63103i −0.183139 + 0.317205i
\(438\) 0 0
\(439\) −4.69239 8.12745i −0.223955 0.387902i 0.732050 0.681251i \(-0.238564\pi\)
−0.956006 + 0.293349i \(0.905230\pi\)
\(440\) 3.41421 0.162766
\(441\) 0 0
\(442\) −14.0000 −0.665912
\(443\) −16.3137 28.2562i −0.775088 1.34249i −0.934745 0.355319i \(-0.884372\pi\)
0.159658 0.987172i \(-0.448961\pi\)
\(444\) 0 0
\(445\) −7.65685 + 13.2621i −0.362970 + 0.628682i
\(446\) 5.70711 + 9.88500i 0.270239 + 0.468068i
\(447\) 0 0
\(448\) −2.62132 + 0.358719i −0.123846 + 0.0169479i
\(449\) −33.6569 −1.58837 −0.794183 0.607679i \(-0.792101\pi\)
−0.794183 + 0.607679i \(0.792101\pi\)
\(450\) 0 0
\(451\) 1.29289 2.23936i 0.0608800 0.105447i
\(452\) −6.91421 + 11.9758i −0.325217 + 0.563293i
\(453\) 0 0
\(454\) −23.1716 −1.08750
\(455\) 10.1213 + 13.0519i 0.474495 + 0.611884i
\(456\) 0 0
\(457\) 0.171573 + 0.297173i 0.00802584 + 0.0139012i 0.870010 0.493033i \(-0.164112\pi\)
−0.861985 + 0.506934i \(0.830779\pi\)
\(458\) 0.343146 0.594346i 0.0160341 0.0277720i
\(459\) 0 0
\(460\) 3.82843 + 6.63103i 0.178501 + 0.309173i
\(461\) −14.3137 −0.666656 −0.333328 0.942811i \(-0.608172\pi\)
−0.333328 + 0.942811i \(0.608172\pi\)
\(462\) 0 0
\(463\) 7.17157 0.333291 0.166646 0.986017i \(-0.446706\pi\)
0.166646 + 0.986017i \(0.446706\pi\)
\(464\) −4.32843 7.49706i −0.200942 0.348042i
\(465\) 0 0
\(466\) 0.707107 1.22474i 0.0327561 0.0567352i
\(467\) −17.0000 29.4449i −0.786666 1.36255i −0.927999 0.372584i \(-0.878472\pi\)
0.141332 0.989962i \(-0.454861\pi\)
\(468\) 0 0
\(469\) 11.2426 27.5387i 0.519137 1.27162i
\(470\) 22.1421 1.02134
\(471\) 0 0
\(472\) 4.20711 7.28692i 0.193648 0.335408i
\(473\) 2.82843 4.89898i 0.130051 0.225255i
\(474\) 0 0
\(475\) −22.7279 −1.04283
\(476\) 12.4142 + 16.0087i 0.569005 + 0.733759i
\(477\) 0 0
\(478\) 11.1066 + 19.2372i 0.508004 + 0.879889i
\(479\) −13.0355 + 22.5782i −0.595609 + 1.03162i 0.397852 + 0.917450i \(0.369756\pi\)
−0.993461 + 0.114175i \(0.963578\pi\)
\(480\) 0 0
\(481\) 6.02082 + 10.4284i 0.274526 + 0.475492i
\(482\) −3.75736 −0.171143
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −3.12132 5.40629i −0.141732 0.245487i
\(486\) 0 0
\(487\) −0.828427 + 1.43488i −0.0375396 + 0.0650205i −0.884185 0.467137i \(-0.845285\pi\)
0.846645 + 0.532158i \(0.178619\pi\)
\(488\) 3.08579 + 5.34474i 0.139687 + 0.241945i
\(489\) 0 0
\(490\) 5.94975 23.1471i 0.268782 1.04568i
\(491\) −24.8284 −1.12049 −0.560246 0.828327i \(-0.689293\pi\)
−0.560246 + 0.828327i \(0.689293\pi\)
\(492\) 0 0
\(493\) −33.1421 + 57.4039i −1.49265 + 2.58534i
\(494\) −3.12132 + 5.40629i −0.140435 + 0.243240i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 8.05025 1.10165i 0.361103 0.0494158i
\(498\) 0 0
\(499\) 3.07107 + 5.31925i 0.137480 + 0.238122i 0.926542 0.376191i \(-0.122766\pi\)
−0.789062 + 0.614313i \(0.789433\pi\)
\(500\) −2.82843 + 4.89898i −0.126491 + 0.219089i
\(501\) 0 0
\(502\) −1.07107 1.85514i −0.0478041 0.0827991i
\(503\) 38.2132 1.70384 0.851921 0.523670i \(-0.175437\pi\)
0.851921 + 0.523670i \(0.175437\pi\)
\(504\) 0 0
\(505\) −40.3848 −1.79710
\(506\) 1.12132 + 1.94218i 0.0498488 + 0.0863406i
\(507\) 0 0
\(508\) 4.86396 8.42463i 0.215803 0.373782i
\(509\) −6.65685 11.5300i −0.295060 0.511059i 0.679939 0.733269i \(-0.262006\pi\)
−0.974999 + 0.222210i \(0.928673\pi\)
\(510\) 0 0
\(511\) −6.58579 + 16.1318i −0.291338 + 0.713630i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −1.57107 + 2.72117i −0.0692968 + 0.120026i
\(515\) −18.0711 + 31.3000i −0.796306 + 1.37924i
\(516\) 0 0
\(517\) 6.48528 0.285222
\(518\) 6.58579 16.1318i 0.289363 0.708791i
\(519\) 0 0
\(520\) 3.12132 + 5.40629i 0.136879 + 0.237081i
\(521\) 14.1421 24.4949i 0.619578 1.07314i −0.369984 0.929038i \(-0.620637\pi\)
0.989563 0.144103i \(-0.0460297\pi\)
\(522\) 0 0
\(523\) −6.36396 11.0227i −0.278277 0.481989i 0.692680 0.721245i \(-0.256430\pi\)
−0.970957 + 0.239256i \(0.923097\pi\)
\(524\) 3.41421 0.149151
\(525\) 0 0
\(526\) 31.0416 1.35348
\(527\) 15.3137 + 26.5241i 0.667076 + 1.15541i
\(528\) 0 0
\(529\) 8.98528 15.5630i 0.390664 0.676651i
\(530\) 20.3137 + 35.1844i 0.882371 + 1.52831i
\(531\) 0 0
\(532\) 8.94975 1.22474i 0.388021 0.0530994i
\(533\) 4.72792 0.204789
\(534\) 0 0
\(535\) 18.8995 32.7349i 0.817096 1.41525i
\(536\) 5.62132 9.73641i 0.242804 0.420549i
\(537\) 0 0
\(538\) 13.6569 0.588789
\(539\) 1.74264 6.77962i 0.0750608 0.292019i
\(540\) 0 0
\(541\) 20.5711 + 35.6301i 0.884419 + 1.53186i 0.846378 + 0.532583i \(0.178779\pi\)
0.0380415 + 0.999276i \(0.487888\pi\)
\(542\) −13.2782 + 22.9985i −0.570346 + 0.987869i
\(543\) 0 0
\(544\) 3.82843 + 6.63103i 0.164142 + 0.284303i
\(545\) −1.65685 −0.0709718
\(546\) 0 0
\(547\) −18.8701 −0.806825 −0.403413 0.915018i \(-0.632176\pi\)
−0.403413 + 0.915018i \(0.632176\pi\)
\(548\) −2.67157 4.62730i −0.114124 0.197668i
\(549\) 0 0
\(550\) −3.32843 + 5.76500i −0.141925 + 0.245821i
\(551\) 14.7782 + 25.5965i 0.629571 + 1.09045i
\(552\) 0 0
\(553\) −7.71320 9.94655i −0.327999 0.422970i
\(554\) 3.82843 0.162654
\(555\) 0 0
\(556\) 0 0
\(557\) 12.2426 21.2049i 0.518737 0.898479i −0.481026 0.876707i \(-0.659736\pi\)
0.999763 0.0217729i \(-0.00693107\pi\)
\(558\) 0 0
\(559\) 10.3431 0.437468
\(560\) 3.41421 8.36308i 0.144277 0.353405i
\(561\) 0 0
\(562\) 8.36396 + 14.4868i 0.352812 + 0.611089i
\(563\) −2.53553 + 4.39167i −0.106860 + 0.185087i −0.914497 0.404594i \(-0.867413\pi\)
0.807637 + 0.589681i \(0.200746\pi\)
\(564\) 0 0
\(565\) −23.6066 40.8878i −0.993137 1.72016i
\(566\) 20.5858 0.865285
\(567\) 0 0
\(568\) 3.07107 0.128859
\(569\) −2.00000 3.46410i −0.0838444 0.145223i 0.821054 0.570851i \(-0.193387\pi\)
−0.904898 + 0.425628i \(0.860053\pi\)
\(570\) 0 0
\(571\) 5.19239 8.99348i 0.217295 0.376365i −0.736685 0.676236i \(-0.763610\pi\)
0.953980 + 0.299870i \(0.0969434\pi\)
\(572\) 0.914214 + 1.58346i 0.0382252 + 0.0662080i
\(573\) 0 0
\(574\) −4.19239 5.40629i −0.174987 0.225654i
\(575\) −14.9289 −0.622580
\(576\) 0 0
\(577\) 16.1569 27.9845i 0.672619 1.16501i −0.304540 0.952499i \(-0.598503\pi\)
0.977159 0.212510i \(-0.0681639\pi\)
\(578\) 20.8137 36.0504i 0.865736 1.49950i
\(579\) 0 0
\(580\) 29.5563 1.22726
\(581\) 42.3137 5.79050i 1.75547 0.240230i
\(582\) 0 0
\(583\) 5.94975 + 10.3053i 0.246413 + 0.426800i
\(584\) −3.29289 + 5.70346i −0.136261 + 0.236011i
\(585\) 0 0
\(586\) 2.58579 + 4.47871i 0.106818 + 0.185014i
\(587\) 44.8995 1.85320 0.926600 0.376048i \(-0.122717\pi\)
0.926600 + 0.376048i \(0.122717\pi\)
\(588\) 0 0
\(589\) 13.6569 0.562721
\(590\) 14.3640 + 24.8791i 0.591355 + 1.02426i
\(591\) 0 0
\(592\) 3.29289 5.70346i 0.135337 0.234411i
\(593\) −17.8492 30.9158i −0.732981 1.26956i −0.955604 0.294655i \(-0.904795\pi\)
0.222623 0.974905i \(-0.428538\pi\)
\(594\) 0 0
\(595\) −68.5269 + 9.37769i −2.80933 + 0.384448i
\(596\) −6.34315 −0.259825
\(597\) 0 0
\(598\) −2.05025 + 3.55114i −0.0838411 + 0.145217i
\(599\) −1.31371 + 2.27541i −0.0536767 + 0.0929707i −0.891615 0.452794i \(-0.850427\pi\)
0.837939 + 0.545765i \(0.183761\pi\)
\(600\) 0 0
\(601\) −35.9411 −1.46607 −0.733035 0.680191i \(-0.761897\pi\)
−0.733035 + 0.680191i \(0.761897\pi\)
\(602\) −9.17157 11.8272i −0.373805 0.482040i
\(603\) 0 0
\(604\) −4.86396 8.42463i −0.197912 0.342793i
\(605\) −1.70711 + 2.95680i −0.0694038 + 0.120211i
\(606\) 0 0
\(607\) 4.51472 + 7.81972i 0.183247 + 0.317393i 0.942984 0.332837i \(-0.108006\pi\)
−0.759738 + 0.650230i \(0.774673\pi\)
\(608\) 3.41421 0.138465
\(609\) 0 0
\(610\) −21.0711 −0.853143
\(611\) 5.92893 + 10.2692i 0.239859 + 0.415448i
\(612\) 0 0
\(613\) 8.31371 14.3998i 0.335788 0.581601i −0.647848 0.761769i \(-0.724331\pi\)
0.983636 + 0.180168i \(0.0576643\pi\)
\(614\) −4.94975 8.57321i −0.199756 0.345987i
\(615\) 0 0
\(616\) 1.00000 2.44949i 0.0402911 0.0986928i
\(617\) 8.02944 0.323253 0.161626 0.986852i \(-0.448326\pi\)
0.161626 + 0.986852i \(0.448326\pi\)
\(618\) 0 0
\(619\) −22.9706 + 39.7862i −0.923265 + 1.59914i −0.128937 + 0.991653i \(0.541156\pi\)
−0.794328 + 0.607489i \(0.792177\pi\)
\(620\) 6.82843 11.8272i 0.274236 0.474991i
\(621\) 0 0
\(622\) −8.72792 −0.349958
\(623\) 7.27208 + 9.37769i 0.291350 + 0.375709i
\(624\) 0 0
\(625\) 6.98528 + 12.0989i 0.279411 + 0.483954i
\(626\) −4.67157 + 8.09140i −0.186714 + 0.323397i
\(627\) 0 0
\(628\) −3.17157 5.49333i −0.126560 0.219208i
\(629\) −50.4264 −2.01063
\(630\) 0 0
\(631\) 48.7279 1.93983 0.969914 0.243448i \(-0.0782785\pi\)
0.969914 + 0.243448i \(0.0782785\pi\)
\(632\) −2.37868 4.11999i −0.0946188 0.163885i
\(633\) 0 0
\(634\) −15.6569 + 27.1185i −0.621813 + 1.07701i
\(635\) 16.6066 + 28.7635i 0.659013 + 1.14144i
\(636\) 0 0
\(637\) 12.3284 3.43861i 0.488470 0.136243i
\(638\) 8.65685 0.342728
\(639\) 0 0
\(640\) 1.70711 2.95680i 0.0674793 0.116878i
\(641\) −20.6421 + 35.7532i −0.815315 + 1.41217i 0.0937859 + 0.995592i \(0.470103\pi\)
−0.909101 + 0.416575i \(0.863230\pi\)
\(642\) 0 0
\(643\) 4.41421 0.174080 0.0870398 0.996205i \(-0.472259\pi\)
0.0870398 + 0.996205i \(0.472259\pi\)
\(644\) 5.87868 0.804479i 0.231652 0.0317009i
\(645\) 0 0
\(646\) −13.0711 22.6398i −0.514274 0.890749i
\(647\) −23.0919 + 39.9963i −0.907836 + 1.57242i −0.0907706 + 0.995872i \(0.528933\pi\)
−0.817065 + 0.576546i \(0.804400\pi\)
\(648\) 0 0
\(649\) 4.20711 + 7.28692i 0.165143 + 0.286037i
\(650\) −12.1716 −0.477408
\(651\) 0 0
\(652\) −15.7279 −0.615953
\(653\) 9.19239 + 15.9217i 0.359726 + 0.623064i 0.987915 0.154997i \(-0.0495369\pi\)
−0.628189 + 0.778061i \(0.716204\pi\)
\(654\) 0 0
\(655\) −5.82843 + 10.0951i −0.227735 + 0.394449i
\(656\) −1.29289 2.23936i −0.0504790 0.0874322i
\(657\) 0 0
\(658\) 6.48528 15.8856i 0.252823 0.619286i
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) 7.48528 12.9649i 0.291144 0.504276i −0.682937 0.730478i \(-0.739298\pi\)
0.974080 + 0.226202i \(0.0726309\pi\)
\(662\) −4.96447 + 8.59871i −0.192949 + 0.334198i
\(663\) 0 0
\(664\) 16.1421 0.626436
\(665\) −11.6569 + 28.5533i −0.452033 + 1.10725i
\(666\) 0 0
\(667\) 9.70711 + 16.8132i 0.375861 + 0.651010i
\(668\) −5.86396 + 10.1567i −0.226883 + 0.392974i
\(669\) 0 0
\(670\) 19.1924 + 33.2422i 0.741467 + 1.28426i
\(671\) −6.17157 −0.238251
\(672\) 0 0
\(673\) −25.5563 −0.985125 −0.492562 0.870277i \(-0.663940\pi\)
−0.492562 + 0.870277i \(0.663940\pi\)
\(674\) −9.87868 17.1104i −0.380513 0.659067i
\(675\) 0 0
\(676\) 4.82843 8.36308i 0.185709 0.321657i
\(677\) −6.34315 10.9867i −0.243787 0.422251i 0.718003 0.696040i \(-0.245056\pi\)
−0.961790 + 0.273789i \(0.911723\pi\)
\(678\) 0 0
\(679\) −4.79289 + 0.655892i −0.183934 + 0.0251708i
\(680\) −26.1421 −1.00251
\(681\) 0 0
\(682\) 2.00000 3.46410i 0.0765840 0.132647i
\(683\) 8.20711 14.2151i 0.314036 0.543927i −0.665196 0.746669i \(-0.731652\pi\)
0.979232 + 0.202742i \(0.0649853\pi\)
\(684\) 0 0
\(685\) 18.2426 0.697015
\(686\) −14.8640 11.0482i −0.567509 0.421822i
\(687\) 0 0
\(688\) −2.82843 4.89898i −0.107833 0.186772i
\(689\) −10.8787 + 18.8424i −0.414445 + 0.717839i
\(690\) 0 0
\(691\) −6.96447 12.0628i −0.264941 0.458891i 0.702607 0.711578i \(-0.252019\pi\)
−0.967548 + 0.252687i \(0.918686\pi\)
\(692\) 4.17157 0.158579
\(693\) 0 0
\(694\) 14.5858 0.553669
\(695\) 0 0
\(696\) 0 0
\(697\) −9.89949 + 17.1464i −0.374970 + 0.649467i
\(698\) 0 0
\(699\) 0 0
\(700\) 10.7929 + 13.9180i 0.407933 + 0.526049i
\(701\) −36.1127 −1.36396 −0.681979 0.731372i \(-0.738880\pi\)
−0.681979 + 0.731372i \(0.738880\pi\)
\(702\) 0 0
\(703\) −11.2426 + 19.4728i −0.424024 + 0.734432i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) 0 0
\(706\) −25.3137 −0.952694
\(707\) −11.8284 + 28.9736i −0.444854 + 1.08966i
\(708\) 0 0
\(709\) −18.0208 31.2130i −0.676786 1.17223i −0.975943 0.218024i \(-0.930039\pi\)
0.299158 0.954204i \(-0.403294\pi\)
\(710\) −5.24264 + 9.08052i −0.196753 + 0.340786i
\(711\) 0 0
\(712\) 2.24264 + 3.88437i 0.0840465 + 0.145573i
\(713\) 8.97056 0.335950
\(714\) 0 0
\(715\) −6.24264 −0.233462
\(716\) −9.44975 16.3674i −0.353154 0.611680i
\(717\) 0 0
\(718\) −5.37868 + 9.31615i −0.200731 + 0.347675i
\(719\) −9.24264 16.0087i −0.344692 0.597025i 0.640605 0.767870i \(-0.278683\pi\)
−0.985298 + 0.170846i \(0.945350\pi\)
\(720\) 0 0
\(721\) 17.1630 + 22.1324i 0.639182 + 0.824255i
\(722\) 7.34315 0.273284
\(723\) 0 0
\(724\) −1.82843 + 3.16693i −0.0679530 + 0.117698i
\(725\) −28.8137 + 49.9068i −1.07011 + 1.85349i
\(726\) 0 0
\(727\) −48.4264 −1.79604 −0.898018 0.439959i \(-0.854993\pi\)
−0.898018 + 0.439959i \(0.854993\pi\)
\(728\) 4.79289 0.655892i 0.177636 0.0243090i
\(729\) 0 0
\(730\) −11.2426 19.4728i −0.416109 0.720722i
\(731\) −21.6569 + 37.5108i −0.801008 + 1.38739i
\(732\) 0 0
\(733\) 6.50000 + 11.2583i 0.240083 + 0.415836i 0.960738 0.277458i \(-0.0894920\pi\)
−0.720655 + 0.693294i \(0.756159\pi\)
\(734\) −14.7279 −0.543618
\(735\) 0 0
\(736\) 2.24264 0.0826648
\(737\) 5.62132 + 9.73641i 0.207064 + 0.358645i
\(738\) 0 0
\(739\) −16.2132 + 28.0821i −0.596412 + 1.03302i 0.396934 + 0.917847i \(0.370074\pi\)
−0.993346 + 0.115169i \(0.963259\pi\)
\(740\) 11.2426 + 19.4728i 0.413288 + 0.715835i
\(741\) 0 0
\(742\) 31.1924 4.26858i 1.14511 0.156705i
\(743\) −9.31371 −0.341687 −0.170843 0.985298i \(-0.554649\pi\)
−0.170843 + 0.985298i \(0.554649\pi\)
\(744\) 0 0
\(745\) 10.8284 18.7554i 0.396723 0.687144i
\(746\) 6.98528 12.0989i 0.255749 0.442971i
\(747\) 0 0
\(748\) −7.65685 −0.279962
\(749\) −17.9497 23.1471i −0.655869 0.845775i
\(750\) 0 0
\(751\) −17.1716 29.7420i −0.626600 1.08530i −0.988229 0.152980i \(-0.951113\pi\)
0.361630 0.932322i \(-0.382220\pi\)
\(752\) 3.24264 5.61642i 0.118247 0.204810i
\(753\) 0 0
\(754\) 7.91421 + 13.7078i 0.288219 + 0.499209i
\(755\) 33.2132 1.20875
\(756\) 0 0
\(757\) 19.6569 0.714441 0.357220 0.934020i \(-0.383725\pi\)
0.357220 + 0.934020i \(0.383725\pi\)
\(758\) −12.9350 22.4041i −0.469821 0.813755i
\(759\) 0 0
\(760\) −5.82843 + 10.0951i −0.211419 + 0.366189i
\(761\) −1.48528 2.57258i −0.0538414 0.0932561i 0.837849 0.545903i \(-0.183813\pi\)
−0.891690 + 0.452647i \(0.850480\pi\)
\(762\) 0 0
\(763\) −0.485281 + 1.18869i −0.0175684 + 0.0430335i
\(764\) 12.8284 0.464116
\(765\) 0 0
\(766\) −15.1924 + 26.3140i −0.548923 + 0.950763i
\(767\) −7.69239 + 13.3236i −0.277756 + 0.481088i
\(768\) 0 0
\(769\) −10.9706 −0.395609 −0.197804 0.980242i \(-0.563381\pi\)
−0.197804 + 0.980242i \(0.563381\pi\)
\(770\) 5.53553 + 7.13834i 0.199487 + 0.257248i
\(771\) 0 0
\(772\) −1.05025 1.81909i −0.0377994 0.0654705i
\(773\) 22.9706 39.7862i 0.826194 1.43101i −0.0748099 0.997198i \(-0.523835\pi\)
0.901004 0.433812i \(-0.142832\pi\)
\(774\) 0 0
\(775\) 13.3137 + 23.0600i 0.478243 + 0.828340i
\(776\) −1.82843 −0.0656367
\(777\) 0 0
\(778\) 2.72792 0.0978007
\(779\) 4.41421 + 7.64564i 0.158156 + 0.273934i
\(780\) 0 0
\(781\) −1.53553 + 2.65962i −0.0549457 + 0.0951688i
\(782\) −8.58579 14.8710i −0.307027 0.531787i
\(783\) 0 0
\(784\) −5.00000 4.89898i −0.178571 0.174964i
\(785\) 21.6569 0.772966
\(786\) 0 0
\(787\) 8.77817 15.2042i 0.312908 0.541973i −0.666082 0.745878i \(-0.732030\pi\)
0.978991 + 0.203905i \(0.0653635\pi\)
\(788\) −8.74264 + 15.1427i −0.311444 + 0.539436i
\(789\) 0 0
\(790\) 16.2426 0.577887