Properties

Label 1386.2.k.j.793.1
Level $1386$
Weight $2$
Character 1386.793
Analytic conductor $11.067$
Analytic rank $0$
Dimension $2$
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: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 462)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 793.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1386.793
Dual form 1386.2.k.j.991.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +(-0.500000 - 0.866025i) q^{11} +6.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} +(-3.00000 + 5.19615i) q^{19} -3.00000 q^{20} +1.00000 q^{22} +(2.50000 - 4.33013i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-3.00000 + 5.19615i) q^{26} +(2.00000 + 1.73205i) q^{28} +6.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +5.00000 q^{34} +(-1.50000 + 7.79423i) q^{35} +(1.00000 - 1.73205i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(1.50000 - 2.59808i) q^{40} -5.00000 q^{41} -10.0000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(2.50000 + 4.33013i) q^{46} +(4.50000 - 7.79423i) q^{47} +(5.50000 - 4.33013i) q^{49} +4.00000 q^{50} +(-3.00000 - 5.19615i) q^{52} +(1.00000 + 1.73205i) q^{53} -3.00000 q^{55} +(-2.50000 + 0.866025i) q^{56} +(-3.00000 + 5.19615i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(2.50000 - 4.33013i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(9.00000 - 15.5885i) q^{65} +(-2.50000 - 4.33013i) q^{67} +(-2.50000 + 4.33013i) q^{68} +(-6.00000 - 5.19615i) q^{70} -4.00000 q^{71} +(-6.00000 - 10.3923i) q^{73} +(1.00000 + 1.73205i) q^{74} +6.00000 q^{76} +(2.00000 + 1.73205i) q^{77} +(0.500000 - 0.866025i) q^{79} +(1.50000 + 2.59808i) q^{80} +(2.50000 - 4.33013i) q^{82} -1.00000 q^{83} -15.0000 q^{85} +(5.00000 - 8.66025i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(3.00000 - 5.19615i) q^{89} +(-15.0000 + 5.19615i) q^{91} -5.00000 q^{92} +(4.50000 + 7.79423i) q^{94} +(9.00000 + 15.5885i) q^{95} +9.00000 q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} + 3 q^{5} - 5 q^{7} + 2 q^{8} + O(q^{10}) \) \( 2 q - q^{2} - q^{4} + 3 q^{5} - 5 q^{7} + 2 q^{8} + 3 q^{10} - q^{11} + 12 q^{13} + q^{14} - q^{16} - 5 q^{17} - 6 q^{19} - 6 q^{20} + 2 q^{22} + 5 q^{23} - 4 q^{25} - 6 q^{26} + 4 q^{28} + 12 q^{29} - 4 q^{31} - q^{32} + 10 q^{34} - 3 q^{35} + 2 q^{37} - 6 q^{38} + 3 q^{40} - 10 q^{41} - 20 q^{43} - q^{44} + 5 q^{46} + 9 q^{47} + 11 q^{49} + 8 q^{50} - 6 q^{52} + 2 q^{53} - 6 q^{55} - 5 q^{56} - 6 q^{58} - 12 q^{59} + 5 q^{61} + 8 q^{62} + 2 q^{64} + 18 q^{65} - 5 q^{67} - 5 q^{68} - 12 q^{70} - 8 q^{71} - 12 q^{73} + 2 q^{74} + 12 q^{76} + 4 q^{77} + q^{79} + 3 q^{80} + 5 q^{82} - 2 q^{83} - 30 q^{85} + 10 q^{86} - q^{88} + 6 q^{89} - 30 q^{91} - 10 q^{92} + 9 q^{94} + 18 q^{95} + 18 q^{97} + 2 q^{98} + O(q^{100}) \)

Character values

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

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

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
\(5\) 1.50000 2.59808i 0.670820 1.16190i −0.306851 0.951757i \(-0.599275\pi\)
0.977672 0.210138i \(-0.0673912\pi\)
\(6\) 0 0
\(7\) −2.50000 + 0.866025i −0.944911 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.50000 + 2.59808i 0.474342 + 0.821584i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) 0 0
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0.500000 2.59808i 0.133631 0.694365i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.50000 4.33013i −0.606339 1.05021i −0.991838 0.127502i \(-0.959304\pi\)
0.385499 0.922708i \(-0.374029\pi\)
\(18\) 0 0
\(19\) −3.00000 + 5.19615i −0.688247 + 1.19208i 0.284157 + 0.958778i \(0.408286\pi\)
−0.972404 + 0.233301i \(0.925047\pi\)
\(20\) −3.00000 −0.670820
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 2.50000 4.33013i 0.521286 0.902894i −0.478407 0.878138i \(-0.658786\pi\)
0.999694 0.0247559i \(-0.00788087\pi\)
\(24\) 0 0
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) −3.00000 + 5.19615i −0.588348 + 1.01905i
\(27\) 0 0
\(28\) 2.00000 + 1.73205i 0.377964 + 0.327327i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i \(-0.283621\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 5.00000 0.857493
\(35\) −1.50000 + 7.79423i −0.253546 + 1.31747i
\(36\) 0 0
\(37\) 1.00000 1.73205i 0.164399 0.284747i −0.772043 0.635571i \(-0.780765\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(38\) −3.00000 5.19615i −0.486664 0.842927i
\(39\) 0 0
\(40\) 1.50000 2.59808i 0.237171 0.410792i
\(41\) −5.00000 −0.780869 −0.390434 0.920631i \(-0.627675\pi\)
−0.390434 + 0.920631i \(0.627675\pi\)
\(42\) 0 0
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 0 0
\(46\) 2.50000 + 4.33013i 0.368605 + 0.638442i
\(47\) 4.50000 7.79423i 0.656392 1.13691i −0.325150 0.945662i \(-0.605415\pi\)
0.981543 0.191243i \(-0.0612518\pi\)
\(48\) 0 0
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 4.00000 0.565685
\(51\) 0 0
\(52\) −3.00000 5.19615i −0.416025 0.720577i
\(53\) 1.00000 + 1.73205i 0.137361 + 0.237915i 0.926497 0.376303i \(-0.122805\pi\)
−0.789136 + 0.614218i \(0.789471\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) −2.50000 + 0.866025i −0.334077 + 0.115728i
\(57\) 0 0
\(58\) −3.00000 + 5.19615i −0.393919 + 0.682288i
\(59\) −6.00000 10.3923i −0.781133 1.35296i −0.931282 0.364299i \(-0.881308\pi\)
0.150148 0.988663i \(-0.452025\pi\)
\(60\) 0 0
\(61\) 2.50000 4.33013i 0.320092 0.554416i −0.660415 0.750901i \(-0.729619\pi\)
0.980507 + 0.196485i \(0.0629528\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 9.00000 15.5885i 1.11631 1.93351i
\(66\) 0 0
\(67\) −2.50000 4.33013i −0.305424 0.529009i 0.671932 0.740613i \(-0.265465\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) −2.50000 + 4.33013i −0.303170 + 0.525105i
\(69\) 0 0
\(70\) −6.00000 5.19615i −0.717137 0.621059i
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) −6.00000 10.3923i −0.702247 1.21633i −0.967676 0.252197i \(-0.918847\pi\)
0.265429 0.964130i \(-0.414486\pi\)
\(74\) 1.00000 + 1.73205i 0.116248 + 0.201347i
\(75\) 0 0
\(76\) 6.00000 0.688247
\(77\) 2.00000 + 1.73205i 0.227921 + 0.197386i
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) 1.50000 + 2.59808i 0.167705 + 0.290474i
\(81\) 0 0
\(82\) 2.50000 4.33013i 0.276079 0.478183i
\(83\) −1.00000 −0.109764 −0.0548821 0.998493i \(-0.517478\pi\)
−0.0548821 + 0.998493i \(0.517478\pi\)
\(84\) 0 0
\(85\) −15.0000 −1.62698
\(86\) 5.00000 8.66025i 0.539164 0.933859i
\(87\) 0 0
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) −15.0000 + 5.19615i −1.57243 + 0.544705i
\(92\) −5.00000 −0.521286
\(93\) 0 0
\(94\) 4.50000 + 7.79423i 0.464140 + 0.803913i
\(95\) 9.00000 + 15.5885i 0.923381 + 1.59934i
\(96\) 0 0
\(97\) 9.00000 0.913812 0.456906 0.889515i \(-0.348958\pi\)
0.456906 + 0.889515i \(0.348958\pi\)
\(98\) 1.00000 + 6.92820i 0.101015 + 0.699854i
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) −4.00000 6.92820i −0.398015 0.689382i 0.595466 0.803380i \(-0.296967\pi\)
−0.993481 + 0.113998i \(0.963634\pi\)
\(102\) 0 0
\(103\) 1.00000 1.73205i 0.0985329 0.170664i −0.812545 0.582899i \(-0.801918\pi\)
0.911078 + 0.412235i \(0.135252\pi\)
\(104\) 6.00000 0.588348
\(105\) 0 0
\(106\) −2.00000 −0.194257
\(107\) −6.50000 + 11.2583i −0.628379 + 1.08838i 0.359498 + 0.933146i \(0.382948\pi\)
−0.987877 + 0.155238i \(0.950386\pi\)
\(108\) 0 0
\(109\) 5.50000 + 9.52628i 0.526804 + 0.912452i 0.999512 + 0.0312328i \(0.00994332\pi\)
−0.472708 + 0.881219i \(0.656723\pi\)
\(110\) 1.50000 2.59808i 0.143019 0.247717i
\(111\) 0 0
\(112\) 0.500000 2.59808i 0.0472456 0.245495i
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) −7.50000 12.9904i −0.699379 1.21136i
\(116\) −3.00000 5.19615i −0.278543 0.482451i
\(117\) 0 0
\(118\) 12.0000 1.10469
\(119\) 10.0000 + 8.66025i 0.916698 + 0.793884i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 2.50000 + 4.33013i 0.226339 + 0.392031i
\(123\) 0 0
\(124\) −2.00000 + 3.46410i −0.179605 + 0.311086i
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 9.00000 + 15.5885i 0.789352 + 1.36720i
\(131\) −2.00000 + 3.46410i −0.174741 + 0.302660i −0.940072 0.340977i \(-0.889242\pi\)
0.765331 + 0.643637i \(0.222575\pi\)
\(132\) 0 0
\(133\) 3.00000 15.5885i 0.260133 1.35169i
\(134\) 5.00000 0.431934
\(135\) 0 0
\(136\) −2.50000 4.33013i −0.214373 0.371305i
\(137\) −1.00000 1.73205i −0.0854358 0.147979i 0.820141 0.572161i \(-0.193895\pi\)
−0.905577 + 0.424182i \(0.860562\pi\)
\(138\) 0 0
\(139\) 22.0000 1.86602 0.933008 0.359856i \(-0.117174\pi\)
0.933008 + 0.359856i \(0.117174\pi\)
\(140\) 7.50000 2.59808i 0.633866 0.219578i
\(141\) 0 0
\(142\) 2.00000 3.46410i 0.167836 0.290701i
\(143\) −3.00000 5.19615i −0.250873 0.434524i
\(144\) 0 0
\(145\) 9.00000 15.5885i 0.747409 1.29455i
\(146\) 12.0000 0.993127
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i \(-0.569430\pi\)
0.953703 0.300750i \(-0.0972370\pi\)
\(150\) 0 0
\(151\) −4.50000 7.79423i −0.366205 0.634285i 0.622764 0.782410i \(-0.286010\pi\)
−0.988969 + 0.148124i \(0.952676\pi\)
\(152\) −3.00000 + 5.19615i −0.243332 + 0.421464i
\(153\) 0 0
\(154\) −2.50000 + 0.866025i −0.201456 + 0.0697863i
\(155\) −12.0000 −0.963863
\(156\) 0 0
\(157\) 12.0000 + 20.7846i 0.957704 + 1.65879i 0.728055 + 0.685519i \(0.240425\pi\)
0.229650 + 0.973273i \(0.426242\pi\)
\(158\) 0.500000 + 0.866025i 0.0397779 + 0.0688973i
\(159\) 0 0
\(160\) −3.00000 −0.237171
\(161\) −2.50000 + 12.9904i −0.197028 + 1.02379i
\(162\) 0 0
\(163\) 0.500000 0.866025i 0.0391630 0.0678323i −0.845780 0.533533i \(-0.820864\pi\)
0.884943 + 0.465700i \(0.154198\pi\)
\(164\) 2.50000 + 4.33013i 0.195217 + 0.338126i
\(165\) 0 0
\(166\) 0.500000 0.866025i 0.0388075 0.0672166i
\(167\) 24.0000 1.85718 0.928588 0.371113i \(-0.121024\pi\)
0.928588 + 0.371113i \(0.121024\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 7.50000 12.9904i 0.575224 0.996317i
\(171\) 0 0
\(172\) 5.00000 + 8.66025i 0.381246 + 0.660338i
\(173\) −6.00000 + 10.3923i −0.456172 + 0.790112i −0.998755 0.0498898i \(-0.984113\pi\)
0.542583 + 0.840002i \(0.317446\pi\)
\(174\) 0 0
\(175\) 8.00000 + 6.92820i 0.604743 + 0.523723i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) 3.00000 + 5.19615i 0.224860 + 0.389468i
\(179\) −4.00000 6.92820i −0.298974 0.517838i 0.676927 0.736050i \(-0.263311\pi\)
−0.975901 + 0.218212i \(0.929978\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 3.00000 15.5885i 0.222375 1.15549i
\(183\) 0 0
\(184\) 2.50000 4.33013i 0.184302 0.319221i
\(185\) −3.00000 5.19615i −0.220564 0.382029i
\(186\) 0 0
\(187\) −2.50000 + 4.33013i −0.182818 + 0.316650i
\(188\) −9.00000 −0.656392
\(189\) 0 0
\(190\) −18.0000 −1.30586
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) 0 0
\(193\) −3.00000 5.19615i −0.215945 0.374027i 0.737620 0.675216i \(-0.235950\pi\)
−0.953564 + 0.301189i \(0.902616\pi\)
\(194\) −4.50000 + 7.79423i −0.323081 + 0.559593i
\(195\) 0 0
\(196\) −6.50000 2.59808i −0.464286 0.185577i
\(197\) 24.0000 1.70993 0.854965 0.518686i \(-0.173579\pi\)
0.854965 + 0.518686i \(0.173579\pi\)
\(198\) 0 0
\(199\) −5.00000 8.66025i −0.354441 0.613909i 0.632581 0.774494i \(-0.281995\pi\)
−0.987022 + 0.160585i \(0.948662\pi\)
\(200\) −2.00000 3.46410i −0.141421 0.244949i
\(201\) 0 0
\(202\) 8.00000 0.562878
\(203\) −15.0000 + 5.19615i −1.05279 + 0.364698i
\(204\) 0 0
\(205\) −7.50000 + 12.9904i −0.523823 + 0.907288i
\(206\) 1.00000 + 1.73205i 0.0696733 + 0.120678i
\(207\) 0 0
\(208\) −3.00000 + 5.19615i −0.208013 + 0.360288i
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) 14.0000 0.963800 0.481900 0.876226i \(-0.339947\pi\)
0.481900 + 0.876226i \(0.339947\pi\)
\(212\) 1.00000 1.73205i 0.0686803 0.118958i
\(213\) 0 0
\(214\) −6.50000 11.2583i −0.444331 0.769604i
\(215\) −15.0000 + 25.9808i −1.02299 + 1.77187i
\(216\) 0 0
\(217\) 8.00000 + 6.92820i 0.543075 + 0.470317i
\(218\) −11.0000 −0.745014
\(219\) 0 0
\(220\) 1.50000 + 2.59808i 0.101130 + 0.175162i
\(221\) −15.0000 25.9808i −1.00901 1.74766i
\(222\) 0 0
\(223\) 16.0000 1.07144 0.535720 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 2.00000 + 1.73205i 0.133631 + 0.115728i
\(225\) 0 0
\(226\) 5.00000 8.66025i 0.332595 0.576072i
\(227\) 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i \(-0.134924\pi\)
−0.811943 + 0.583736i \(0.801590\pi\)
\(228\) 0 0
\(229\) −13.0000 + 22.5167i −0.859064 + 1.48794i 0.0137585 + 0.999905i \(0.495620\pi\)
−0.872823 + 0.488037i \(0.837713\pi\)
\(230\) 15.0000 0.989071
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) −14.5000 + 25.1147i −0.949927 + 1.64532i −0.204354 + 0.978897i \(0.565509\pi\)
−0.745573 + 0.666424i \(0.767824\pi\)
\(234\) 0 0
\(235\) −13.5000 23.3827i −0.880643 1.52532i
\(236\) −6.00000 + 10.3923i −0.390567 + 0.676481i
\(237\) 0 0
\(238\) −12.5000 + 4.33013i −0.810255 + 0.280680i
\(239\) −26.0000 −1.68180 −0.840900 0.541190i \(-0.817974\pi\)
−0.840900 + 0.541190i \(0.817974\pi\)
\(240\) 0 0
\(241\) 13.0000 + 22.5167i 0.837404 + 1.45043i 0.892058 + 0.451920i \(0.149261\pi\)
−0.0546547 + 0.998505i \(0.517406\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) 0 0
\(244\) −5.00000 −0.320092
\(245\) −3.00000 20.7846i −0.191663 1.32788i
\(246\) 0 0
\(247\) −18.0000 + 31.1769i −1.14531 + 1.98374i
\(248\) −2.00000 3.46410i −0.127000 0.219971i
\(249\) 0 0
\(250\) −1.50000 + 2.59808i −0.0948683 + 0.164317i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) −5.00000 −0.314347
\(254\) −2.50000 + 4.33013i −0.156864 + 0.271696i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −7.00000 + 12.1244i −0.436648 + 0.756297i −0.997429 0.0716680i \(-0.977168\pi\)
0.560781 + 0.827964i \(0.310501\pi\)
\(258\) 0 0
\(259\) −1.00000 + 5.19615i −0.0621370 + 0.322873i
\(260\) −18.0000 −1.11631
\(261\) 0 0
\(262\) −2.00000 3.46410i −0.123560 0.214013i
\(263\) 12.0000 + 20.7846i 0.739952 + 1.28163i 0.952517 + 0.304487i \(0.0984850\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) 12.0000 + 10.3923i 0.735767 + 0.637193i
\(267\) 0 0
\(268\) −2.50000 + 4.33013i −0.152712 + 0.264505i
\(269\) −4.50000 7.79423i −0.274370 0.475223i 0.695606 0.718423i \(-0.255136\pi\)
−0.969976 + 0.243201i \(0.921803\pi\)
\(270\) 0 0
\(271\) 12.0000 20.7846i 0.728948 1.26258i −0.228380 0.973572i \(-0.573343\pi\)
0.957328 0.289003i \(-0.0933238\pi\)
\(272\) 5.00000 0.303170
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) −2.00000 + 3.46410i −0.120605 + 0.208893i
\(276\) 0 0
\(277\) −9.00000 15.5885i −0.540758 0.936620i −0.998861 0.0477206i \(-0.984804\pi\)
0.458103 0.888899i \(-0.348529\pi\)
\(278\) −11.0000 + 19.0526i −0.659736 + 1.14270i
\(279\) 0 0
\(280\) −1.50000 + 7.79423i −0.0896421 + 0.465794i
\(281\) −11.0000 −0.656205 −0.328102 0.944642i \(-0.606409\pi\)
−0.328102 + 0.944642i \(0.606409\pi\)
\(282\) 0 0
\(283\) 3.00000 + 5.19615i 0.178331 + 0.308879i 0.941309 0.337546i \(-0.109597\pi\)
−0.762978 + 0.646425i \(0.776263\pi\)
\(284\) 2.00000 + 3.46410i 0.118678 + 0.205557i
\(285\) 0 0
\(286\) 6.00000 0.354787
\(287\) 12.5000 4.33013i 0.737852 0.255599i
\(288\) 0 0
\(289\) −4.00000 + 6.92820i −0.235294 + 0.407541i
\(290\) 9.00000 + 15.5885i 0.528498 + 0.915386i
\(291\) 0 0
\(292\) −6.00000 + 10.3923i −0.351123 + 0.608164i
\(293\) −8.00000 −0.467365 −0.233682 0.972313i \(-0.575078\pi\)
−0.233682 + 0.972313i \(0.575078\pi\)
\(294\) 0 0
\(295\) −36.0000 −2.09600
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) 0 0
\(298\) 9.00000 + 15.5885i 0.521356 + 0.903015i
\(299\) 15.0000 25.9808i 0.867472 1.50251i
\(300\) 0 0
\(301\) 25.0000 8.66025i 1.44098 0.499169i
\(302\) 9.00000 0.517892
\(303\) 0 0
\(304\) −3.00000 5.19615i −0.172062 0.298020i
\(305\) −7.50000 12.9904i −0.429449 0.743827i
\(306\) 0 0
\(307\) 18.0000 1.02731 0.513657 0.857996i \(-0.328290\pi\)
0.513657 + 0.857996i \(0.328290\pi\)
\(308\) 0.500000 2.59808i 0.0284901 0.148039i
\(309\) 0 0
\(310\) 6.00000 10.3923i 0.340777 0.590243i
\(311\) −10.5000 18.1865i −0.595400 1.03126i −0.993490 0.113917i \(-0.963660\pi\)
0.398090 0.917346i \(-0.369673\pi\)
\(312\) 0 0
\(313\) 3.00000 5.19615i 0.169570 0.293704i −0.768699 0.639611i \(-0.779095\pi\)
0.938269 + 0.345907i \(0.112429\pi\)
\(314\) −24.0000 −1.35440
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) 4.50000 7.79423i 0.252745 0.437767i −0.711535 0.702650i \(-0.752000\pi\)
0.964281 + 0.264883i \(0.0853332\pi\)
\(318\) 0 0
\(319\) −3.00000 5.19615i −0.167968 0.290929i
\(320\) 1.50000 2.59808i 0.0838525 0.145237i
\(321\) 0 0
\(322\) −10.0000 8.66025i −0.557278 0.482617i
\(323\) 30.0000 1.66924
\(324\) 0 0
\(325\) −12.0000 20.7846i −0.665640 1.15292i
\(326\) 0.500000 + 0.866025i 0.0276924 + 0.0479647i
\(327\) 0 0
\(328\) −5.00000 −0.276079
\(329\) −4.50000 + 23.3827i −0.248093 + 1.28913i
\(330\) 0 0
\(331\) −17.5000 + 30.3109i −0.961887 + 1.66604i −0.244131 + 0.969742i \(0.578503\pi\)
−0.717756 + 0.696295i \(0.754831\pi\)
\(332\) 0.500000 + 0.866025i 0.0274411 + 0.0475293i
\(333\) 0 0
\(334\) −12.0000 + 20.7846i −0.656611 + 1.13728i
\(335\) −15.0000 −0.819538
\(336\) 0 0
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) −11.5000 + 19.9186i −0.625518 + 1.08343i
\(339\) 0 0
\(340\) 7.50000 + 12.9904i 0.406745 + 0.704502i
\(341\) −2.00000 + 3.46410i −0.108306 + 0.187592i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) −10.0000 −0.539164
\(345\) 0 0
\(346\) −6.00000 10.3923i −0.322562 0.558694i
\(347\) 3.50000 + 6.06218i 0.187890 + 0.325435i 0.944547 0.328378i \(-0.106502\pi\)
−0.756657 + 0.653812i \(0.773169\pi\)
\(348\) 0 0
\(349\) −19.0000 −1.01705 −0.508523 0.861048i \(-0.669808\pi\)
−0.508523 + 0.861048i \(0.669808\pi\)
\(350\) −10.0000 + 3.46410i −0.534522 + 0.185164i
\(351\) 0 0
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 12.0000 + 20.7846i 0.638696 + 1.10625i 0.985719 + 0.168397i \(0.0538590\pi\)
−0.347024 + 0.937856i \(0.612808\pi\)
\(354\) 0 0
\(355\) −6.00000 + 10.3923i −0.318447 + 0.551566i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 8.00000 0.422813
\(359\) −5.00000 + 8.66025i −0.263890 + 0.457071i −0.967272 0.253741i \(-0.918339\pi\)
0.703382 + 0.710812i \(0.251672\pi\)
\(360\) 0 0
\(361\) −8.50000 14.7224i −0.447368 0.774865i
\(362\) 11.0000 19.0526i 0.578147 1.00138i
\(363\) 0 0
\(364\) 12.0000 + 10.3923i 0.628971 + 0.544705i
\(365\) −36.0000 −1.88433
\(366\) 0 0
\(367\) 7.00000 + 12.1244i 0.365397 + 0.632886i 0.988840 0.148983i \(-0.0475999\pi\)
−0.623443 + 0.781869i \(0.714267\pi\)
\(368\) 2.50000 + 4.33013i 0.130322 + 0.225723i
\(369\) 0 0
\(370\) 6.00000 0.311925
\(371\) −4.00000 3.46410i −0.207670 0.179847i
\(372\) 0 0
\(373\) 3.50000 6.06218i 0.181223 0.313888i −0.761074 0.648665i \(-0.775328\pi\)
0.942297 + 0.334777i \(0.108661\pi\)
\(374\) −2.50000 4.33013i −0.129272 0.223906i
\(375\) 0 0
\(376\) 4.50000 7.79423i 0.232070 0.401957i
\(377\) 36.0000 1.85409
\(378\) 0 0
\(379\) 13.0000 0.667765 0.333883 0.942615i \(-0.391641\pi\)
0.333883 + 0.942615i \(0.391641\pi\)
\(380\) 9.00000 15.5885i 0.461690 0.799671i
\(381\) 0 0
\(382\) 0 0
\(383\) 4.00000 6.92820i 0.204390 0.354015i −0.745548 0.666452i \(-0.767812\pi\)
0.949938 + 0.312437i \(0.101145\pi\)
\(384\) 0 0
\(385\) 7.50000 2.59808i 0.382235 0.132410i
\(386\) 6.00000 0.305392
\(387\) 0 0
\(388\) −4.50000 7.79423i −0.228453 0.395692i
\(389\) −10.5000 18.1865i −0.532371 0.922094i −0.999286 0.0377914i \(-0.987968\pi\)
0.466915 0.884302i \(-0.345366\pi\)
\(390\) 0 0
\(391\) −25.0000 −1.26430
\(392\) 5.50000 4.33013i 0.277792 0.218704i
\(393\) 0 0
\(394\) −12.0000 + 20.7846i −0.604551 + 1.04711i
\(395\) −1.50000 2.59808i −0.0754732 0.130723i
\(396\) 0 0
\(397\) −13.0000 + 22.5167i −0.652451 + 1.13008i 0.330075 + 0.943955i \(0.392926\pi\)
−0.982526 + 0.186124i \(0.940407\pi\)
\(398\) 10.0000 0.501255
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) −3.00000 + 5.19615i −0.149813 + 0.259483i −0.931158 0.364615i \(-0.881200\pi\)
0.781345 + 0.624099i \(0.214534\pi\)
\(402\) 0 0
\(403\) −12.0000 20.7846i −0.597763 1.03536i
\(404\) −4.00000 + 6.92820i −0.199007 + 0.344691i
\(405\) 0 0
\(406\) 3.00000 15.5885i 0.148888 0.773642i
\(407\) −2.00000 −0.0991363
\(408\) 0 0
\(409\) −5.00000 8.66025i −0.247234 0.428222i 0.715523 0.698589i \(-0.246188\pi\)
−0.962757 + 0.270367i \(0.912855\pi\)
\(410\) −7.50000 12.9904i −0.370399 0.641549i
\(411\) 0 0
\(412\) −2.00000 −0.0985329
\(413\) 24.0000 + 20.7846i 1.18096 + 1.02274i
\(414\) 0 0
\(415\) −1.50000 + 2.59808i −0.0736321 + 0.127535i
\(416\) −3.00000 5.19615i −0.147087 0.254762i
\(417\) 0 0
\(418\) −3.00000 + 5.19615i −0.146735 + 0.254152i
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 0 0
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) −7.00000 + 12.1244i −0.340755 + 0.590204i
\(423\) 0 0
\(424\) 1.00000 + 1.73205i 0.0485643 + 0.0841158i
\(425\) −10.0000 + 17.3205i −0.485071 + 0.840168i
\(426\) 0 0
\(427\) −2.50000 + 12.9904i −0.120983 + 0.628649i
\(428\) 13.0000 0.628379
\(429\) 0 0
\(430\) −15.0000 25.9808i −0.723364 1.25290i
\(431\) 11.0000 + 19.0526i 0.529851 + 0.917729i 0.999394 + 0.0348195i \(0.0110856\pi\)
−0.469542 + 0.882910i \(0.655581\pi\)
\(432\) 0 0
\(433\) 11.0000 0.528626 0.264313 0.964437i \(-0.414855\pi\)
0.264313 + 0.964437i \(0.414855\pi\)
\(434\) −10.0000 + 3.46410i −0.480015 + 0.166282i
\(435\) 0 0
\(436\) 5.50000 9.52628i 0.263402 0.456226i
\(437\) 15.0000 + 25.9808i 0.717547 + 1.24283i
\(438\) 0 0
\(439\) 2.50000 4.33013i 0.119318 0.206666i −0.800179 0.599761i \(-0.795262\pi\)
0.919498 + 0.393095i \(0.128596\pi\)
\(440\) −3.00000 −0.143019
\(441\) 0 0
\(442\) 30.0000 1.42695
\(443\) 1.00000 1.73205i 0.0475114 0.0822922i −0.841292 0.540581i \(-0.818204\pi\)
0.888803 + 0.458289i \(0.151538\pi\)
\(444\) 0 0
\(445\) −9.00000 15.5885i −0.426641 0.738964i
\(446\) −8.00000 + 13.8564i −0.378811 + 0.656120i
\(447\) 0 0
\(448\) −2.50000 + 0.866025i −0.118114 + 0.0409159i
\(449\) −2.00000 −0.0943858 −0.0471929 0.998886i \(-0.515028\pi\)
−0.0471929 + 0.998886i \(0.515028\pi\)
\(450\) 0 0
\(451\) 2.50000 + 4.33013i 0.117720 + 0.203898i
\(452\) 5.00000 + 8.66025i 0.235180 + 0.407344i
\(453\) 0 0
\(454\) −3.00000 −0.140797
\(455\) −9.00000 + 46.7654i −0.421927 + 2.19239i
\(456\) 0 0
\(457\) 13.0000 22.5167i 0.608114 1.05328i −0.383437 0.923567i \(-0.625260\pi\)
0.991551 0.129718i \(-0.0414071\pi\)
\(458\) −13.0000 22.5167i −0.607450 1.05213i
\(459\) 0 0
\(460\) −7.50000 + 12.9904i −0.349689 + 0.605680i
\(461\) 10.0000 0.465746 0.232873 0.972507i \(-0.425187\pi\)
0.232873 + 0.972507i \(0.425187\pi\)
\(462\) 0 0
\(463\) 28.0000 1.30127 0.650635 0.759390i \(-0.274503\pi\)
0.650635 + 0.759390i \(0.274503\pi\)
\(464\) −3.00000 + 5.19615i −0.139272 + 0.241225i
\(465\) 0 0
\(466\) −14.5000 25.1147i −0.671700 1.16342i
\(467\) 8.00000 13.8564i 0.370196 0.641198i −0.619400 0.785076i \(-0.712624\pi\)
0.989595 + 0.143878i \(0.0459572\pi\)
\(468\) 0 0
\(469\) 10.0000 + 8.66025i 0.461757 + 0.399893i
\(470\) 27.0000 1.24542
\(471\) 0 0
\(472\) −6.00000 10.3923i −0.276172 0.478345i
\(473\) 5.00000 + 8.66025i 0.229900 + 0.398199i
\(474\) 0 0
\(475\) 24.0000 1.10120
\(476\) 2.50000 12.9904i 0.114587 0.595413i
\(477\) 0 0
\(478\) 13.0000 22.5167i 0.594606 1.02989i
\(479\) 6.00000 + 10.3923i 0.274147 + 0.474837i 0.969920 0.243426i \(-0.0782712\pi\)
−0.695773 + 0.718262i \(0.744938\pi\)
\(480\) 0 0
\(481\) 6.00000 10.3923i 0.273576 0.473848i
\(482\) −26.0000 −1.18427
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 13.5000 23.3827i 0.613003 1.06175i
\(486\) 0 0
\(487\) 2.00000 + 3.46410i 0.0906287 + 0.156973i 0.907776 0.419456i \(-0.137779\pi\)
−0.817147 + 0.576429i \(0.804446\pi\)
\(488\) 2.50000 4.33013i 0.113170 0.196016i
\(489\) 0 0
\(490\) 19.5000 + 7.79423i 0.880920 + 0.352107i
\(491\) 3.00000 0.135388 0.0676941 0.997706i \(-0.478436\pi\)
0.0676941 + 0.997706i \(0.478436\pi\)
\(492\) 0 0
\(493\) −15.0000 25.9808i −0.675566 1.17011i
\(494\) −18.0000 31.1769i −0.809858 1.40272i
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) 10.0000 3.46410i 0.448561 0.155386i
\(498\) 0 0
\(499\) −6.00000 + 10.3923i −0.268597 + 0.465223i −0.968500 0.249015i \(-0.919893\pi\)
0.699903 + 0.714238i \(0.253227\pi\)
\(500\) −1.50000 2.59808i −0.0670820 0.116190i
\(501\) 0 0
\(502\) 6.00000 10.3923i 0.267793 0.463831i
\(503\) 42.0000 1.87269 0.936344 0.351085i \(-0.114187\pi\)
0.936344 + 0.351085i \(0.114187\pi\)
\(504\) 0 0
\(505\) −24.0000 −1.06799
\(506\) 2.50000 4.33013i 0.111139 0.192498i
\(507\) 0 0
\(508\) −2.50000 4.33013i −0.110920 0.192118i
\(509\) 1.00000 1.73205i 0.0443242 0.0767718i −0.843012 0.537895i \(-0.819220\pi\)
0.887336 + 0.461123i \(0.152553\pi\)
\(510\) 0 0
\(511\) 24.0000 + 20.7846i 1.06170 + 0.919457i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −7.00000 12.1244i −0.308757 0.534782i
\(515\) −3.00000 5.19615i −0.132196 0.228970i
\(516\) 0 0
\(517\) −9.00000 −0.395820
\(518\) −4.00000 3.46410i −0.175750 0.152204i
\(519\) 0 0
\(520\) 9.00000 15.5885i 0.394676 0.683599i
\(521\) 1.00000 + 1.73205i 0.0438108 + 0.0758825i 0.887099 0.461579i \(-0.152717\pi\)
−0.843288 + 0.537461i \(0.819383\pi\)
\(522\) 0 0
\(523\) −3.00000 + 5.19615i −0.131181 + 0.227212i −0.924132 0.382073i \(-0.875210\pi\)
0.792951 + 0.609285i \(0.208544\pi\)
\(524\) 4.00000 0.174741
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) −10.0000 + 17.3205i −0.435607 + 0.754493i
\(528\) 0 0
\(529\) −1.00000 1.73205i −0.0434783 0.0753066i
\(530\) −3.00000 + 5.19615i −0.130312 + 0.225706i
\(531\) 0 0
\(532\) −15.0000 + 5.19615i −0.650332 + 0.225282i
\(533\) −30.0000 −1.29944
\(534\) 0 0
\(535\) 19.5000 + 33.7750i 0.843059 + 1.46022i
\(536\) −2.50000 4.33013i −0.107984 0.187033i
\(537\) 0 0
\(538\) 9.00000 0.388018
\(539\) −6.50000 2.59808i −0.279975 0.111907i
\(540\) 0 0
\(541\) 19.5000 33.7750i 0.838370 1.45210i −0.0528859 0.998601i \(-0.516842\pi\)
0.891256 0.453500i \(-0.149825\pi\)
\(542\) 12.0000 + 20.7846i 0.515444 + 0.892775i
\(543\) 0 0
\(544\) −2.50000 + 4.33013i −0.107187 + 0.185653i
\(545\) 33.0000 1.41356
\(546\) 0 0
\(547\) −42.0000 −1.79579 −0.897895 0.440209i \(-0.854904\pi\)
−0.897895 + 0.440209i \(0.854904\pi\)
\(548\) −1.00000 + 1.73205i −0.0427179 + 0.0739895i
\(549\) 0 0
\(550\) −2.00000 3.46410i −0.0852803 0.147710i
\(551\) −18.0000 + 31.1769i −0.766826 + 1.32818i
\(552\) 0 0
\(553\) −0.500000 + 2.59808i −0.0212622 + 0.110481i
\(554\) 18.0000 0.764747
\(555\) 0 0
\(556\) −11.0000 19.0526i −0.466504 0.808008i
\(557\) −16.0000 27.7128i −0.677942 1.17423i −0.975600 0.219557i \(-0.929539\pi\)
0.297658 0.954673i \(-0.403795\pi\)
\(558\) 0 0
\(559\) −60.0000 −2.53773
\(560\) −6.00000 5.19615i −0.253546 0.219578i
\(561\) 0 0
\(562\) 5.50000 9.52628i 0.232003 0.401842i
\(563\) −8.00000 13.8564i −0.337160 0.583978i 0.646737 0.762713i \(-0.276133\pi\)
−0.983897 + 0.178735i \(0.942800\pi\)
\(564\) 0 0
\(565\) −15.0000 + 25.9808i −0.631055 + 1.09302i
\(566\) −6.00000 −0.252199
\(567\) 0 0
\(568\) −4.00000 −0.167836
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) 0 0
\(571\) 17.0000 + 29.4449i 0.711428 + 1.23223i 0.964321 + 0.264735i \(0.0852845\pi\)
−0.252893 + 0.967494i \(0.581382\pi\)
\(572\) −3.00000 + 5.19615i −0.125436 + 0.217262i
\(573\) 0 0
\(574\) −2.50000 + 12.9904i −0.104348 + 0.542208i
\(575\) −20.0000 −0.834058
\(576\) 0 0
\(577\) 3.50000 + 6.06218i 0.145707 + 0.252372i 0.929636 0.368478i \(-0.120121\pi\)
−0.783930 + 0.620850i \(0.786788\pi\)
\(578\) −4.00000 6.92820i −0.166378 0.288175i
\(579\) 0 0
\(580\) −18.0000 −0.747409
\(581\) 2.50000 0.866025i 0.103717 0.0359288i
\(582\) 0 0
\(583\) 1.00000 1.73205i 0.0414158 0.0717342i
\(584\) −6.00000 10.3923i −0.248282 0.430037i
\(585\) 0 0
\(586\) 4.00000 6.92820i 0.165238 0.286201i
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 0 0
\(589\) 24.0000 0.988903
\(590\) 18.0000 31.1769i 0.741048 1.28353i
\(591\) 0 0
\(592\) 1.00000 + 1.73205i 0.0410997 + 0.0711868i
\(593\) 7.00000 12.1244i 0.287456 0.497888i −0.685746 0.727841i \(-0.740524\pi\)
0.973202 + 0.229953i \(0.0738573\pi\)
\(594\) 0 0
\(595\) 37.5000 12.9904i 1.53735 0.532554i
\(596\) −18.0000 −0.737309
\(597\) 0 0
\(598\) 15.0000 + 25.9808i 0.613396 + 1.06243i
\(599\) −1.50000 2.59808i −0.0612883 0.106155i 0.833753 0.552137i \(-0.186188\pi\)
−0.895042 + 0.445983i \(0.852854\pi\)
\(600\) 0 0
\(601\) −44.0000 −1.79480 −0.897399 0.441221i \(-0.854546\pi\)
−0.897399 + 0.441221i \(0.854546\pi\)
\(602\) −5.00000 + 25.9808i −0.203785 + 1.05890i
\(603\) 0 0
\(604\) −4.50000 + 7.79423i −0.183102 + 0.317143i
\(605\) 1.50000 + 2.59808i 0.0609837 + 0.105627i
\(606\) 0 0
\(607\) −16.5000 + 28.5788i −0.669714 + 1.15998i 0.308270 + 0.951299i \(0.400250\pi\)
−0.977984 + 0.208680i \(0.933083\pi\)
\(608\) 6.00000 0.243332
\(609\) 0 0
\(610\) 15.0000 0.607332
\(611\) 27.0000 46.7654i 1.09230 1.89192i
\(612\) 0 0
\(613\) 20.5000 + 35.5070i 0.827987 + 1.43412i 0.899615 + 0.436684i \(0.143847\pi\)
−0.0716275 + 0.997431i \(0.522819\pi\)
\(614\) −9.00000 + 15.5885i −0.363210 + 0.629099i
\(615\) 0 0
\(616\) 2.00000 + 1.73205i 0.0805823 + 0.0697863i
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) 14.5000 + 25.1147i 0.582804 + 1.00945i 0.995145 + 0.0984169i \(0.0313779\pi\)
−0.412341 + 0.911030i \(0.635289\pi\)
\(620\) 6.00000 + 10.3923i 0.240966 + 0.417365i
\(621\) 0 0
\(622\) 21.0000 0.842023
\(623\) −3.00000 + 15.5885i −0.120192 + 0.624538i
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 3.00000 + 5.19615i 0.119904 + 0.207680i
\(627\) 0 0
\(628\) 12.0000 20.7846i 0.478852 0.829396i
\(629\) −10.0000 −0.398726
\(630\) 0 0
\(631\) 28.0000 1.11466 0.557331 0.830290i \(-0.311825\pi\)
0.557331 + 0.830290i \(0.311825\pi\)
\(632\) 0.500000 0.866025i 0.0198889 0.0344486i
\(633\) 0 0
\(634\) 4.50000 + 7.79423i 0.178718 + 0.309548i
\(635\) 7.50000 12.9904i 0.297628 0.515508i
\(636\) 0 0
\(637\) 33.0000 25.9808i 1.30751 1.02940i
\(638\) 6.00000 0.237542
\(639\) 0 0
\(640\) 1.50000 + 2.59808i 0.0592927 + 0.102698i
\(641\) −20.0000 34.6410i −0.789953 1.36824i −0.925995 0.377535i \(-0.876772\pi\)
0.136043 0.990703i \(-0.456562\pi\)
\(642\) 0 0
\(643\) 36.0000 1.41970 0.709851 0.704352i \(-0.248762\pi\)
0.709851 + 0.704352i \(0.248762\pi\)
\(644\) 12.5000 4.33013i 0.492569 0.170631i
\(645\) 0 0
\(646\) −15.0000 + 25.9808i −0.590167 + 1.02220i
\(647\) 8.50000 + 14.7224i 0.334169 + 0.578799i 0.983325 0.181857i \(-0.0582109\pi\)
−0.649155 + 0.760656i \(0.724878\pi\)
\(648\) 0 0
\(649\) −6.00000 + 10.3923i −0.235521 + 0.407934i
\(650\) 24.0000 0.941357
\(651\) 0 0
\(652\) −1.00000 −0.0391630
\(653\) −13.5000 + 23.3827i −0.528296 + 0.915035i 0.471160 + 0.882048i \(0.343835\pi\)
−0.999456 + 0.0329874i \(0.989498\pi\)
\(654\) 0 0
\(655\) 6.00000 + 10.3923i 0.234439 + 0.406061i
\(656\) 2.50000 4.33013i 0.0976086 0.169063i
\(657\) 0 0
\(658\) −18.0000 15.5885i −0.701713 0.607701i
\(659\) −31.0000 −1.20759 −0.603794 0.797140i \(-0.706345\pi\)
−0.603794 + 0.797140i \(0.706345\pi\)
\(660\) 0 0
\(661\) −2.00000 3.46410i −0.0777910 0.134738i 0.824506 0.565854i \(-0.191453\pi\)
−0.902297 + 0.431116i \(0.858120\pi\)
\(662\) −17.5000 30.3109i −0.680157 1.17807i
\(663\) 0 0
\(664\) −1.00000 −0.0388075
\(665\) −36.0000 31.1769i −1.39602 1.20899i
\(666\) 0 0
\(667\) 15.0000 25.9808i 0.580802 1.00598i
\(668\) −12.0000 20.7846i −0.464294 0.804181i
\(669\) 0 0
\(670\) 7.50000 12.9904i 0.289750 0.501862i
\(671\) −5.00000 −0.193023
\(672\) 0 0
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) 1.00000 1.73205i 0.0385186 0.0667161i
\(675\) 0 0
\(676\) −11.5000 19.9186i −0.442308 0.766099i
\(677\) −9.00000 + 15.5885i −0.345898 + 0.599113i −0.985517 0.169580i \(-0.945759\pi\)
0.639618 + 0.768693i \(0.279092\pi\)
\(678\) 0 0
\(679\) −22.5000 + 7.79423i −0.863471 + 0.299115i
\(680\) −15.0000 −0.575224
\(681\) 0 0
\(682\) −2.00000 3.46410i −0.0765840 0.132647i
\(683\) −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) 0 0
\(685\) −6.00000 −0.229248
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 0 0
\(688\) 5.00000 8.66025i 0.190623 0.330169i
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) 0 0
\(691\) 13.5000 23.3827i 0.513564 0.889519i −0.486312 0.873785i \(-0.661658\pi\)
0.999876 0.0157341i \(-0.00500851\pi\)
\(692\) 12.0000 0.456172
\(693\) 0 0
\(694\) −7.00000 −0.265716
\(695\) 33.0000 57.1577i 1.25176 2.16811i
\(696\) 0 0
\(697\) 12.5000 + 21.6506i 0.473471 + 0.820076i
\(698\) 9.50000 16.4545i 0.359580 0.622811i
\(699\) 0 0
\(700\) 2.00000 10.3923i 0.0755929 0.392792i
\(701\) 10.0000 0.377695 0.188847 0.982006i \(-0.439525\pi\)
0.188847 + 0.982006i \(0.439525\pi\)
\(702\) 0 0
\(703\) 6.00000 + 10.3923i 0.226294 + 0.391953i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 0 0
\(706\) −24.0000 −0.903252
\(707\) 16.0000 + 13.8564i 0.601742 + 0.521124i
\(708\) 0 0
\(709\) −10.0000 + 17.3205i −0.375558 + 0.650485i −0.990410 0.138157i \(-0.955882\pi\)
0.614852 + 0.788642i \(0.289216\pi\)
\(710\) −6.00000 10.3923i −0.225176 0.390016i
\(711\) 0 0
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) −20.0000 −0.749006
\(714\) 0 0
\(715\) −18.0000 −0.673162
\(716\) −4.00000 + 6.92820i −0.149487 + 0.258919i
\(717\) 0 0
\(718\) −5.00000 8.66025i −0.186598 0.323198i
\(719\) 18.5000 32.0429i 0.689934 1.19500i −0.281925 0.959436i \(-0.590973\pi\)
0.971859 0.235564i \(-0.0756936\pi\)
\(720\) 0 0
\(721\) −1.00000 + 5.19615i −0.0372419 + 0.193515i
\(722\) 17.0000 0.632674
\(723\) 0 0
\(724\) 11.0000 + 19.0526i 0.408812 + 0.708083i
\(725\) −12.0000 20.7846i −0.445669 0.771921i
\(726\) 0 0
\(727\) 22.0000 0.815935 0.407967 0.912996i \(-0.366238\pi\)
0.407967 + 0.912996i \(0.366238\pi\)
\(728\) −15.0000 + 5.19615i −0.555937 + 0.192582i
\(729\) 0 0
\(730\) 18.0000 31.1769i 0.666210 1.15391i
\(731\) 25.0000 + 43.3013i 0.924658 + 1.60156i
\(732\) 0 0
\(733\) 7.50000 12.9904i 0.277019 0.479811i −0.693624 0.720338i \(-0.743987\pi\)
0.970642 + 0.240527i \(0.0773202\pi\)
\(734\) −14.0000 −0.516749
\(735\) 0 0
\(736\) −5.00000 −0.184302
\(737\) −2.50000 + 4.33013i −0.0920887 + 0.159502i
\(738\) 0 0
\(739\) 5.00000 + 8.66025i 0.183928 + 0.318573i 0.943215 0.332184i \(-0.107785\pi\)
−0.759287 + 0.650756i \(0.774452\pi\)
\(740\) −3.00000 + 5.19615i −0.110282 + 0.191014i
\(741\) 0 0
\(742\) 5.00000 1.73205i 0.183556 0.0635856i
\(743\) −22.0000 −0.807102 −0.403551 0.914957i \(-0.632224\pi\)
−0.403551 + 0.914957i \(0.632224\pi\)
\(744\) 0 0
\(745\) −27.0000 46.7654i −0.989203 1.71335i
\(746\) 3.50000 + 6.06218i 0.128144 + 0.221952i
\(747\) 0 0
\(748\) 5.00000 0.182818
\(749\) 6.50000 33.7750i 0.237505 1.23411i
\(750\) 0 0
\(751\) 1.00000 1.73205i 0.0364905 0.0632034i −0.847203 0.531269i \(-0.821715\pi\)
0.883694 + 0.468065i \(0.155049\pi\)
\(752\) 4.50000 + 7.79423i 0.164098 + 0.284226i
\(753\) 0 0
\(754\) −18.0000 + 31.1769i −0.655521 + 1.13540i
\(755\) −27.0000 −0.982631
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −6.50000 + 11.2583i −0.236091 + 0.408921i
\(759\) 0 0
\(760\) 9.00000 + 15.5885i 0.326464 + 0.565453i
\(761\) 23.5000 40.7032i 0.851874 1.47549i −0.0276404 0.999618i \(-0.508799\pi\)
0.879515 0.475872i \(-0.157867\pi\)
\(762\) 0 0
\(763\) −22.0000 19.0526i −0.796453 0.689749i
\(764\) 0 0
\(765\) 0 0
\(766\) 4.00000 + 6.92820i 0.144526 + 0.250326i
\(767\) −36.0000 62.3538i −1.29988 2.25147i
\(768\) 0 0
\(769\) 46.0000 1.65880 0.829401 0.558653i \(-0.188682\pi\)
0.829401 + 0.558653i \(0.188682\pi\)
\(770\) −1.50000 + 7.79423i −0.0540562 + 0.280885i
\(771\) 0 0
\(772\) −3.00000 + 5.19615i −0.107972 + 0.187014i
\(773\) 5.50000 + 9.52628i 0.197821 + 0.342636i 0.947822 0.318801i \(-0.103280\pi\)
−0.750000 + 0.661437i \(0.769947\pi\)
\(774\) 0 0
\(775\) −8.00000 + 13.8564i −0.287368 + 0.497737i
\(776\) 9.00000 0.323081
\(777\) 0 0
\(778\) 21.0000 0.752886
\(779\) 15.0000 25.9808i 0.537431 0.930857i
\(780\) 0 0
\(781\) 2.00000 + 3.46410i 0.0715656 + 0.123955i
\(782\) 12.5000 21.6506i 0.446999 0.774225i
\(783\) 0 0
\(784\) 1.00000 + 6.92820i 0.0357143 + 0.247436i
\(785\) 72.0000 2.56979
\(786\) 0 0
\(787\) 25.0000 + 43.3013i 0.891154 + 1.54352i 0.838494 + 0.544911i \(0.183437\pi\)
0.0526599 + 0.998613i \(0.483230\pi\)
\(788\) −12.0000 20.7846i −0.427482 0.740421i
\(789\)