Properties

Label 1386.2.k.w.991.3
Level $1386$
Weight $2$
Character 1386.991
Analytic conductor $11.067$
Analytic rank $0$
Dimension $6$
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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1156923.1
Defining polynomial: \(x^{6} - 3 x^{5} + 12 x^{4} - 19 x^{3} + 27 x^{2} - 18 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 462)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.3
Root \(0.500000 - 0.0585812i\) of defining polynomial
Character \(\chi\) \(=\) 1386.991
Dual form 1386.2.k.w.793.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.37328 + 2.37860i) q^{5} +(-1.37328 + 2.26144i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.37328 + 2.37860i) q^{5} +(-1.37328 + 2.26144i) q^{7} -1.00000 q^{8} +(-1.37328 + 2.37860i) q^{10} +(0.500000 - 0.866025i) q^{11} +5.49314 q^{13} +(-2.64510 - 0.0585812i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{17} +(4.01839 + 6.96005i) q^{19} -2.74657 q^{20} +1.00000 q^{22} +(-0.645103 - 1.11735i) q^{23} +(-1.27182 + 2.20285i) q^{25} +(2.74657 + 4.75720i) q^{26} +(-1.27182 - 2.32002i) q^{28} -4.54364 q^{29} +(-2.54364 + 4.40571i) q^{31} +(0.500000 - 0.866025i) q^{32} +1.00000 q^{34} +(-7.26496 - 0.160897i) q^{35} +(2.01839 + 3.49595i) q^{37} +(-4.01839 + 6.96005i) q^{38} +(-1.37328 - 2.37860i) q^{40} -5.54364 q^{41} -4.03677 q^{43} +(0.500000 + 0.866025i) q^{44} +(0.645103 - 1.11735i) q^{46} +(-4.64510 - 8.04555i) q^{47} +(-3.22818 - 6.21119i) q^{49} -2.54364 q^{50} +(-2.74657 + 4.75720i) q^{52} +(2.74657 - 4.75720i) q^{53} +2.74657 q^{55} +(1.37328 - 2.26144i) q^{56} +(-2.27182 - 3.93491i) q^{58} +(-4.76496 + 8.25314i) q^{59} +(0.829647 + 1.43699i) q^{61} -5.08727 q^{62} +1.00000 q^{64} +(7.54364 + 13.0660i) q^{65} +(-1.77182 + 3.06888i) q^{67} +(0.500000 + 0.866025i) q^{68} +(-3.49314 - 6.37208i) q^{70} -2.54364 q^{71} +(4.29021 - 7.43085i) q^{73} +(-2.01839 + 3.49595i) q^{74} -8.03677 q^{76} +(1.27182 + 2.32002i) q^{77} +(-6.11985 - 10.5999i) q^{79} +(1.37328 - 2.37860i) q^{80} +(-2.77182 - 4.80093i) q^{82} +14.5299 q^{83} +2.74657 q^{85} +(-2.01839 - 3.49595i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(-3.25343 - 5.63511i) q^{89} +(-7.54364 + 12.4224i) q^{91} +1.29021 q^{92} +(4.64510 - 8.04555i) q^{94} +(-11.0368 + 19.1163i) q^{95} -0.0872743 q^{97} +(3.76496 - 5.90128i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{2} - 3q^{4} - 6q^{8} + O(q^{10}) \) \( 6q + 3q^{2} - 3q^{4} - 6q^{8} + 3q^{11} - 3q^{14} - 3q^{16} + 3q^{17} + 3q^{19} + 6q^{22} + 9q^{23} - 3q^{25} - 3q^{28} - 18q^{29} - 6q^{31} + 3q^{32} + 6q^{34} - 6q^{35} - 9q^{37} - 3q^{38} - 24q^{41} + 18q^{43} + 3q^{44} - 9q^{46} - 15q^{47} - 24q^{49} - 6q^{50} - 9q^{58} + 9q^{59} + 6q^{61} - 12q^{62} + 6q^{64} + 36q^{65} - 6q^{67} + 3q^{68} + 12q^{70} - 6q^{71} + 9q^{74} - 6q^{76} + 3q^{77} - 12q^{79} - 12q^{82} + 12q^{83} + 9q^{86} - 3q^{88} - 36q^{89} - 36q^{91} - 18q^{92} + 15q^{94} - 24q^{95} + 18q^{97} - 15q^{98} + O(q^{100}) \)

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
\(5\) 1.37328 + 2.37860i 0.614151 + 1.06374i 0.990533 + 0.137277i \(0.0438349\pi\)
−0.376381 + 0.926465i \(0.622832\pi\)
\(6\) 0 0
\(7\) −1.37328 + 2.26144i −0.519053 + 0.854742i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.37328 + 2.37860i −0.434271 + 0.752179i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 0 0
\(13\) 5.49314 1.52352 0.761761 0.647858i \(-0.224335\pi\)
0.761761 + 0.647858i \(0.224335\pi\)
\(14\) −2.64510 0.0585812i −0.706933 0.0156565i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.500000 0.866025i 0.121268 0.210042i −0.799000 0.601331i \(-0.794637\pi\)
0.920268 + 0.391289i \(0.127971\pi\)
\(18\) 0 0
\(19\) 4.01839 + 6.96005i 0.921881 + 1.59675i 0.796502 + 0.604636i \(0.206681\pi\)
0.125379 + 0.992109i \(0.459985\pi\)
\(20\) −2.74657 −0.614151
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −0.645103 1.11735i −0.134513 0.232984i 0.790898 0.611948i \(-0.209614\pi\)
−0.925411 + 0.378964i \(0.876280\pi\)
\(24\) 0 0
\(25\) −1.27182 + 2.20285i −0.254364 + 0.440571i
\(26\) 2.74657 + 4.75720i 0.538646 + 0.932963i
\(27\) 0 0
\(28\) −1.27182 2.32002i −0.240351 0.438442i
\(29\) −4.54364 −0.843732 −0.421866 0.906658i \(-0.638625\pi\)
−0.421866 + 0.906658i \(0.638625\pi\)
\(30\) 0 0
\(31\) −2.54364 + 4.40571i −0.456851 + 0.791289i −0.998793 0.0491274i \(-0.984356\pi\)
0.541942 + 0.840416i \(0.317689\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 1.00000 0.171499
\(35\) −7.26496 0.160897i −1.22800 0.0271966i
\(36\) 0 0
\(37\) 2.01839 + 3.49595i 0.331821 + 0.574730i 0.982869 0.184306i \(-0.0590038\pi\)
−0.651048 + 0.759036i \(0.725670\pi\)
\(38\) −4.01839 + 6.96005i −0.651868 + 1.12907i
\(39\) 0 0
\(40\) −1.37328 2.37860i −0.217135 0.376089i
\(41\) −5.54364 −0.865771 −0.432885 0.901449i \(-0.642505\pi\)
−0.432885 + 0.901449i \(0.642505\pi\)
\(42\) 0 0
\(43\) −4.03677 −0.615602 −0.307801 0.951451i \(-0.599593\pi\)
−0.307801 + 0.951451i \(0.599593\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) 0 0
\(46\) 0.645103 1.11735i 0.0951152 0.164744i
\(47\) −4.64510 8.04555i −0.677558 1.17356i −0.975714 0.219048i \(-0.929705\pi\)
0.298156 0.954517i \(-0.403628\pi\)
\(48\) 0 0
\(49\) −3.22818 6.21119i −0.461169 0.887312i
\(50\) −2.54364 −0.359725
\(51\) 0 0
\(52\) −2.74657 + 4.75720i −0.380880 + 0.659704i
\(53\) 2.74657 4.75720i 0.377270 0.653451i −0.613394 0.789777i \(-0.710196\pi\)
0.990664 + 0.136326i \(0.0435295\pi\)
\(54\) 0 0
\(55\) 2.74657 0.370347
\(56\) 1.37328 2.26144i 0.183513 0.302197i
\(57\) 0 0
\(58\) −2.27182 3.93491i −0.298304 0.516678i
\(59\) −4.76496 + 8.25314i −0.620344 + 1.07447i 0.369077 + 0.929399i \(0.379674\pi\)
−0.989422 + 0.145069i \(0.953660\pi\)
\(60\) 0 0
\(61\) 0.829647 + 1.43699i 0.106225 + 0.183988i 0.914238 0.405177i \(-0.132790\pi\)
−0.808013 + 0.589165i \(0.799457\pi\)
\(62\) −5.08727 −0.646084
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 7.54364 + 13.0660i 0.935673 + 1.62063i
\(66\) 0 0
\(67\) −1.77182 + 3.06888i −0.216462 + 0.374923i −0.953724 0.300684i \(-0.902785\pi\)
0.737262 + 0.675607i \(0.236118\pi\)
\(68\) 0.500000 + 0.866025i 0.0606339 + 0.105021i
\(69\) 0 0
\(70\) −3.49314 6.37208i −0.417510 0.761610i
\(71\) −2.54364 −0.301874 −0.150937 0.988543i \(-0.548229\pi\)
−0.150937 + 0.988543i \(0.548229\pi\)
\(72\) 0 0
\(73\) 4.29021 7.43085i 0.502131 0.869716i −0.497866 0.867254i \(-0.665883\pi\)
0.999997 0.00246191i \(-0.000783650\pi\)
\(74\) −2.01839 + 3.49595i −0.234633 + 0.406396i
\(75\) 0 0
\(76\) −8.03677 −0.921881
\(77\) 1.27182 + 2.32002i 0.144937 + 0.264390i
\(78\) 0 0
\(79\) −6.11985 10.5999i −0.688537 1.19258i −0.972311 0.233690i \(-0.924920\pi\)
0.283774 0.958891i \(-0.408413\pi\)
\(80\) 1.37328 2.37860i 0.153538 0.265935i
\(81\) 0 0
\(82\) −2.77182 4.80093i −0.306096 0.530174i
\(83\) 14.5299 1.59486 0.797432 0.603408i \(-0.206191\pi\)
0.797432 + 0.603408i \(0.206191\pi\)
\(84\) 0 0
\(85\) 2.74657 0.297907
\(86\) −2.01839 3.49595i −0.217648 0.376978i
\(87\) 0 0
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) −3.25343 5.63511i −0.344863 0.597320i 0.640466 0.767987i \(-0.278741\pi\)
−0.985329 + 0.170666i \(0.945408\pi\)
\(90\) 0 0
\(91\) −7.54364 + 12.4224i −0.790788 + 1.30222i
\(92\) 1.29021 0.134513
\(93\) 0 0
\(94\) 4.64510 8.04555i 0.479106 0.829836i
\(95\) −11.0368 + 19.1163i −1.13235 + 1.96129i
\(96\) 0 0
\(97\) −0.0872743 −0.00886136 −0.00443068 0.999990i \(-0.501410\pi\)
−0.00443068 + 0.999990i \(0.501410\pi\)
\(98\) 3.76496 5.90128i 0.380318 0.596119i
\(99\) 0 0
\(100\) −1.27182 2.20285i −0.127182 0.220285i
\(101\) 6.51152 11.2783i 0.647921 1.12223i −0.335698 0.941970i \(-0.608972\pi\)
0.983619 0.180262i \(-0.0576946\pi\)
\(102\) 0 0
\(103\) 9.03677 + 15.6522i 0.890420 + 1.54225i 0.839373 + 0.543556i \(0.182922\pi\)
0.0510469 + 0.998696i \(0.483744\pi\)
\(104\) −5.49314 −0.538646
\(105\) 0 0
\(106\) 5.49314 0.533541
\(107\) 8.72132 + 15.1058i 0.843122 + 1.46033i 0.887243 + 0.461303i \(0.152618\pi\)
−0.0441209 + 0.999026i \(0.514049\pi\)
\(108\) 0 0
\(109\) −0.829647 + 1.43699i −0.0794658 + 0.137639i −0.903020 0.429599i \(-0.858655\pi\)
0.823554 + 0.567238i \(0.191988\pi\)
\(110\) 1.37328 + 2.37860i 0.130938 + 0.226790i
\(111\) 0 0
\(112\) 2.64510 + 0.0585812i 0.249939 + 0.00553540i
\(113\) 7.08727 0.666715 0.333357 0.942801i \(-0.391818\pi\)
0.333357 + 0.942801i \(0.391818\pi\)
\(114\) 0 0
\(115\) 1.77182 3.06888i 0.165223 0.286175i
\(116\) 2.27182 3.93491i 0.210933 0.365347i
\(117\) 0 0
\(118\) −9.52991 −0.877299
\(119\) 1.27182 + 2.32002i 0.116587 + 0.212676i
\(120\) 0 0
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −0.829647 + 1.43699i −0.0751127 + 0.130099i
\(123\) 0 0
\(124\) −2.54364 4.40571i −0.228425 0.395644i
\(125\) 6.74657 0.603431
\(126\) 0 0
\(127\) −6.78334 −0.601924 −0.300962 0.953636i \(-0.597308\pi\)
−0.300962 + 0.953636i \(0.597308\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −7.54364 + 13.0660i −0.661621 + 1.14596i
\(131\) −6.94950 12.0369i −0.607181 1.05167i −0.991703 0.128552i \(-0.958967\pi\)
0.384522 0.923116i \(-0.374366\pi\)
\(132\) 0 0
\(133\) −21.2581 0.470804i −1.84331 0.0408238i
\(134\) −3.54364 −0.306124
\(135\) 0 0
\(136\) −0.500000 + 0.866025i −0.0428746 + 0.0742611i
\(137\) 2.74657 4.75720i 0.234655 0.406435i −0.724517 0.689257i \(-0.757937\pi\)
0.959172 + 0.282822i \(0.0912706\pi\)
\(138\) 0 0
\(139\) 13.6309 1.15616 0.578079 0.815981i \(-0.303802\pi\)
0.578079 + 0.815981i \(0.303802\pi\)
\(140\) 3.77182 6.21119i 0.318777 0.524941i
\(141\) 0 0
\(142\) −1.27182 2.20285i −0.106729 0.184859i
\(143\) 2.74657 4.75720i 0.229680 0.397817i
\(144\) 0 0
\(145\) −6.23970 10.8075i −0.518179 0.897513i
\(146\) 8.58041 0.710120
\(147\) 0 0
\(148\) −4.03677 −0.331821
\(149\) 8.01839 + 13.8883i 0.656892 + 1.13777i 0.981416 + 0.191893i \(0.0614625\pi\)
−0.324524 + 0.945877i \(0.605204\pi\)
\(150\) 0 0
\(151\) 2.84803 4.93294i 0.231770 0.401437i −0.726559 0.687104i \(-0.758882\pi\)
0.958329 + 0.285667i \(0.0922151\pi\)
\(152\) −4.01839 6.96005i −0.325934 0.564535i
\(153\) 0 0
\(154\) −1.37328 + 2.26144i −0.110662 + 0.182232i
\(155\) −13.9725 −1.12230
\(156\) 0 0
\(157\) −9.05516 + 15.6840i −0.722680 + 1.25172i 0.237241 + 0.971451i \(0.423757\pi\)
−0.959922 + 0.280269i \(0.909576\pi\)
\(158\) 6.11985 10.5999i 0.486869 0.843282i
\(159\) 0 0
\(160\) 2.74657 0.217135
\(161\) 3.41273 + 0.0755817i 0.268960 + 0.00595668i
\(162\) 0 0
\(163\) 6.72132 + 11.6417i 0.526454 + 0.911846i 0.999525 + 0.0308210i \(0.00981219\pi\)
−0.473071 + 0.881024i \(0.656854\pi\)
\(164\) 2.77182 4.80093i 0.216443 0.374890i
\(165\) 0 0
\(166\) 7.26496 + 12.5833i 0.563870 + 0.976651i
\(167\) −23.5667 −1.82364 −0.911822 0.410585i \(-0.865325\pi\)
−0.911822 + 0.410585i \(0.865325\pi\)
\(168\) 0 0
\(169\) 17.1745 1.32112
\(170\) 1.37328 + 2.37860i 0.105326 + 0.182430i
\(171\) 0 0
\(172\) 2.01839 3.49595i 0.153901 0.266564i
\(173\) −5.45636 9.45070i −0.414840 0.718523i 0.580572 0.814209i \(-0.302829\pi\)
−0.995412 + 0.0956857i \(0.969496\pi\)
\(174\) 0 0
\(175\) −3.23504 5.90128i −0.244546 0.446095i
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) 3.25343 5.63511i 0.243855 0.422369i
\(179\) −6.47475 + 11.2146i −0.483946 + 0.838218i −0.999830 0.0184400i \(-0.994130\pi\)
0.515884 + 0.856658i \(0.327463\pi\)
\(180\) 0 0
\(181\) 7.59414 0.564468 0.282234 0.959346i \(-0.408925\pi\)
0.282234 + 0.959346i \(0.408925\pi\)
\(182\) −14.5299 0.321794i −1.07703 0.0238530i
\(183\) 0 0
\(184\) 0.645103 + 1.11735i 0.0475576 + 0.0823722i
\(185\) −5.54364 + 9.60186i −0.407576 + 0.705943i
\(186\) 0 0
\(187\) −0.500000 0.866025i −0.0365636 0.0633300i
\(188\) 9.29021 0.677558
\(189\) 0 0
\(190\) −22.0735 −1.60138
\(191\) 9.49314 + 16.4426i 0.686899 + 1.18974i 0.972836 + 0.231496i \(0.0743620\pi\)
−0.285937 + 0.958249i \(0.592305\pi\)
\(192\) 0 0
\(193\) 10.7833 18.6773i 0.776202 1.34442i −0.157915 0.987453i \(-0.550477\pi\)
0.934116 0.356968i \(-0.116190\pi\)
\(194\) −0.0436371 0.0755817i −0.00313296 0.00542645i
\(195\) 0 0
\(196\) 6.99314 + 0.309906i 0.499510 + 0.0221362i
\(197\) 3.12405 0.222579 0.111290 0.993788i \(-0.464502\pi\)
0.111290 + 0.993788i \(0.464502\pi\)
\(198\) 0 0
\(199\) 13.0368 22.5804i 0.924152 1.60068i 0.131234 0.991351i \(-0.458106\pi\)
0.792919 0.609327i \(-0.208560\pi\)
\(200\) 1.27182 2.20285i 0.0899312 0.155765i
\(201\) 0 0
\(202\) 13.0230 0.916298
\(203\) 6.23970 10.2751i 0.437941 0.721174i
\(204\) 0 0
\(205\) −7.61299 13.1861i −0.531714 0.920956i
\(206\) −9.03677 + 15.6522i −0.629622 + 1.09054i
\(207\) 0 0
\(208\) −2.74657 4.75720i −0.190440 0.329852i
\(209\) 8.03677 0.555915
\(210\) 0 0
\(211\) 15.6677 1.07861 0.539304 0.842111i \(-0.318687\pi\)
0.539304 + 0.842111i \(0.318687\pi\)
\(212\) 2.74657 + 4.75720i 0.188635 + 0.326726i
\(213\) 0 0
\(214\) −8.72132 + 15.1058i −0.596177 + 1.03261i
\(215\) −5.54364 9.60186i −0.378073 0.654841i
\(216\) 0 0
\(217\) −6.47009 11.8026i −0.439218 0.801210i
\(218\) −1.65929 −0.112382
\(219\) 0 0
\(220\) −1.37328 + 2.37860i −0.0925868 + 0.160365i
\(221\) 2.74657 4.75720i 0.184754 0.320004i
\(222\) 0 0
\(223\) 2.40586 0.161108 0.0805542 0.996750i \(-0.474331\pi\)
0.0805542 + 0.996750i \(0.474331\pi\)
\(224\) 1.27182 + 2.32002i 0.0849770 + 0.155013i
\(225\) 0 0
\(226\) 3.54364 + 6.13776i 0.235719 + 0.408278i
\(227\) 1.22818 2.12727i 0.0815173 0.141192i −0.822385 0.568932i \(-0.807357\pi\)
0.903902 + 0.427740i \(0.140690\pi\)
\(228\) 0 0
\(229\) 5.29021 + 9.16290i 0.349587 + 0.605502i 0.986176 0.165701i \(-0.0529887\pi\)
−0.636589 + 0.771203i \(0.719655\pi\)
\(230\) 3.54364 0.233661
\(231\) 0 0
\(232\) 4.54364 0.298304
\(233\) −3.53677 6.12587i −0.231702 0.401319i 0.726607 0.687053i \(-0.241096\pi\)
−0.958309 + 0.285734i \(0.907763\pi\)
\(234\) 0 0
\(235\) 12.7581 22.0977i 0.832246 1.44149i
\(236\) −4.76496 8.25314i −0.310172 0.537234i
\(237\) 0 0
\(238\) −1.37328 + 2.26144i −0.0890168 + 0.146587i
\(239\) −7.66769 −0.495981 −0.247991 0.968762i \(-0.579770\pi\)
−0.247991 + 0.968762i \(0.579770\pi\)
\(240\) 0 0
\(241\) 12.5299 21.7024i 0.807122 1.39798i −0.107726 0.994181i \(-0.534357\pi\)
0.914849 0.403797i \(-0.132310\pi\)
\(242\) 0.500000 0.866025i 0.0321412 0.0556702i
\(243\) 0 0
\(244\) −1.65929 −0.106225
\(245\) 10.3407 16.2083i 0.660643 1.03551i
\(246\) 0 0
\(247\) 22.0735 + 38.2325i 1.40451 + 2.43268i
\(248\) 2.54364 4.40571i 0.161521 0.279763i
\(249\) 0 0
\(250\) 3.37328 + 5.84270i 0.213345 + 0.369525i
\(251\) 25.0230 1.57944 0.789720 0.613467i \(-0.210226\pi\)
0.789720 + 0.613467i \(0.210226\pi\)
\(252\) 0 0
\(253\) −1.29021 −0.0811145
\(254\) −3.39167 5.87455i −0.212812 0.368602i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −5.25343 9.09921i −0.327700 0.567593i 0.654355 0.756187i \(-0.272940\pi\)
−0.982055 + 0.188594i \(0.939607\pi\)
\(258\) 0 0
\(259\) −10.6777 0.236479i −0.663479 0.0146941i
\(260\) −15.0873 −0.935673
\(261\) 0 0
\(262\) 6.94950 12.0369i 0.429342 0.743641i
\(263\) 11.8201 20.4730i 0.728860 1.26242i −0.228506 0.973543i \(-0.573384\pi\)
0.957366 0.288879i \(-0.0932826\pi\)
\(264\) 0 0
\(265\) 15.0873 0.926804
\(266\) −10.2213 18.6454i −0.626709 1.14323i
\(267\) 0 0
\(268\) −1.77182 3.06888i −0.108231 0.187462i
\(269\) −7.57622 + 13.1224i −0.461930 + 0.800086i −0.999057 0.0434151i \(-0.986176\pi\)
0.537127 + 0.843501i \(0.319510\pi\)
\(270\) 0 0
\(271\) −9.49314 16.4426i −0.576667 0.998816i −0.995858 0.0909186i \(-0.971020\pi\)
0.419191 0.907898i \(-0.362314\pi\)
\(272\) −1.00000 −0.0606339
\(273\) 0 0
\(274\) 5.49314 0.331853
\(275\) 1.27182 + 2.20285i 0.0766935 + 0.132837i
\(276\) 0 0
\(277\) −12.2397 + 21.1998i −0.735413 + 1.27377i 0.219130 + 0.975696i \(0.429678\pi\)
−0.954542 + 0.298076i \(0.903655\pi\)
\(278\) 6.81546 + 11.8047i 0.408764 + 0.708000i
\(279\) 0 0
\(280\) 7.26496 + 0.160897i 0.434164 + 0.00961545i
\(281\) 12.0873 0.721066 0.360533 0.932746i \(-0.382595\pi\)
0.360533 + 0.932746i \(0.382595\pi\)
\(282\) 0 0
\(283\) −2.34071 + 4.05422i −0.139141 + 0.240998i −0.927172 0.374637i \(-0.877767\pi\)
0.788031 + 0.615636i \(0.211101\pi\)
\(284\) 1.27182 2.20285i 0.0754685 0.130715i
\(285\) 0 0
\(286\) 5.49314 0.324816
\(287\) 7.61299 12.5366i 0.449381 0.740011i
\(288\) 0 0
\(289\) 8.00000 + 13.8564i 0.470588 + 0.815083i
\(290\) 6.23970 10.8075i 0.366408 0.634637i
\(291\) 0 0
\(292\) 4.29021 + 7.43085i 0.251065 + 0.434858i
\(293\) 11.6309 0.679485 0.339743 0.940518i \(-0.389660\pi\)
0.339743 + 0.940518i \(0.389660\pi\)
\(294\) 0 0
\(295\) −26.1745 −1.52394
\(296\) −2.01839 3.49595i −0.117316 0.203198i
\(297\) 0 0
\(298\) −8.01839 + 13.8883i −0.464493 + 0.804525i
\(299\) −3.54364 6.13776i −0.204934 0.354956i
\(300\) 0 0
\(301\) 5.54364 9.12890i 0.319530 0.526181i
\(302\) 5.69607 0.327772
\(303\) 0 0
\(304\) 4.01839 6.96005i 0.230470 0.399186i
\(305\) −2.27868 + 3.94679i −0.130477 + 0.225993i
\(306\) 0 0
\(307\) −14.0735 −0.803220 −0.401610 0.915811i \(-0.631549\pi\)
−0.401610 + 0.915811i \(0.631549\pi\)
\(308\) −2.64510 0.0585812i −0.150719 0.00333797i
\(309\) 0 0
\(310\) −6.98627 12.1006i −0.396794 0.687267i
\(311\) 6.13824 10.6317i 0.348068 0.602871i −0.637839 0.770170i \(-0.720171\pi\)
0.985906 + 0.167299i \(0.0535046\pi\)
\(312\) 0 0
\(313\) −11.7282 20.3138i −0.662916 1.14820i −0.979846 0.199755i \(-0.935985\pi\)
0.316930 0.948449i \(-0.397348\pi\)
\(314\) −18.1103 −1.02202
\(315\) 0 0
\(316\) 12.2397 0.688537
\(317\) −0.286010 0.495384i −0.0160639 0.0278235i 0.857882 0.513847i \(-0.171780\pi\)
−0.873946 + 0.486024i \(0.838447\pi\)
\(318\) 0 0
\(319\) −2.27182 + 3.93491i −0.127197 + 0.220312i
\(320\) 1.37328 + 2.37860i 0.0767689 + 0.132968i
\(321\) 0 0
\(322\) 1.64091 + 2.99330i 0.0914442 + 0.166810i
\(323\) 8.03677 0.447178
\(324\) 0 0
\(325\) −6.98627 + 12.1006i −0.387529 + 0.671219i
\(326\) −6.72132 + 11.6417i −0.372259 + 0.644772i
\(327\) 0 0
\(328\) 5.54364 0.306096
\(329\) 24.5735 + 0.544231i 1.35478 + 0.0300044i
\(330\) 0 0
\(331\) −3.85909 6.68414i −0.212115 0.367394i 0.740261 0.672319i \(-0.234702\pi\)
−0.952376 + 0.304925i \(0.901368\pi\)
\(332\) −7.26496 + 12.5833i −0.398716 + 0.690597i
\(333\) 0 0
\(334\) −11.7833 20.4093i −0.644756 1.11675i
\(335\) −9.73284 −0.531762
\(336\) 0 0
\(337\) 28.5530 1.55538 0.777689 0.628649i \(-0.216392\pi\)
0.777689 + 0.628649i \(0.216392\pi\)
\(338\) 8.58727 + 14.8736i 0.467086 + 0.809017i
\(339\) 0 0
\(340\) −1.37328 + 2.37860i −0.0744768 + 0.128998i
\(341\) 2.54364 + 4.40571i 0.137746 + 0.238583i
\(342\) 0 0
\(343\) 18.4794 + 1.22940i 0.997794 + 0.0663814i
\(344\) 4.03677 0.217648
\(345\) 0 0
\(346\) 5.45636 9.45070i 0.293336 0.508073i
\(347\) −11.7213 + 20.3019i −0.629233 + 1.08986i 0.358473 + 0.933540i \(0.383298\pi\)
−0.987706 + 0.156324i \(0.950036\pi\)
\(348\) 0 0
\(349\) 25.7328 1.37745 0.688724 0.725024i \(-0.258171\pi\)
0.688724 + 0.725024i \(0.258171\pi\)
\(350\) 3.49314 5.75227i 0.186716 0.307472i
\(351\) 0 0
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) −9.20293 + 15.9399i −0.489823 + 0.848398i −0.999931 0.0117122i \(-0.996272\pi\)
0.510109 + 0.860110i \(0.329605\pi\)
\(354\) 0 0
\(355\) −3.49314 6.05029i −0.185396 0.321116i
\(356\) 6.50686 0.344863
\(357\) 0 0
\(358\) −12.9495 −0.684402
\(359\) −15.9863 27.6890i −0.843723 1.46137i −0.886725 0.462297i \(-0.847026\pi\)
0.0430022 0.999075i \(-0.486308\pi\)
\(360\) 0 0
\(361\) −22.7949 + 39.4819i −1.19973 + 2.07799i
\(362\) 3.79707 + 6.57672i 0.199570 + 0.345665i
\(363\) 0 0
\(364\) −6.98627 12.7442i −0.366180 0.667976i
\(365\) 23.5667 1.23354
\(366\) 0 0
\(367\) −18.2397 + 31.5921i −0.952105 + 1.64909i −0.211246 + 0.977433i \(0.567752\pi\)
−0.740859 + 0.671661i \(0.765581\pi\)
\(368\) −0.645103 + 1.11735i −0.0336283 + 0.0582459i
\(369\) 0 0
\(370\) −11.0873 −0.576400
\(371\) 6.98627 + 12.7442i 0.362709 + 0.661644i
\(372\) 0 0
\(373\) 10.1566 + 17.5918i 0.525890 + 0.910868i 0.999545 + 0.0301580i \(0.00960104\pi\)
−0.473655 + 0.880710i \(0.657066\pi\)
\(374\) 0.500000 0.866025i 0.0258544 0.0447811i
\(375\) 0 0
\(376\) 4.64510 + 8.04555i 0.239553 + 0.414918i
\(377\) −24.9588 −1.28544
\(378\) 0 0
\(379\) 9.44264 0.485036 0.242518 0.970147i \(-0.422027\pi\)
0.242518 + 0.970147i \(0.422027\pi\)
\(380\) −11.0368 19.1163i −0.566175 0.980643i
\(381\) 0 0
\(382\) −9.49314 + 16.4426i −0.485711 + 0.841276i
\(383\) 11.8522 + 20.5287i 0.605621 + 1.04897i 0.991953 + 0.126606i \(0.0404084\pi\)
−0.386332 + 0.922360i \(0.626258\pi\)
\(384\) 0 0
\(385\) −3.77182 + 6.21119i −0.192230 + 0.316551i
\(386\) 21.5667 1.09772
\(387\) 0 0
\(388\) 0.0436371 0.0755817i 0.00221534 0.00383708i
\(389\) −0.626716 + 1.08550i −0.0317758 + 0.0550372i −0.881476 0.472229i \(-0.843450\pi\)
0.849700 + 0.527266i \(0.176783\pi\)
\(390\) 0 0
\(391\) −1.29021 −0.0652485
\(392\) 3.22818 + 6.21119i 0.163048 + 0.313712i
\(393\) 0 0
\(394\) 1.56202 + 2.70550i 0.0786936 + 0.136301i
\(395\) 16.8086 29.1133i 0.845732 1.46485i
\(396\) 0 0
\(397\) −14.3086 24.7832i −0.718128 1.24383i −0.961741 0.273961i \(-0.911666\pi\)
0.243613 0.969872i \(-0.421667\pi\)
\(398\) 26.0735 1.30695
\(399\) 0 0
\(400\) 2.54364 0.127182
\(401\) 0.202931 + 0.351487i 0.0101339 + 0.0175524i 0.871048 0.491198i \(-0.163441\pi\)
−0.860914 + 0.508751i \(0.830108\pi\)
\(402\) 0 0
\(403\) −13.9725 + 24.2012i −0.696022 + 1.20555i
\(404\) 6.51152 + 11.2783i 0.323960 + 0.561116i
\(405\) 0 0
\(406\) 12.0184 + 0.266172i 0.596463 + 0.0132099i
\(407\) 4.03677 0.200095
\(408\) 0 0
\(409\) 16.3775 28.3666i 0.809814 1.40264i −0.103178 0.994663i \(-0.532901\pi\)
0.912992 0.407977i \(-0.133765\pi\)
\(410\) 7.61299 13.1861i 0.375979 0.651214i
\(411\) 0 0
\(412\) −18.0735 −0.890420
\(413\) −12.1203 22.1096i −0.596402 1.08794i
\(414\) 0 0
\(415\) 19.9537 + 34.5608i 0.979488 + 1.69652i
\(416\) 2.74657 4.75720i 0.134662 0.233241i
\(417\) 0 0
\(418\) 4.01839 + 6.96005i 0.196546 + 0.340427i
\(419\) 15.9358 0.778513 0.389257 0.921129i \(-0.372732\pi\)
0.389257 + 0.921129i \(0.372732\pi\)
\(420\) 0 0
\(421\) −27.1240 −1.32195 −0.660973 0.750410i \(-0.729856\pi\)
−0.660973 + 0.750410i \(0.729856\pi\)
\(422\) 7.83384 + 13.5686i 0.381345 + 0.660510i
\(423\) 0 0
\(424\) −2.74657 + 4.75720i −0.133385 + 0.231030i
\(425\) 1.27182 + 2.20285i 0.0616923 + 0.106854i
\(426\) 0 0
\(427\) −4.38900 0.0972034i −0.212399 0.00470400i
\(428\) −17.4426 −0.843122
\(429\) 0 0
\(430\) 5.54364 9.60186i 0.267338 0.463043i
\(431\) −20.3133 + 35.1836i −0.978455 + 1.69473i −0.310427 + 0.950597i \(0.600472\pi\)
−0.668028 + 0.744137i \(0.732861\pi\)
\(432\) 0 0
\(433\) 1.10100 0.0529107 0.0264554 0.999650i \(-0.491578\pi\)
0.0264554 + 0.999650i \(0.491578\pi\)
\(434\) 6.98627 11.5045i 0.335352 0.552236i
\(435\) 0 0
\(436\) −0.829647 1.43699i −0.0397329 0.0688194i
\(437\) 5.18454 8.97989i 0.248010 0.429567i
\(438\) 0 0
\(439\) −11.4284 19.7946i −0.545450 0.944747i −0.998578 0.0533018i \(-0.983025\pi\)
0.453129 0.891445i \(-0.350308\pi\)
\(440\) −2.74657 −0.130938
\(441\) 0 0
\(442\) 5.49314 0.261282
\(443\) −4.77868 8.27692i −0.227042 0.393248i 0.729888 0.683567i \(-0.239572\pi\)
−0.956930 + 0.290318i \(0.906239\pi\)
\(444\) 0 0
\(445\) 8.93577 15.4772i 0.423596 0.733690i
\(446\) 1.20293 + 2.08354i 0.0569604 + 0.0986584i
\(447\) 0 0
\(448\) −1.37328 + 2.26144i −0.0648816 + 0.106843i
\(449\) −0.681412 −0.0321578 −0.0160789 0.999871i \(-0.505118\pi\)
−0.0160789 + 0.999871i \(0.505118\pi\)
\(450\) 0 0
\(451\) −2.77182 + 4.80093i −0.130520 + 0.226067i
\(452\) −3.54364 + 6.13776i −0.166679 + 0.288696i
\(453\) 0 0
\(454\) 2.45636 0.115283
\(455\) −39.9074 0.883830i −1.87089 0.0414346i
\(456\) 0 0
\(457\) −9.07355 15.7158i −0.424443 0.735156i 0.571926 0.820306i \(-0.306197\pi\)
−0.996368 + 0.0851493i \(0.972863\pi\)
\(458\) −5.29021 + 9.16290i −0.247195 + 0.428154i
\(459\) 0 0
\(460\) 1.77182 + 3.06888i 0.0826115 + 0.143087i
\(461\) 41.7045 1.94237 0.971185 0.238326i \(-0.0765988\pi\)
0.971185 + 0.238326i \(0.0765988\pi\)
\(462\) 0 0
\(463\) −28.5804 −1.32824 −0.664122 0.747624i \(-0.731195\pi\)
−0.664122 + 0.747624i \(0.731195\pi\)
\(464\) 2.27182 + 3.93491i 0.105467 + 0.182673i
\(465\) 0 0
\(466\) 3.53677 6.12587i 0.163838 0.283776i
\(467\) 2.69141 + 4.66166i 0.124544 + 0.215716i 0.921554 0.388249i \(-0.126920\pi\)
−0.797011 + 0.603965i \(0.793587\pi\)
\(468\) 0 0
\(469\) −4.50686 8.22130i −0.208108 0.379624i
\(470\) 25.5162 1.17697
\(471\) 0 0
\(472\) 4.76496 8.25314i 0.219325 0.379882i
\(473\) −2.01839 + 3.49595i −0.0928055 + 0.160744i
\(474\) 0 0
\(475\) −20.4426 −0.937972
\(476\) −2.64510 0.0585812i −0.121238 0.00268506i
\(477\) 0 0
\(478\) −3.83384 6.64041i −0.175356 0.303725i
\(479\) 7.23970 12.5395i 0.330791 0.572946i −0.651877 0.758325i \(-0.726018\pi\)
0.982667 + 0.185379i \(0.0593513\pi\)
\(480\) 0 0
\(481\) 11.0873 + 19.2037i 0.505536 + 0.875614i
\(482\) 25.0598 1.14144
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −0.119852 0.207590i −0.00544222 0.00942619i
\(486\) 0 0
\(487\) 4.21666 7.30347i 0.191075 0.330952i −0.754532 0.656264i \(-0.772136\pi\)
0.945607 + 0.325312i \(0.105469\pi\)
\(488\) −0.829647 1.43699i −0.0375564 0.0650495i
\(489\) 0 0
\(490\) 19.2071 + 0.851179i 0.867690 + 0.0384524i
\(491\) 38.6770 1.74547 0.872734 0.488195i \(-0.162345\pi\)
0.872734 + 0.488195i \(0.162345\pi\)
\(492\) 0 0
\(493\) −2.27182 + 3.93491i −0.102318 + 0.177219i
\(494\) −22.0735 + 38.2325i −0.993136 + 1.72016i
\(495\) 0 0
\(496\) 5.08727 0.228425
\(497\) 3.49314 5.75227i 0.156689 0.258025i
\(498\) 0 0
\(499\) −19.0230 32.9489i −0.851589 1.47499i −0.879774 0.475392i \(-0.842306\pi\)
0.0281856 0.999603i \(-0.491027\pi\)
\(500\) −3.37328 + 5.84270i −0.150858 + 0.261293i
\(501\) 0 0
\(502\) 12.5115 + 21.6706i 0.558417 + 0.967206i
\(503\) −21.5667 −0.961611 −0.480805 0.876827i \(-0.659656\pi\)
−0.480805 + 0.876827i \(0.659656\pi\)
\(504\) 0 0
\(505\) 35.7687 1.59169
\(506\) −0.645103 1.11735i −0.0286783 0.0496723i
\(507\) 0 0
\(508\) 3.39167 5.87455i 0.150481 0.260641i
\(509\) −13.3270 23.0830i −0.590708 1.02314i −0.994137 0.108125i \(-0.965515\pi\)
0.403429 0.915011i \(-0.367818\pi\)
\(510\) 0 0
\(511\) 10.9127 + 19.9067i 0.482751 + 0.880620i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 5.25343 9.09921i 0.231719 0.401349i
\(515\) −24.8201 + 42.9897i −1.09370 + 1.89435i
\(516\) 0 0
\(517\) −9.29021 −0.408583
\(518\) −5.13404 9.36538i −0.225577 0.411491i
\(519\) 0 0
\(520\) −7.54364 13.0660i −0.330810 0.572980i
\(521\) −11.9863 + 20.7608i −0.525128 + 0.909549i 0.474444 + 0.880286i \(0.342649\pi\)
−0.999572 + 0.0292627i \(0.990684\pi\)
\(522\) 0 0
\(523\) −10.3407 17.9106i −0.452168 0.783177i 0.546353 0.837555i \(-0.316016\pi\)
−0.998520 + 0.0543780i \(0.982682\pi\)
\(524\) 13.8990 0.607181
\(525\) 0 0
\(526\) 23.6402 1.03076
\(527\) 2.54364 + 4.40571i 0.110803 + 0.191916i
\(528\) 0 0
\(529\) 10.6677 18.4770i 0.463812 0.803347i
\(530\) 7.54364 + 13.0660i 0.327675 + 0.567549i
\(531\) 0 0
\(532\) 11.0368 18.1746i 0.478505 0.787971i
\(533\) −30.4520 −1.31902
\(534\) 0 0
\(535\) −23.9537 + 41.4890i −1.03561 + 1.79373i
\(536\) 1.77182 3.06888i 0.0765309 0.132555i
\(537\) 0 0
\(538\) −15.1524 −0.653268
\(539\) −6.99314 0.309906i −0.301216 0.0133486i
\(540\) 0 0
\(541\) −17.9537 31.0967i −0.771890 1.33695i −0.936526 0.350598i \(-0.885978\pi\)
0.164637 0.986354i \(-0.447355\pi\)
\(542\) 9.49314 16.4426i 0.407765 0.706270i
\(543\) 0 0
\(544\) −0.500000 0.866025i −0.0214373 0.0371305i
\(545\) −4.55736 −0.195216
\(546\) 0 0
\(547\) −5.12405 −0.219088 −0.109544 0.993982i \(-0.534939\pi\)
−0.109544 + 0.993982i \(0.534939\pi\)
\(548\) 2.74657 + 4.75720i 0.117328 + 0.203217i
\(549\) 0 0
\(550\) −1.27182 + 2.20285i −0.0542305 + 0.0939300i
\(551\) −18.2581 31.6239i −0.777821 1.34723i
\(552\) 0 0
\(553\) 32.3753 + 0.717016i 1.37674 + 0.0304906i
\(554\) −24.4794 −1.04003
\(555\) 0 0
\(556\) −6.81546 + 11.8047i −0.289040 + 0.500631i
\(557\) −6.43798 + 11.1509i −0.272786 + 0.472479i −0.969574 0.244798i \(-0.921278\pi\)
0.696788 + 0.717277i \(0.254612\pi\)
\(558\) 0 0
\(559\) −22.1745 −0.937883
\(560\) 3.49314 + 6.37208i 0.147612 + 0.269270i
\(561\) 0 0
\(562\) 6.04364 + 10.4679i 0.254935 + 0.441561i
\(563\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 0 0
\(565\) 9.73284 + 16.8578i 0.409464 + 0.709212i
\(566\) −4.68141 −0.196774
\(567\) 0 0
\(568\) 2.54364 0.106729
\(569\) 10.6777 + 18.4943i 0.447632 + 0.775321i 0.998231 0.0594486i \(-0.0189342\pi\)
−0.550600 + 0.834769i \(0.685601\pi\)
\(570\) 0 0
\(571\) −3.72818 + 6.45740i −0.156020 + 0.270234i −0.933430 0.358760i \(-0.883200\pi\)
0.777410 + 0.628994i \(0.216533\pi\)
\(572\) 2.74657 + 4.75720i 0.114840 + 0.198908i
\(573\) 0 0
\(574\) 14.6635 + 0.324753i 0.612042 + 0.0135549i
\(575\) 3.28181 0.136861
\(576\) 0 0
\(577\) −2.82232 + 4.88840i −0.117495 + 0.203507i −0.918774 0.394783i \(-0.870820\pi\)
0.801280 + 0.598290i \(0.204153\pi\)
\(578\) −8.00000 + 13.8564i −0.332756 + 0.576351i
\(579\) 0 0
\(580\) 12.4794 0.518179
\(581\) −19.9537 + 32.8585i −0.827819 + 1.36320i
\(582\) 0 0
\(583\) −2.74657 4.75720i −0.113751 0.197023i
\(584\) −4.29021 + 7.43085i −0.177530 + 0.307491i
\(585\) 0 0
\(586\) 5.81546 + 10.0727i 0.240234 + 0.416098i
\(587\) 34.4059 1.42008 0.710041 0.704160i \(-0.248676\pi\)
0.710041 + 0.704160i \(0.248676\pi\)
\(588\) 0 0
\(589\) −40.8853 −1.68465
\(590\) −13.0873 22.6678i −0.538795 0.933220i
\(591\) 0 0
\(592\) 2.01839 3.49595i 0.0829552 0.143683i
\(593\) −9.35909 16.2104i −0.384332 0.665682i 0.607344 0.794439i \(-0.292235\pi\)
−0.991676 + 0.128756i \(0.958901\pi\)
\(594\) 0 0
\(595\) −3.77182 + 6.21119i −0.154629 + 0.254634i
\(596\) −16.0368 −0.656892
\(597\) 0 0
\(598\) 3.54364 6.13776i 0.144910 0.250992i
\(599\) 5.20713 9.01901i 0.212757 0.368507i −0.739819 0.672806i \(-0.765089\pi\)
0.952577 + 0.304299i \(0.0984223\pi\)
\(600\) 0 0
\(601\) 25.0873 1.02333 0.511666 0.859185i \(-0.329029\pi\)
0.511666 + 0.859185i \(0.329029\pi\)
\(602\) 10.6777 + 0.236479i 0.435190 + 0.00963816i
\(603\) 0 0
\(604\) 2.84803 + 4.93294i 0.115885 + 0.200718i
\(605\) 1.37328 2.37860i 0.0558319 0.0967038i
\(606\) 0 0
\(607\) −15.9537 27.6326i −0.647541 1.12157i −0.983708 0.179771i \(-0.942464\pi\)
0.336168 0.941802i \(-0.390869\pi\)
\(608\) 8.03677 0.325934
\(609\) 0 0
\(610\) −4.55736 −0.184522
\(611\) −25.5162 44.1953i −1.03227 1.78795i
\(612\) 0 0
\(613\) −1.71399 + 2.96872i −0.0692274 + 0.119905i −0.898561 0.438848i \(-0.855387\pi\)
0.829334 + 0.558753i \(0.188720\pi\)
\(614\) −7.03677 12.1880i −0.283981 0.491870i
\(615\) 0 0
\(616\) −1.27182 2.32002i −0.0512430 0.0934761i
\(617\) −12.7550 −0.513495 −0.256748 0.966478i \(-0.582651\pi\)
−0.256748 + 0.966478i \(0.582651\pi\)
\(618\) 0 0
\(619\) 10.7949 18.6973i 0.433882 0.751506i −0.563321 0.826238i \(-0.690477\pi\)
0.997204 + 0.0747317i \(0.0238100\pi\)
\(620\) 6.98627 12.1006i 0.280575 0.485971i
\(621\) 0 0
\(622\) 12.2765 0.492242
\(623\) 17.2113 + 0.381180i 0.689557 + 0.0152716i
\(624\) 0 0
\(625\) 15.6240 + 27.0616i 0.624962 + 1.08247i
\(626\) 11.7282 20.3138i 0.468752 0.811903i
\(627\) 0 0
\(628\) −9.05516 15.6840i −0.361340 0.625860i
\(629\) 4.03677 0.160957
\(630\) 0 0
\(631\) 4.23131 0.168446 0.0842230 0.996447i \(-0.473159\pi\)
0.0842230 + 0.996447i \(0.473159\pi\)
\(632\) 6.11985 + 10.5999i 0.243435 + 0.421641i
\(633\) 0 0
\(634\) 0.286010 0.495384i 0.0113589 0.0196742i
\(635\) −9.31546 16.1348i −0.369673 0.640292i
\(636\) 0 0
\(637\) −17.7328 34.1189i −0.702601 1.35184i
\(638\) −4.54364 −0.179884
\(639\) 0 0
\(640\) −1.37328 + 2.37860i −0.0542838 + 0.0940223i
\(641\) 2.03677 3.52780i 0.0804477 0.139340i −0.822995 0.568049i \(-0.807698\pi\)
0.903442 + 0.428710i \(0.141032\pi\)
\(642\) 0 0
\(643\) −19.2618 −0.759612 −0.379806 0.925066i \(-0.624009\pi\)
−0.379806 + 0.925066i \(0.624009\pi\)
\(644\) −1.77182 + 2.91772i −0.0698194 + 0.114974i
\(645\) 0 0
\(646\) 4.01839 + 6.96005i 0.158101 + 0.273840i
\(647\) −9.44683 + 16.3624i −0.371393 + 0.643272i −0.989780 0.142602i \(-0.954453\pi\)
0.618387 + 0.785874i \(0.287786\pi\)
\(648\) 0 0
\(649\) 4.76496 + 8.25314i 0.187041 + 0.323964i
\(650\) −13.9725 −0.548048
\(651\) 0 0
\(652\) −13.4426 −0.526454
\(653\) −4.46056 7.72591i −0.174555 0.302338i 0.765452 0.643493i \(-0.222515\pi\)
−0.940007 + 0.341155i \(0.889182\pi\)
\(654\) 0 0
\(655\) 19.0873 33.0601i 0.745802 1.29177i
\(656\) 2.77182 + 4.80093i 0.108221 + 0.187445i
\(657\) 0 0
\(658\) 11.8155 + 21.5534i 0.460614 + 0.840240i
\(659\) −45.4426 −1.77019 −0.885097 0.465407i \(-0.845908\pi\)
−0.885097 + 0.465407i \(0.845908\pi\)
\(660\) 0 0
\(661\) 14.5115 25.1347i 0.564433 0.977626i −0.432669 0.901553i \(-0.642428\pi\)
0.997102 0.0760737i \(-0.0242384\pi\)
\(662\) 3.85909 6.68414i 0.149988 0.259787i
\(663\) 0 0
\(664\) −14.5299 −0.563870
\(665\) −28.0735 51.2110i −1.08865 1.98588i
\(666\) 0 0
\(667\) 2.93111 + 5.07684i 0.113493 + 0.196576i
\(668\) 11.7833 20.4093i 0.455911 0.789661i
\(669\) 0 0
\(670\) −4.86642 8.42889i −0.188006 0.325636i
\(671\) 1.65929 0.0640563
\(672\) 0 0
\(673\) −16.2481 −0.626318 −0.313159 0.949701i \(-0.601387\pi\)
−0.313159 + 0.949701i \(0.601387\pi\)
\(674\) 14.2765 + 24.7276i 0.549909 + 0.952471i
\(675\) 0 0
\(676\) −8.58727 + 14.8736i −0.330280 + 0.572061i
\(677\) −1.94484 3.36856i −0.0747463 0.129464i 0.826230 0.563333i \(-0.190481\pi\)
−0.900976 + 0.433869i \(0.857148\pi\)
\(678\) 0 0
\(679\) 0.119852 0.197365i 0.00459951 0.00757418i
\(680\) −2.74657 −0.105326
\(681\) 0 0
\(682\) −2.54364 + 4.40571i −0.0974009 + 0.168703i
\(683\) 2.90273 5.02768i 0.111070 0.192379i −0.805132 0.593096i \(-0.797906\pi\)
0.916202 + 0.400717i \(0.131239\pi\)
\(684\) 0 0
\(685\) 15.0873 0.576455
\(686\) 8.17501 + 16.6183i 0.312123 + 0.634491i
\(687\) 0 0
\(688\) 2.01839 + 3.49595i 0.0769503 + 0.133282i
\(689\) 15.0873 26.1319i 0.574779 0.995547i
\(690\) 0 0
\(691\) 3.17768 + 5.50390i 0.120885 + 0.209378i 0.920117 0.391644i \(-0.128094\pi\)
−0.799232 + 0.601022i \(0.794760\pi\)
\(692\) 10.9127 0.414840
\(693\) 0 0
\(694\) −23.4426 −0.889870
\(695\) 18.7191 + 32.4225i 0.710056 + 1.22985i
\(696\) 0 0
\(697\) −2.77182 + 4.80093i −0.104990 + 0.181848i
\(698\) 12.8664 + 22.2853i 0.487001 + 0.843511i
\(699\) 0 0
\(700\) 6.72818 + 0.149009i 0.254301 + 0.00563202i
\(701\) −5.86223 −0.221413 −0.110707 0.993853i \(-0.535311\pi\)
−0.110707 + 0.993853i \(0.535311\pi\)
\(702\) 0 0
\(703\) −16.2213 + 28.0961i −0.611799 + 1.05967i
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) 0 0
\(706\) −18.4059 −0.692714
\(707\) 16.5630 + 30.2137i 0.622914 + 1.13630i
\(708\) 0 0
\(709\) 6.72818 + 11.6536i 0.252682 + 0.437658i 0.964263 0.264946i \(-0.0853540\pi\)
−0.711581 + 0.702604i \(0.752021\pi\)
\(710\) 3.49314 6.05029i 0.131095 0.227063i
\(711\) 0 0
\(712\) 3.25343 + 5.63511i 0.121928 + 0.211185i
\(713\) 6.56363 0.245810
\(714\) 0 0
\(715\) 15.0873 0.564232
\(716\) −6.47475 11.2146i −0.241973 0.419109i
\(717\) 0 0
\(718\) 15.9863 27.6890i 0.596602 1.03335i
\(719\) −12.1382 21.0240i −0.452680 0.784065i 0.545872 0.837869i \(-0.316199\pi\)
−0.998552 + 0.0538042i \(0.982865\pi\)
\(720\) 0 0
\(721\) −47.8064 1.05877i −1.78040 0.0394306i
\(722\) −45.5897 −1.69667
\(723\) 0 0
\(724\) −3.79707 + 6.57672i −0.141117 + 0.244422i
\(725\) 5.77868 10.0090i 0.214615 0.371724i
\(726\) 0 0
\(727\) −22.1471 −0.821390 −0.410695 0.911773i \(-0.634714\pi\)
−0.410695 + 0.911773i \(0.634714\pi\)
\(728\) 7.54364 12.4224i 0.279586 0.460404i
\(729\) 0 0
\(730\) 11.7833 + 20.4093i 0.436121 + 0.755384i
\(731\) −2.01839 + 3.49595i −0.0746527 + 0.129302i
\(732\) 0 0
\(733\) 2.66349 + 4.61330i 0.0983782 + 0.170396i 0.911014 0.412377i \(-0.135301\pi\)
−0.812635 + 0.582773i \(0.801968\pi\)
\(734\) −36.4794 −1.34648
\(735\) 0 0
\(736\) −1.29021 −0.0475576
\(737\) 1.77182 + 3.06888i 0.0652658 + 0.113044i
\(738\) 0 0
\(739\) 12.6309 21.8774i 0.464636 0.804772i −0.534549 0.845137i \(-0.679519\pi\)
0.999185 + 0.0403648i \(0.0128520\pi\)
\(740\) −5.54364 9.60186i −0.203788 0.352971i
\(741\) 0 0
\(742\) −7.54364 + 12.4224i −0.276936 + 0.456040i
\(743\) 25.4196 0.932554 0.466277 0.884639i \(-0.345595\pi\)
0.466277 + 0.884639i \(0.345595\pi\)
\(744\) 0 0
\(745\) −22.0230 + 38.1450i −0.806862 + 1.39753i
\(746\) −10.1566 + 17.5918i −0.371860 + 0.644081i
\(747\) 0 0
\(748\) 1.00000 0.0365636
\(749\) −46.1376 1.02181i −1.68583 0.0373361i
\(750\) 0 0
\(751\) 20.2765 + 35.1199i 0.739899 + 1.28154i 0.952540 + 0.304413i \(0.0984602\pi\)
−0.212641 + 0.977130i \(0.568206\pi\)
\(752\) −4.64510 + 8.04555i −0.169389 + 0.293391i
\(753\) 0 0
\(754\) −12.4794 21.6150i −0.454473 0.787171i
\(755\) 15.6446 0.569367
\(756\) 0 0
\(757\) 13.3554 0.485409 0.242704 0.970100i \(-0.421965\pi\)
0.242704 + 0.970100i \(0.421965\pi\)
\(758\) 4.72132 + 8.17756i 0.171486 + 0.297022i
\(759\) 0 0
\(760\) 11.0368 19.1163i 0.400346 0.693419i
\(761\) 9.22818 + 15.9837i 0.334521 + 0.579408i 0.983393 0.181490i \(-0.0580920\pi\)
−0.648871 + 0.760898i \(0.724759\pi\)
\(762\) 0 0
\(763\) −2.11032 3.84959i −0.0763987 0.139365i
\(764\) −18.9863 −0.686899
\(765\) 0 0
\(766\) −11.8522 + 20.5287i −0.428238 + 0.741731i
\(767\) −26.1745 + 45.3356i −0.945108 + 1.63698i
\(768\) 0 0
\(769\) 49.9158 1.80001 0.900005 0.435881i \(-0.143563\pi\)
0.900005 + 0.435881i \(0.143563\pi\)
\(770\) −7.26496 0.160897i −0.261811 0.00579833i
\(771\) 0 0
\(772\) 10.7833 + 18.6773i 0.388101 + 0.672211i
\(773\) −21.0694 + 36.4932i −0.757812 + 1.31257i 0.186152 + 0.982521i \(0.440398\pi\)
−0.943964 + 0.330048i \(0.892935\pi\)
\(774\) 0 0
\(775\) −6.47009 11.2065i −0.232412 0.402550i
\(776\) 0.0872743 0.00313296
\(777\) 0 0
\(778\) −1.25343 −0.0449377
\(779\) −22.2765 38.5840i −0.798138 1.38241i
\(780\) 0 0
\(781\) −1.27182 + 2.20285i −0.0455092 + 0.0788243i
\(782\) −0.645103 1.11735i −0.0230688 0.0399564i
\(783\) 0 0
\(784\) −3.76496 + 5.90128i −0.134463 + 0.210760i
\(785\) −49.7412 −1.77534
\(786\) 0 0
\(787\) 17.1792 29.7553i 0.612373 1.06066i −0.378467 0.925615i \(-0.623549\pi\)
0.990839 0.135046i \(-0.0431181\pi\)
\(788\) −1.56202 + 2.70550i −0.0556448 + 0.0963796i
\(789\) 0 0
\(790\) 33.6172 1.19605
\(791\) −9.73284 + 16.0274i −0.346060 + 0.569869i
\(792\) 0 0
\(793\) 4.55736 + 7.89359i 0.161837 + 0.280309i
\(794\) 14.3086 24.7832i 0.507793 0.879523i
\(795\) 0 0
\(796\) 13.0368 + 22.5804i 0.462076 + 0.800339i