Properties

Label 224.3.o.b.79.1
Level 224
Weight 3
Character 224.79
Analytic conductor 6.104
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 + 0.866025i\) of \(x^{2} - x + 1\)
Character \(\chi\) \(=\) 224.79
Dual form 224.3.o.b.207.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(4.50000 + 2.59808i) q^{5} +(-1.00000 - 6.92820i) q^{7} +(4.00000 - 6.92820i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(4.50000 + 2.59808i) q^{5} +(-1.00000 - 6.92820i) q^{7} +(4.00000 - 6.92820i) q^{9} +(8.50000 + 14.7224i) q^{11} -13.8564i q^{13} +5.19615i q^{15} +(12.5000 + 21.6506i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(5.50000 - 4.33013i) q^{21} +(4.50000 + 2.59808i) q^{23} +(1.00000 + 1.73205i) q^{25} +17.0000 q^{27} +13.8564i q^{29} +(28.5000 - 16.4545i) q^{31} +(-8.50000 + 14.7224i) q^{33} +(13.5000 - 33.7750i) q^{35} +(-7.50000 - 4.33013i) q^{37} +(12.0000 - 6.92820i) q^{39} +26.0000 q^{41} -14.0000 q^{43} +(36.0000 - 20.7846i) q^{45} +(-43.5000 - 25.1147i) q^{47} +(-47.0000 + 13.8564i) q^{49} +(-12.5000 + 21.6506i) q^{51} +(-79.5000 + 45.8993i) q^{53} +88.3346i q^{55} -7.00000 q^{57} +(-27.5000 - 47.6314i) q^{59} +(-19.5000 - 11.2583i) q^{61} +(-52.0000 - 20.7846i) q^{63} +(36.0000 - 62.3538i) q^{65} +(8.50000 + 14.7224i) q^{67} +5.19615i q^{69} +(-59.5000 - 103.057i) q^{73} +(-1.00000 + 1.73205i) q^{75} +(93.5000 - 73.6122i) q^{77} +(64.5000 + 37.2391i) q^{79} +(-27.5000 - 47.6314i) q^{81} -110.000 q^{83} +129.904i q^{85} +(-12.0000 + 6.92820i) q^{87} +(-35.5000 + 61.4878i) q^{89} +(-96.0000 + 13.8564i) q^{91} +(28.5000 + 16.4545i) q^{93} +(-31.5000 + 18.1865i) q^{95} -22.0000 q^{97} +136.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} + 9q^{5} - 2q^{7} + 8q^{9} + O(q^{10}) \) \( 2q + q^{3} + 9q^{5} - 2q^{7} + 8q^{9} + 17q^{11} + 25q^{17} - 7q^{19} + 11q^{21} + 9q^{23} + 2q^{25} + 34q^{27} + 57q^{31} - 17q^{33} + 27q^{35} - 15q^{37} + 24q^{39} + 52q^{41} - 28q^{43} + 72q^{45} - 87q^{47} - 94q^{49} - 25q^{51} - 159q^{53} - 14q^{57} - 55q^{59} - 39q^{61} - 104q^{63} + 72q^{65} + 17q^{67} - 119q^{73} - 2q^{75} + 187q^{77} + 129q^{79} - 55q^{81} - 220q^{83} - 24q^{87} - 71q^{89} - 192q^{91} + 57q^{93} - 63q^{95} - 44q^{97} + 272q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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 0
\(3\) 0.500000 + 0.866025i 0.166667 + 0.288675i 0.937246 0.348669i \(-0.113366\pi\)
−0.770579 + 0.637344i \(0.780033\pi\)
\(4\) 0 0
\(5\) 4.50000 + 2.59808i 0.900000 + 0.519615i 0.877200 0.480125i \(-0.159409\pi\)
0.0227998 + 0.999740i \(0.492742\pi\)
\(6\) 0 0
\(7\) −1.00000 6.92820i −0.142857 0.989743i
\(8\) 0 0
\(9\) 4.00000 6.92820i 0.444444 0.769800i
\(10\) 0 0
\(11\) 8.50000 + 14.7224i 0.772727 + 1.33840i 0.936063 + 0.351832i \(0.114441\pi\)
−0.163336 + 0.986571i \(0.552225\pi\)
\(12\) 0 0
\(13\) 13.8564i 1.06588i −0.846154 0.532939i \(-0.821088\pi\)
0.846154 0.532939i \(-0.178912\pi\)
\(14\) 0 0
\(15\) 5.19615i 0.346410i
\(16\) 0 0
\(17\) 12.5000 + 21.6506i 0.735294 + 1.27357i 0.954594 + 0.297909i \(0.0962893\pi\)
−0.219300 + 0.975657i \(0.570377\pi\)
\(18\) 0 0
\(19\) −3.50000 + 6.06218i −0.184211 + 0.319062i −0.943310 0.331912i \(-0.892306\pi\)
0.759100 + 0.650974i \(0.225639\pi\)
\(20\) 0 0
\(21\) 5.50000 4.33013i 0.261905 0.206197i
\(22\) 0 0
\(23\) 4.50000 + 2.59808i 0.195652 + 0.112960i 0.594626 0.804003i \(-0.297300\pi\)
−0.398974 + 0.916962i \(0.630634\pi\)
\(24\) 0 0
\(25\) 1.00000 + 1.73205i 0.0400000 + 0.0692820i
\(26\) 0 0
\(27\) 17.0000 0.629630
\(28\) 0 0
\(29\) 13.8564i 0.477807i 0.971043 + 0.238904i \(0.0767880\pi\)
−0.971043 + 0.238904i \(0.923212\pi\)
\(30\) 0 0
\(31\) 28.5000 16.4545i 0.919355 0.530790i 0.0359257 0.999354i \(-0.488562\pi\)
0.883429 + 0.468565i \(0.155229\pi\)
\(32\) 0 0
\(33\) −8.50000 + 14.7224i −0.257576 + 0.446134i
\(34\) 0 0
\(35\) 13.5000 33.7750i 0.385714 0.965000i
\(36\) 0 0
\(37\) −7.50000 4.33013i −0.202703 0.117030i 0.395213 0.918590i \(-0.370671\pi\)
−0.597916 + 0.801559i \(0.704004\pi\)
\(38\) 0 0
\(39\) 12.0000 6.92820i 0.307692 0.177646i
\(40\) 0 0
\(41\) 26.0000 0.634146 0.317073 0.948401i \(-0.397300\pi\)
0.317073 + 0.948401i \(0.397300\pi\)
\(42\) 0 0
\(43\) −14.0000 −0.325581 −0.162791 0.986661i \(-0.552050\pi\)
−0.162791 + 0.986661i \(0.552050\pi\)
\(44\) 0 0
\(45\) 36.0000 20.7846i 0.800000 0.461880i
\(46\) 0 0
\(47\) −43.5000 25.1147i −0.925532 0.534356i −0.0401362 0.999194i \(-0.512779\pi\)
−0.885396 + 0.464838i \(0.846113\pi\)
\(48\) 0 0
\(49\) −47.0000 + 13.8564i −0.959184 + 0.282784i
\(50\) 0 0
\(51\) −12.5000 + 21.6506i −0.245098 + 0.424522i
\(52\) 0 0
\(53\) −79.5000 + 45.8993i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(-1.00000\pi\)
\(54\) 0 0
\(55\) 88.3346i 1.60608i
\(56\) 0 0
\(57\) −7.00000 −0.122807
\(58\) 0 0
\(59\) −27.5000 47.6314i −0.466102 0.807312i 0.533149 0.846021i \(-0.321009\pi\)
−0.999250 + 0.0387097i \(0.987675\pi\)
\(60\) 0 0
\(61\) −19.5000 11.2583i −0.319672 0.184563i 0.331574 0.943429i \(-0.392420\pi\)
−0.651246 + 0.758866i \(0.725754\pi\)
\(62\) 0 0
\(63\) −52.0000 20.7846i −0.825397 0.329914i
\(64\) 0 0
\(65\) 36.0000 62.3538i 0.553846 0.959290i
\(66\) 0 0
\(67\) 8.50000 + 14.7224i 0.126866 + 0.219738i 0.922461 0.386091i \(-0.126175\pi\)
−0.795595 + 0.605829i \(0.792842\pi\)
\(68\) 0 0
\(69\) 5.19615i 0.0753066i
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −59.5000 103.057i −0.815068 1.41174i −0.909279 0.416188i \(-0.863366\pi\)
0.0942102 0.995552i \(-0.469967\pi\)
\(74\) 0 0
\(75\) −1.00000 + 1.73205i −0.0133333 + 0.0230940i
\(76\) 0 0
\(77\) 93.5000 73.6122i 1.21429 0.956002i
\(78\) 0 0
\(79\) 64.5000 + 37.2391i 0.816456 + 0.471381i 0.849193 0.528083i \(-0.177089\pi\)
−0.0327370 + 0.999464i \(0.510422\pi\)
\(80\) 0 0
\(81\) −27.5000 47.6314i −0.339506 0.588042i
\(82\) 0 0
\(83\) −110.000 −1.32530 −0.662651 0.748929i \(-0.730569\pi\)
−0.662651 + 0.748929i \(0.730569\pi\)
\(84\) 0 0
\(85\) 129.904i 1.52828i
\(86\) 0 0
\(87\) −12.0000 + 6.92820i −0.137931 + 0.0796345i
\(88\) 0 0
\(89\) −35.5000 + 61.4878i −0.398876 + 0.690874i −0.993588 0.113065i \(-0.963933\pi\)
0.594711 + 0.803939i \(0.297266\pi\)
\(90\) 0 0
\(91\) −96.0000 + 13.8564i −1.05495 + 0.152268i
\(92\) 0 0
\(93\) 28.5000 + 16.4545i 0.306452 + 0.176930i
\(94\) 0 0
\(95\) −31.5000 + 18.1865i −0.331579 + 0.191437i
\(96\) 0 0
\(97\) −22.0000 −0.226804 −0.113402 0.993549i \(-0.536175\pi\)
−0.113402 + 0.993549i \(0.536175\pi\)
\(98\) 0 0
\(99\) 136.000 1.37374
\(100\) 0 0
\(101\) −67.5000 + 38.9711i −0.668317 + 0.385853i −0.795439 0.606034i \(-0.792759\pi\)
0.127122 + 0.991887i \(0.459426\pi\)
\(102\) 0 0
\(103\) −139.500 80.5404i −1.35437 0.781945i −0.365511 0.930807i \(-0.619106\pi\)
−0.988858 + 0.148862i \(0.952439\pi\)
\(104\) 0 0
\(105\) 36.0000 5.19615i 0.342857 0.0494872i
\(106\) 0 0
\(107\) 32.5000 56.2917i 0.303738 0.526090i −0.673241 0.739423i \(-0.735098\pi\)
0.976980 + 0.213333i \(0.0684318\pi\)
\(108\) 0 0
\(109\) −7.50000 + 4.33013i −0.0688073 + 0.0397259i −0.534009 0.845479i \(-0.679315\pi\)
0.465202 + 0.885205i \(0.345982\pi\)
\(110\) 0 0
\(111\) 8.66025i 0.0780203i
\(112\) 0 0
\(113\) 122.000 1.07965 0.539823 0.841779i \(-0.318491\pi\)
0.539823 + 0.841779i \(0.318491\pi\)
\(114\) 0 0
\(115\) 13.5000 + 23.3827i 0.117391 + 0.203328i
\(116\) 0 0
\(117\) −96.0000 55.4256i −0.820513 0.473723i
\(118\) 0 0
\(119\) 137.500 108.253i 1.15546 0.909691i
\(120\) 0 0
\(121\) −84.0000 + 145.492i −0.694215 + 1.20242i
\(122\) 0 0
\(123\) 13.0000 + 22.5167i 0.105691 + 0.183062i
\(124\) 0 0
\(125\) 119.512i 0.956092i
\(126\) 0 0
\(127\) 166.277i 1.30927i 0.755947 + 0.654633i \(0.227177\pi\)
−0.755947 + 0.654633i \(0.772823\pi\)
\(128\) 0 0
\(129\) −7.00000 12.1244i −0.0542636 0.0939873i
\(130\) 0 0
\(131\) 8.50000 14.7224i 0.0648855 0.112385i −0.831758 0.555139i \(-0.812665\pi\)
0.896643 + 0.442754i \(0.145998\pi\)
\(132\) 0 0
\(133\) 45.5000 + 18.1865i 0.342105 + 0.136741i
\(134\) 0 0
\(135\) 76.5000 + 44.1673i 0.566667 + 0.327165i
\(136\) 0 0
\(137\) 72.5000 + 125.574i 0.529197 + 0.916596i 0.999420 + 0.0340486i \(0.0108401\pi\)
−0.470223 + 0.882548i \(0.655827\pi\)
\(138\) 0 0
\(139\) 82.0000 0.589928 0.294964 0.955508i \(-0.404692\pi\)
0.294964 + 0.955508i \(0.404692\pi\)
\(140\) 0 0
\(141\) 50.2295i 0.356237i
\(142\) 0 0
\(143\) 204.000 117.779i 1.42657 0.823633i
\(144\) 0 0
\(145\) −36.0000 + 62.3538i −0.248276 + 0.430026i
\(146\) 0 0
\(147\) −35.5000 33.7750i −0.241497 0.229762i
\(148\) 0 0
\(149\) 4.50000 + 2.59808i 0.0302013 + 0.0174368i 0.515025 0.857175i \(-0.327783\pi\)
−0.484823 + 0.874612i \(0.661116\pi\)
\(150\) 0 0
\(151\) −31.5000 + 18.1865i −0.208609 + 0.120441i −0.600665 0.799501i \(-0.705097\pi\)
0.392056 + 0.919942i \(0.371764\pi\)
\(152\) 0 0
\(153\) 200.000 1.30719
\(154\) 0 0
\(155\) 171.000 1.10323
\(156\) 0 0
\(157\) 268.500 155.019i 1.71019 0.987379i 0.775909 0.630845i \(-0.217292\pi\)
0.934282 0.356534i \(-0.116042\pi\)
\(158\) 0 0
\(159\) −79.5000 45.8993i −0.500000 0.288675i
\(160\) 0 0
\(161\) 13.5000 33.7750i 0.0838509 0.209783i
\(162\) 0 0
\(163\) 8.50000 14.7224i 0.0521472 0.0903217i −0.838773 0.544481i \(-0.816727\pi\)
0.890921 + 0.454159i \(0.150060\pi\)
\(164\) 0 0
\(165\) −76.5000 + 44.1673i −0.463636 + 0.267681i
\(166\) 0 0
\(167\) 13.8564i 0.0829725i 0.999139 + 0.0414862i \(0.0132093\pi\)
−0.999139 + 0.0414862i \(0.986791\pi\)
\(168\) 0 0
\(169\) −23.0000 −0.136095
\(170\) 0 0
\(171\) 28.0000 + 48.4974i 0.163743 + 0.283611i
\(172\) 0 0
\(173\) −91.5000 52.8275i −0.528902 0.305362i 0.211667 0.977342i \(-0.432111\pi\)
−0.740569 + 0.671980i \(0.765444\pi\)
\(174\) 0 0
\(175\) 11.0000 8.66025i 0.0628571 0.0494872i
\(176\) 0 0
\(177\) 27.5000 47.6314i 0.155367 0.269104i
\(178\) 0 0
\(179\) 44.5000 + 77.0763i 0.248603 + 0.430594i 0.963139 0.269006i \(-0.0866951\pi\)
−0.714535 + 0.699600i \(0.753362\pi\)
\(180\) 0 0
\(181\) 249.415i 1.37799i 0.724768 + 0.688993i \(0.241947\pi\)
−0.724768 + 0.688993i \(0.758053\pi\)
\(182\) 0 0
\(183\) 22.5167i 0.123042i
\(184\) 0 0
\(185\) −22.5000 38.9711i −0.121622 0.210655i
\(186\) 0 0
\(187\) −212.500 + 368.061i −1.13636 + 1.96824i
\(188\) 0 0
\(189\) −17.0000 117.779i −0.0899471 0.623172i
\(190\) 0 0
\(191\) −187.500 108.253i −0.981675 0.566771i −0.0788999 0.996883i \(-0.525141\pi\)
−0.902776 + 0.430112i \(0.858474\pi\)
\(192\) 0 0
\(193\) 36.5000 + 63.2199i 0.189119 + 0.327564i 0.944957 0.327195i \(-0.106103\pi\)
−0.755838 + 0.654759i \(0.772770\pi\)
\(194\) 0 0
\(195\) 72.0000 0.369231
\(196\) 0 0
\(197\) 207.846i 1.05506i 0.849538 + 0.527528i \(0.176881\pi\)
−0.849538 + 0.527528i \(0.823119\pi\)
\(198\) 0 0
\(199\) −55.5000 + 32.0429i −0.278894 + 0.161020i −0.632923 0.774215i \(-0.718145\pi\)
0.354028 + 0.935235i \(0.384812\pi\)
\(200\) 0 0
\(201\) −8.50000 + 14.7224i −0.0422886 + 0.0732459i
\(202\) 0 0
\(203\) 96.0000 13.8564i 0.472906 0.0682582i
\(204\) 0 0
\(205\) 117.000 + 67.5500i 0.570732 + 0.329512i
\(206\) 0 0
\(207\) 36.0000 20.7846i 0.173913 0.100409i
\(208\) 0 0
\(209\) −119.000 −0.569378
\(210\) 0 0
\(211\) −302.000 −1.43128 −0.715640 0.698470i \(-0.753865\pi\)
−0.715640 + 0.698470i \(0.753865\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −63.0000 36.3731i −0.293023 0.169177i
\(216\) 0 0
\(217\) −142.500 180.999i −0.656682 0.834098i
\(218\) 0 0
\(219\) 59.5000 103.057i 0.271689 0.470580i
\(220\) 0 0
\(221\) 300.000 173.205i 1.35747 0.783733i
\(222\) 0 0
\(223\) 138.564i 0.621364i −0.950514 0.310682i \(-0.899443\pi\)
0.950514 0.310682i \(-0.100557\pi\)
\(224\) 0 0
\(225\) 16.0000 0.0711111
\(226\) 0 0
\(227\) −27.5000 47.6314i −0.121145 0.209830i 0.799074 0.601232i \(-0.205323\pi\)
−0.920220 + 0.391402i \(0.871990\pi\)
\(228\) 0 0
\(229\) −283.500 163.679i −1.23799 0.714755i −0.269308 0.963054i \(-0.586795\pi\)
−0.968683 + 0.248300i \(0.920128\pi\)
\(230\) 0 0
\(231\) 110.500 + 44.1673i 0.478355 + 0.191200i
\(232\) 0 0
\(233\) 192.500 333.420i 0.826180 1.43099i −0.0748337 0.997196i \(-0.523843\pi\)
0.901014 0.433790i \(-0.142824\pi\)
\(234\) 0 0
\(235\) −130.500 226.033i −0.555319 0.961841i
\(236\) 0 0
\(237\) 74.4782i 0.314254i
\(238\) 0 0
\(239\) 429.549i 1.79727i 0.438693 + 0.898637i \(0.355442\pi\)
−0.438693 + 0.898637i \(0.644558\pi\)
\(240\) 0 0
\(241\) 72.5000 + 125.574i 0.300830 + 0.521053i 0.976324 0.216313i \(-0.0694030\pi\)
−0.675494 + 0.737365i \(0.736070\pi\)
\(242\) 0 0
\(243\) 104.000 180.133i 0.427984 0.741289i
\(244\) 0 0
\(245\) −247.500 59.7558i −1.01020 0.243901i
\(246\) 0 0
\(247\) 84.0000 + 48.4974i 0.340081 + 0.196346i
\(248\) 0 0
\(249\) −55.0000 95.2628i −0.220884 0.382582i
\(250\) 0 0
\(251\) 58.0000 0.231076 0.115538 0.993303i \(-0.463141\pi\)
0.115538 + 0.993303i \(0.463141\pi\)
\(252\) 0 0
\(253\) 88.3346i 0.349149i
\(254\) 0 0
\(255\) −112.500 + 64.9519i −0.441176 + 0.254713i
\(256\) 0 0
\(257\) −59.5000 + 103.057i −0.231518 + 0.401000i −0.958255 0.285915i \(-0.907702\pi\)
0.726737 + 0.686915i \(0.241036\pi\)
\(258\) 0 0
\(259\) −22.5000 + 56.2917i −0.0868726 + 0.217342i
\(260\) 0 0
\(261\) 96.0000 + 55.4256i 0.367816 + 0.212359i
\(262\) 0 0
\(263\) −283.500 + 163.679i −1.07795 + 0.622353i −0.930342 0.366694i \(-0.880490\pi\)
−0.147605 + 0.989046i \(0.547156\pi\)
\(264\) 0 0
\(265\) −477.000 −1.80000
\(266\) 0 0
\(267\) −71.0000 −0.265918
\(268\) 0 0
\(269\) −115.500 + 66.6840i −0.429368 + 0.247896i −0.699077 0.715046i \(-0.746406\pi\)
0.269709 + 0.962942i \(0.413072\pi\)
\(270\) 0 0
\(271\) 376.500 + 217.372i 1.38930 + 0.802112i 0.993236 0.116111i \(-0.0370430\pi\)
0.396063 + 0.918223i \(0.370376\pi\)
\(272\) 0 0
\(273\) −60.0000 76.2102i −0.219780 0.279158i
\(274\) 0 0
\(275\) −17.0000 + 29.4449i −0.0618182 + 0.107072i
\(276\) 0 0
\(277\) −175.500 + 101.325i −0.633574 + 0.365794i −0.782135 0.623109i \(-0.785869\pi\)
0.148561 + 0.988903i \(0.452536\pi\)
\(278\) 0 0
\(279\) 263.272i 0.943626i
\(280\) 0 0
\(281\) 74.0000 0.263345 0.131673 0.991293i \(-0.457965\pi\)
0.131673 + 0.991293i \(0.457965\pi\)
\(282\) 0 0
\(283\) −231.500 400.970i −0.818021 1.41685i −0.907138 0.420833i \(-0.861738\pi\)
0.0891169 0.996021i \(-0.471596\pi\)
\(284\) 0 0
\(285\) −31.5000 18.1865i −0.110526 0.0638124i
\(286\) 0 0
\(287\) −26.0000 180.133i −0.0905923 0.627642i
\(288\) 0 0
\(289\) −168.000 + 290.985i −0.581315 + 1.00687i
\(290\) 0 0
\(291\) −11.0000 19.0526i −0.0378007 0.0654727i
\(292\) 0 0
\(293\) 110.851i 0.378332i 0.981945 + 0.189166i \(0.0605784\pi\)
−0.981945 + 0.189166i \(0.939422\pi\)
\(294\) 0 0
\(295\) 285.788i 0.968774i
\(296\) 0 0
\(297\) 144.500 + 250.281i 0.486532 + 0.842698i
\(298\) 0 0
\(299\) 36.0000 62.3538i 0.120401 0.208541i
\(300\) 0 0
\(301\) 14.0000 + 96.9948i 0.0465116 + 0.322242i
\(302\) 0 0
\(303\) −67.5000 38.9711i −0.222772 0.128618i
\(304\) 0 0
\(305\) −58.5000 101.325i −0.191803 0.332213i
\(306\) 0 0
\(307\) 274.000 0.892508 0.446254 0.894906i \(-0.352758\pi\)
0.446254 + 0.894906i \(0.352758\pi\)
\(308\) 0 0
\(309\) 161.081i 0.521297i
\(310\) 0 0
\(311\) −43.5000 + 25.1147i −0.139871 + 0.0807548i −0.568303 0.822820i \(-0.692400\pi\)
0.428431 + 0.903574i \(0.359066\pi\)
\(312\) 0 0
\(313\) 204.500 354.204i 0.653355 1.13164i −0.328949 0.944348i \(-0.606694\pi\)
0.982304 0.187296i \(-0.0599723\pi\)
\(314\) 0 0
\(315\) −180.000 228.631i −0.571429 0.725812i
\(316\) 0 0
\(317\) −163.500 94.3968i −0.515773 0.297782i 0.219431 0.975628i \(-0.429580\pi\)
−0.735203 + 0.677847i \(0.762913\pi\)
\(318\) 0 0
\(319\) −204.000 + 117.779i −0.639498 + 0.369215i
\(320\) 0 0
\(321\) 65.0000 0.202492
\(322\) 0 0
\(323\) −175.000 −0.541796
\(324\) 0 0
\(325\) 24.0000 13.8564i 0.0738462 0.0426351i
\(326\) 0 0
\(327\) −7.50000 4.33013i −0.0229358 0.0132420i
\(328\) 0 0
\(329\) −130.500 + 326.492i −0.396657 + 0.992376i
\(330\) 0 0
\(331\) −147.500 + 255.477i −0.445619 + 0.771835i −0.998095 0.0616936i \(-0.980350\pi\)
0.552476 + 0.833529i \(0.313683\pi\)
\(332\) 0 0
\(333\) −60.0000 + 34.6410i −0.180180 + 0.104027i
\(334\) 0 0
\(335\) 88.3346i 0.263685i
\(336\) 0 0
\(337\) 26.0000 0.0771513 0.0385757 0.999256i \(-0.487718\pi\)
0.0385757 + 0.999256i \(0.487718\pi\)
\(338\) 0 0
\(339\) 61.0000 + 105.655i 0.179941 + 0.311667i
\(340\) 0 0
\(341\) 484.500 + 279.726i 1.42082 + 0.820311i
\(342\) 0 0
\(343\) 143.000 + 311.769i 0.416910 + 0.908948i
\(344\) 0 0
\(345\) −13.5000 + 23.3827i −0.0391304 + 0.0677759i
\(346\) 0 0
\(347\) 188.500 + 326.492i 0.543228 + 0.940898i 0.998716 + 0.0506562i \(0.0161313\pi\)
−0.455488 + 0.890242i \(0.650535\pi\)
\(348\) 0 0
\(349\) 96.9948i 0.277922i 0.990298 + 0.138961i \(0.0443763\pi\)
−0.990298 + 0.138961i \(0.955624\pi\)
\(350\) 0 0
\(351\) 235.559i 0.671108i
\(352\) 0 0
\(353\) −251.500 435.611i −0.712465 1.23402i −0.963929 0.266158i \(-0.914246\pi\)
0.251465 0.967866i \(-0.419088\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 162.500 + 64.9519i 0.455182 + 0.181938i
\(358\) 0 0
\(359\) 160.500 + 92.6647i 0.447075 + 0.258119i 0.706594 0.707619i \(-0.250231\pi\)
−0.259519 + 0.965738i \(0.583564\pi\)
\(360\) 0 0
\(361\) 156.000 + 270.200i 0.432133 + 0.748476i
\(362\) 0 0
\(363\) −168.000 −0.462810
\(364\) 0 0
\(365\) 618.342i 1.69409i
\(366\) 0 0
\(367\) 256.500 148.090i 0.698910 0.403516i −0.108031 0.994147i \(-0.534455\pi\)
0.806941 + 0.590632i \(0.201121\pi\)
\(368\) 0 0
\(369\) 104.000 180.133i 0.281843 0.488166i
\(370\) 0 0
\(371\) 397.500 + 504.893i 1.07143 + 1.36090i
\(372\) 0 0
\(373\) −103.500 59.7558i −0.277480 0.160203i 0.354802 0.934941i \(-0.384548\pi\)
−0.632282 + 0.774738i \(0.717882\pi\)
\(374\) 0 0
\(375\) 103.500 59.7558i 0.276000 0.159349i
\(376\) 0 0
\(377\) 192.000 0.509284
\(378\) 0 0
\(379\) 634.000 1.67282 0.836412 0.548102i \(-0.184649\pi\)
0.836412 + 0.548102i \(0.184649\pi\)
\(380\) 0 0
\(381\) −144.000 + 83.1384i −0.377953 + 0.218211i
\(382\) 0 0
\(383\) −211.500 122.110i −0.552219 0.318824i 0.197797 0.980243i \(-0.436621\pi\)
−0.750017 + 0.661419i \(0.769955\pi\)
\(384\) 0 0
\(385\) 612.000 88.3346i 1.58961 0.229440i
\(386\) 0 0
\(387\) −56.0000 + 96.9948i −0.144703 + 0.250633i
\(388\) 0 0
\(389\) 508.500 293.583i 1.30720 0.754711i 0.325570 0.945518i \(-0.394444\pi\)
0.981628 + 0.190807i \(0.0611104\pi\)
\(390\) 0 0
\(391\) 129.904i 0.332235i
\(392\) 0 0
\(393\) 17.0000 0.0432570
\(394\) 0 0
\(395\) 193.500 + 335.152i 0.489873 + 0.848486i
\(396\) 0 0
\(397\) 208.500 + 120.378i 0.525189 + 0.303218i 0.739055 0.673645i \(-0.235272\pi\)
−0.213866 + 0.976863i \(0.568606\pi\)
\(398\) 0 0
\(399\) 7.00000 + 48.4974i 0.0175439 + 0.121547i
\(400\) 0 0
\(401\) −59.5000 + 103.057i −0.148379 + 0.257000i −0.930629 0.365965i \(-0.880739\pi\)
0.782249 + 0.622965i \(0.214072\pi\)
\(402\) 0 0
\(403\) −228.000 394.908i −0.565757 0.979920i
\(404\) 0 0
\(405\) 285.788i 0.705650i
\(406\) 0 0
\(407\) 147.224i 0.361731i
\(408\) 0 0
\(409\) 72.5000 + 125.574i 0.177262 + 0.307026i 0.940942 0.338569i \(-0.109943\pi\)
−0.763680 + 0.645595i \(0.776609\pi\)
\(410\) 0 0
\(411\) −72.5000 + 125.574i −0.176399 + 0.305532i
\(412\) 0 0
\(413\) −302.500 + 238.157i −0.732446 + 0.576651i
\(414\) 0 0
\(415\) −495.000 285.788i −1.19277 0.688647i
\(416\) 0 0
\(417\) 41.0000 + 71.0141i 0.0983213 + 0.170298i
\(418\) 0 0
\(419\) −302.000 −0.720764 −0.360382 0.932805i \(-0.617354\pi\)
−0.360382 + 0.932805i \(0.617354\pi\)
\(420\) 0 0
\(421\) 401.836i 0.954479i −0.878773 0.477240i \(-0.841637\pi\)
0.878773 0.477240i \(-0.158363\pi\)
\(422\) 0 0
\(423\) −348.000 + 200.918i −0.822695 + 0.474983i
\(424\) 0 0
\(425\) −25.0000 + 43.3013i −0.0588235 + 0.101885i
\(426\) 0 0
\(427\) −58.5000 + 146.358i −0.137002 + 0.342759i
\(428\) 0 0
\(429\) 204.000 + 117.779i 0.475524 + 0.274544i
\(430\) 0 0
\(431\) 700.500 404.434i 1.62529 0.938362i 0.639817 0.768527i \(-0.279010\pi\)
0.985473 0.169835i \(-0.0543234\pi\)
\(432\) 0 0
\(433\) 410.000 0.946882 0.473441 0.880825i \(-0.343012\pi\)
0.473441 + 0.880825i \(0.343012\pi\)
\(434\) 0 0
\(435\) −72.0000 −0.165517
\(436\) 0 0
\(437\) −31.5000 + 18.1865i −0.0720824 + 0.0416168i
\(438\) 0 0
\(439\) 424.500 + 245.085i 0.966970 + 0.558281i 0.898311 0.439360i \(-0.144795\pi\)
0.0686591 + 0.997640i \(0.478128\pi\)
\(440\) 0 0
\(441\) −92.0000 + 381.051i −0.208617 + 0.864062i
\(442\) 0 0
\(443\) 200.500 347.276i 0.452596 0.783919i −0.545950 0.837817i \(-0.683831\pi\)
0.998546 + 0.0538983i \(0.0171647\pi\)
\(444\) 0 0
\(445\) −319.500 + 184.463i −0.717978 + 0.414525i
\(446\) 0 0
\(447\) 5.19615i 0.0116245i
\(448\) 0 0
\(449\) −310.000 −0.690423 −0.345212 0.938525i \(-0.612193\pi\)
−0.345212 + 0.938525i \(0.612193\pi\)
\(450\) 0 0
\(451\) 221.000 + 382.783i 0.490022 + 0.848743i
\(452\) 0 0
\(453\) −31.5000 18.1865i −0.0695364 0.0401469i
\(454\) 0 0
\(455\) −468.000 187.061i −1.02857 0.411124i
\(456\) 0 0
\(457\) −83.5000 + 144.626i −0.182713 + 0.316469i −0.942804 0.333349i \(-0.891821\pi\)
0.760090 + 0.649818i \(0.225155\pi\)
\(458\) 0 0
\(459\) 212.500 + 368.061i 0.462963 + 0.801875i
\(460\) 0 0
\(461\) 13.8564i 0.0300573i 0.999887 + 0.0150286i \(0.00478394\pi\)
−0.999887 + 0.0150286i \(0.995216\pi\)
\(462\) 0 0
\(463\) 609.682i 1.31681i −0.752665 0.658404i \(-0.771232\pi\)
0.752665 0.658404i \(-0.228768\pi\)
\(464\) 0 0
\(465\) 85.5000 + 148.090i 0.183871 + 0.318474i
\(466\) 0 0
\(467\) 392.500 679.830i 0.840471 1.45574i −0.0490258 0.998798i \(-0.515612\pi\)
0.889497 0.456941i \(-0.151055\pi\)
\(468\) 0 0
\(469\) 93.5000 73.6122i 0.199360 0.156956i
\(470\) 0 0
\(471\) 268.500 + 155.019i 0.570064 + 0.329126i
\(472\) 0 0
\(473\) −119.000 206.114i −0.251586 0.435759i
\(474\) 0 0
\(475\) −14.0000 −0.0294737
\(476\) 0 0
\(477\) 734.390i 1.53960i
\(478\) 0 0
\(479\) −535.500 + 309.171i −1.11795 + 0.645451i −0.940878 0.338746i \(-0.889997\pi\)
−0.177076 + 0.984197i \(0.556664\pi\)
\(480\) 0 0
\(481\) −60.0000 + 103.923i −0.124740 + 0.216056i
\(482\) 0 0
\(483\) 36.0000 5.19615i 0.0745342 0.0107581i
\(484\) 0 0
\(485\) −99.0000 57.1577i −0.204124 0.117851i
\(486\) 0 0
\(487\) 340.500 196.588i 0.699179 0.403671i −0.107863 0.994166i \(-0.534401\pi\)
0.807041 + 0.590495i \(0.201067\pi\)
\(488\) 0 0
\(489\) 17.0000 0.0347648
\(490\) 0 0
\(491\) −422.000 −0.859470 −0.429735 0.902955i \(-0.641393\pi\)
−0.429735 + 0.902955i \(0.641393\pi\)
\(492\) 0 0
\(493\) −300.000 + 173.205i −0.608519 + 0.351329i
\(494\) 0 0
\(495\) 612.000 + 353.338i 1.23636 + 0.713815i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 32.5000 56.2917i 0.0651303 0.112809i −0.831622 0.555343i \(-0.812587\pi\)
0.896752 + 0.442534i \(0.145920\pi\)
\(500\) 0 0
\(501\) −12.0000 + 6.92820i −0.0239521 + 0.0138287i
\(502\) 0 0
\(503\) 249.415i 0.495855i 0.968779 + 0.247928i \(0.0797496\pi\)
−0.968779 + 0.247928i \(0.920250\pi\)
\(504\) 0 0
\(505\) −405.000 −0.801980
\(506\) 0 0
\(507\) −11.5000 19.9186i −0.0226824 0.0392871i
\(508\) 0 0
\(509\) 472.500 + 272.798i 0.928291 + 0.535949i 0.886271 0.463168i \(-0.153287\pi\)
0.0420202 + 0.999117i \(0.486621\pi\)
\(510\) 0 0
\(511\) −654.500 + 515.285i −1.28082 + 1.00839i
\(512\) 0 0
\(513\) −59.5000 + 103.057i −0.115984 + 0.200891i
\(514\) 0 0
\(515\) −418.500 724.863i −0.812621 1.40750i
\(516\) 0 0
\(517\) 853.901i 1.65165i
\(518\) 0 0
\(519\) 105.655i 0.203574i
\(520\) 0 0
\(521\) 12.5000 + 21.6506i 0.0239923 + 0.0415559i 0.877772 0.479078i \(-0.159029\pi\)
−0.853780 + 0.520634i \(0.825696\pi\)
\(522\) 0 0
\(523\) 296.500 513.553i 0.566922 0.981937i −0.429946 0.902854i \(-0.641468\pi\)
0.996868 0.0790826i \(-0.0251991\pi\)
\(524\) 0 0
\(525\) 13.0000 + 5.19615i 0.0247619 + 0.00989743i
\(526\) 0 0
\(527\) 712.500 + 411.362i 1.35199 + 0.780573i
\(528\) 0 0
\(529\) −251.000 434.745i −0.474480 0.821824i
\(530\) 0 0
\(531\) −440.000 −0.828625
\(532\) 0 0
\(533\) 360.267i 0.675922i
\(534\) 0 0
\(535\) 292.500 168.875i 0.546729 0.315654i
\(536\) 0 0
\(537\) −44.5000 + 77.0763i −0.0828678 + 0.143531i
\(538\) 0 0
\(539\) −603.500 574.175i −1.11967 1.06526i
\(540\) 0 0
\(541\) −655.500 378.453i −1.21165 0.699544i −0.248528 0.968625i \(-0.579947\pi\)
−0.963117 + 0.269081i \(0.913280\pi\)
\(542\) 0 0
\(543\) −216.000 + 124.708i −0.397790 + 0.229664i
\(544\) 0 0
\(545\) −45.0000 −0.0825688
\(546\) 0 0
\(547\) −662.000 −1.21024 −0.605119 0.796135i \(-0.706874\pi\)
−0.605119 + 0.796135i \(0.706874\pi\)
\(548\) 0 0
\(549\) −156.000 + 90.0666i −0.284153 + 0.164056i
\(550\) 0 0
\(551\) −84.0000 48.4974i −0.152450 0.0880171i
\(552\) 0 0
\(553\) 193.500 484.108i 0.349910 0.875422i
\(554\) 0 0
\(555\) 22.5000 38.9711i 0.0405405 0.0702183i
\(556\) 0 0
\(557\) −511.500 + 295.315i −0.918312 + 0.530188i −0.883096 0.469192i \(-0.844545\pi\)
−0.0352161 + 0.999380i \(0.511212\pi\)
\(558\) 0 0
\(559\) 193.990i 0.347030i
\(560\) 0 0
\(561\) −425.000 −0.757576
\(562\) 0 0
\(563\) 368.500 + 638.261i 0.654529 + 1.13368i 0.982012 + 0.188821i \(0.0604665\pi\)
−0.327482 + 0.944857i \(0.606200\pi\)
\(564\) 0 0
\(565\) 549.000 + 316.965i 0.971681 + 0.561001i
\(566\) 0 0
\(567\) −302.500 + 238.157i −0.533510 + 0.420030i
\(568\) 0 0
\(569\) 60.5000 104.789i 0.106327 0.184164i −0.807953 0.589247i \(-0.799424\pi\)
0.914280 + 0.405084i \(0.132758\pi\)
\(570\) 0 0
\(571\) 368.500 + 638.261i 0.645359 + 1.11779i 0.984218 + 0.176958i \(0.0566255\pi\)
−0.338859 + 0.940837i \(0.610041\pi\)
\(572\) 0 0
\(573\) 216.506i 0.377847i
\(574\) 0 0
\(575\) 10.3923i 0.0180736i
\(576\) 0 0
\(577\) −23.5000 40.7032i −0.0407279 0.0705428i 0.844943 0.534857i \(-0.179634\pi\)
−0.885671 + 0.464314i \(0.846301\pi\)
\(578\) 0 0
\(579\) −36.5000 + 63.2199i −0.0630397 + 0.109188i
\(580\) 0 0
\(581\) 110.000 + 762.102i 0.189329 + 1.31171i
\(582\) 0 0
\(583\) −1351.50 780.289i −2.31818 1.33840i
\(584\) 0 0
\(585\) −288.000 498.831i −0.492308 0.852702i
\(586\) 0 0
\(587\) −446.000 −0.759796 −0.379898 0.925028i \(-0.624041\pi\)
−0.379898 + 0.925028i \(0.624041\pi\)
\(588\) 0 0
\(589\) 230.363i 0.391108i
\(590\) 0 0
\(591\) −180.000 + 103.923i −0.304569 + 0.175843i
\(592\) 0 0
\(593\) −107.500 + 186.195i −0.181282 + 0.313989i −0.942317 0.334721i \(-0.891358\pi\)
0.761036 + 0.648710i \(0.224691\pi\)
\(594\) 0 0
\(595\) 900.000 129.904i 1.51261 0.218326i
\(596\) 0 0
\(597\) −55.5000 32.0429i −0.0929648 0.0536733i
\(598\) 0 0
\(599\) 244.500 141.162i 0.408180 0.235663i −0.281827 0.959465i \(-0.590941\pi\)
0.690008 + 0.723802i \(0.257607\pi\)
\(600\) 0 0
\(601\) 266.000 0.442596 0.221298 0.975206i \(-0.428971\pi\)
0.221298 + 0.975206i \(0.428971\pi\)
\(602\) 0 0
\(603\) 136.000 0.225539
\(604\) 0 0
\(605\) −756.000 + 436.477i −1.24959 + 0.721449i
\(606\) 0 0
\(607\) −571.500 329.956i −0.941516 0.543584i −0.0510805 0.998695i \(-0.516267\pi\)
−0.890435 + 0.455110i \(0.849600\pi\)
\(608\) 0 0
\(609\) 60.0000 + 76.2102i 0.0985222 + 0.125140i
\(610\) 0 0
\(611\) −348.000 + 602.754i −0.569558 + 0.986504i
\(612\) 0 0
\(613\) 604.500 349.008i 0.986134 0.569345i 0.0820174 0.996631i \(-0.473864\pi\)
0.904116 + 0.427286i \(0.140530\pi\)
\(614\) 0 0
\(615\) 135.100i 0.219675i
\(616\) 0 0
\(617\) −118.000 −0.191248 −0.0956240 0.995418i \(-0.530485\pi\)
−0.0956240 + 0.995418i \(0.530485\pi\)
\(618\) 0 0
\(619\) −459.500 795.877i −0.742326 1.28575i −0.951434 0.307854i \(-0.900389\pi\)
0.209107 0.977893i \(-0.432944\pi\)
\(620\) 0 0
\(621\) 76.5000 + 44.1673i 0.123188 + 0.0711229i
\(622\) 0 0
\(623\) 461.500 + 184.463i 0.740770 + 0.296089i
\(624\) 0 0
\(625\) 335.500 581.103i 0.536800 0.929765i
\(626\) 0 0
\(627\) −59.5000 103.057i −0.0948963 0.164365i
\(628\) 0 0
\(629\) 216.506i 0.344207i
\(630\) 0 0
\(631\) 166.277i 0.263513i 0.991282 + 0.131757i \(0.0420617\pi\)
−0.991282 + 0.131757i \(0.957938\pi\)
\(632\) 0 0
\(633\) −151.000 261.540i −0.238547 0.413175i
\(634\) 0 0
\(635\) −432.000 + 748.246i −0.680315 + 1.17834i
\(636\) 0 0
\(637\) 192.000 + 651.251i 0.301413 + 1.02237i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.500000 + 0.866025i 0.000780031 + 0.00135105i 0.866415 0.499324i \(-0.166418\pi\)
−0.865635 + 0.500675i \(0.833085\pi\)
\(642\) 0 0
\(643\) 514.000 0.799378 0.399689 0.916651i \(-0.369118\pi\)
0.399689 + 0.916651i \(0.369118\pi\)
\(644\) 0 0
\(645\) 72.7461i 0.112785i
\(646\) 0 0
\(647\) 52.5000 30.3109i 0.0811437 0.0468484i −0.458879 0.888499i \(-0.651749\pi\)
0.540023 + 0.841650i \(0.318416\pi\)
\(648\) 0 0
\(649\) 467.500 809.734i 0.720339 1.24766i
\(650\) 0 0
\(651\) 85.5000 213.908i 0.131336 0.328584i
\(652\) 0 0
\(653\) −283.500 163.679i −0.434150 0.250657i 0.266963 0.963707i \(-0.413980\pi\)
−0.701113 + 0.713050i \(0.747313\pi\)
\(654\) 0 0
\(655\) 76.5000 44.1673i 0.116794 0.0674310i
\(656\) 0 0
\(657\) −952.000 −1.44901
\(658\) 0 0
\(659\) −542.000 −0.822458 −0.411229 0.911532i \(-0.634900\pi\)
−0.411229 + 0.911532i \(0.634900\pi\)
\(660\) 0 0
\(661\) 1024.50 591.495i 1.54992 0.894849i 0.551778 0.833991i \(-0.313950\pi\)
0.998146 0.0608582i \(-0.0193837\pi\)
\(662\) 0 0
\(663\) 300.000 + 173.205i 0.452489 + 0.261244i
\(664\) 0 0
\(665\) 157.500 + 200.052i 0.236842 + 0.300830i
\(666\) 0 0
\(667\) −36.0000 + 62.3538i −0.0539730 + 0.0934840i
\(668\) 0 0
\(669\) 120.000 69.2820i 0.179372 0.103561i
\(670\) 0 0
\(671\) 382.783i 0.570467i
\(672\) 0 0
\(673\) 218.000 0.323923 0.161961 0.986797i \(-0.448218\pi\)
0.161961 + 0.986797i \(0.448218\pi\)
\(674\) 0 0
\(675\) 17.0000 + 29.4449i 0.0251852 + 0.0436220i
\(676\) 0 0
\(677\) 556.500 + 321.295i 0.822009 + 0.474587i 0.851109 0.524989i \(-0.175931\pi\)
−0.0290999 + 0.999577i \(0.509264\pi\)
\(678\) 0 0
\(679\) 22.0000 + 152.420i 0.0324006 + 0.224478i
\(680\) 0 0
\(681\) 27.5000 47.6314i 0.0403818 0.0699433i
\(682\) 0 0
\(683\) −183.500 317.831i −0.268668 0.465346i 0.699850 0.714289i \(-0.253250\pi\)
−0.968518 + 0.248943i \(0.919917\pi\)
\(684\) 0 0
\(685\) 753.442i 1.09992i
\(686\) 0 0
\(687\) 327.358i 0.476503i
\(688\) 0 0
\(689\) 636.000 + 1101.58i 0.923077 + 1.59882i
\(690\) 0 0
\(691\) 248.500 430.415i 0.359624 0.622887i −0.628274 0.777992i \(-0.716238\pi\)
0.987898 + 0.155105i \(0.0495717\pi\)
\(692\) 0 0
\(693\) −136.000 942.236i −0.196248 1.35965i
\(694\) 0 0
\(695\) 369.000 + 213.042i 0.530935 + 0.306536i
\(696\) 0 0
\(697\) 325.000 + 562.917i 0.466284 + 0.807628i
\(698\) 0 0
\(699\) 385.000 0.550787
\(700\) 0 0
\(701\) 332.554i 0.474399i −0.971461 0.237200i \(-0.923770\pi\)
0.971461 0.237200i \(-0.0762295\pi\)
\(702\) 0 0
\(703\) 52.5000 30.3109i 0.0746799 0.0431165i
\(704\) 0 0
\(705\) 130.500 226.033i 0.185106 0.320614i
\(706\) 0 0
\(707\) 337.500 + 428.683i 0.477369 + 0.606340i
\(708\) 0 0
\(709\) −343.500 198.320i −0.484485 0.279718i 0.237799 0.971314i \(-0.423574\pi\)
−0.722284 + 0.691597i \(0.756908\pi\)
\(710\) 0 0
\(711\) 516.000 297.913i 0.725738 0.419005i
\(712\) 0 0
\(713\) 171.000 0.239832
\(714\) 0 0
\(715\) 1224.00 1.71189
\(716\) 0 0
\(717\) −372.000 + 214.774i −0.518828 + 0.299546i
\(718\) 0 0
\(719\) −55.5000 32.0429i −0.0771905 0.0445660i 0.460908 0.887448i \(-0.347524\pi\)
−0.538098 + 0.842882i \(0.680857\pi\)
\(720\) 0 0
\(721\) −418.500 + 1047.02i −0.580444 + 1.45218i
\(722\) 0 0
\(723\) −72.5000 + 125.574i −0.100277 + 0.173684i
\(724\) 0 0
\(725\) −24.0000 + 13.8564i −0.0331034 + 0.0191123i
\(726\) 0 0
\(727\) 55.4256i 0.0762388i −0.999273 0.0381194i \(-0.987863\pi\)
0.999273 0.0381194i \(-0.0121367\pi\)
\(728\) 0 0
\(729\) −287.000 −0.393690
\(730\) 0 0
\(731\) −175.000 303.109i −0.239398 0.414650i
\(732\) 0 0
\(733\) −715.500 413.094i −0.976126 0.563566i −0.0750273 0.997181i \(-0.523904\pi\)
−0.901098 + 0.433615i \(0.857238\pi\)
\(734\) 0 0
\(735\) −72.0000 244.219i −0.0979592 0.332271i
\(736\) 0 0
\(737\) −144.500 + 250.281i −0.196065 + 0.339595i
\(738\) 0 0
\(739\) 356.500 + 617.476i 0.482409 + 0.835556i 0.999796 0.0201950i \(-0.00642870\pi\)
−0.517387 + 0.855751i \(0.673095\pi\)
\(740\) 0 0
\(741\) 96.9948i 0.130897i
\(742\) 0 0
\(743\) 637.395i 0.857866i 0.903336 + 0.428933i \(0.141110\pi\)
−0.903336 + 0.428933i \(0.858890\pi\)
\(744\) 0 0
\(745\) 13.5000 + 23.3827i 0.0181208 + 0.0313862i
\(746\) 0 0
\(747\) −440.000 + 762.102i −0.589023 + 1.02022i
\(748\) 0 0
\(749\) −422.500 168.875i −0.564085 0.225467i
\(750\) 0 0
\(751\) 1012.50 + 584.567i 1.34820 + 0.778385i 0.987995 0.154487i \(-0.0493725\pi\)
0.360208 + 0.932872i \(0.382706\pi\)
\(752\) 0 0
\(753\) 29.0000 + 50.2295i 0.0385126 + 0.0667058i
\(754\) 0 0
\(755\) −189.000 −0.250331
\(756\) 0 0
\(757\) 1039.23i 1.37283i −0.727211 0.686414i \(-0.759184\pi\)
0.727211 0.686414i \(-0.240816\pi\)
\(758\) 0 0
\(759\) −76.5000 + 44.1673i −0.100791 + 0.0581914i
\(760\) 0 0
\(761\) −431.500 + 747.380i −0.567017 + 0.982102i 0.429842 + 0.902904i \(0.358569\pi\)
−0.996859 + 0.0791982i \(0.974764\pi\)
\(762\) 0 0
\(763\) 37.5000 + 47.6314i 0.0491481 + 0.0624265i
\(764\) 0 0
\(765\) 900.000 + 519.615i 1.17647 + 0.679236i
\(766\) 0 0
\(767\) −660.000 + 381.051i −0.860495 + 0.496807i
\(768\) 0 0
\(769\) 410.000 0.533160 0.266580 0.963813i \(-0.414106\pi\)
0.266580 + 0.963813i \(0.414106\pi\)
\(770\) 0 0
\(771\) −119.000 −0.154345
\(772\) 0 0
\(773\) −691.500 + 399.238i −0.894567 + 0.516478i −0.875433 0.483339i \(-0.839424\pi\)
−0.0191332 + 0.999817i \(0.506091\pi\)
\(774\) 0 0
\(775\) 57.0000 + 32.9090i 0.0735484 + 0.0424632i
\(776\) 0 0
\(777\) −60.0000 + 8.66025i −0.0772201 + 0.0111458i
\(778\) 0 0
\(779\) −91.0000 + 157.617i −0.116816 + 0.202332i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 235.559i 0.300842i
\(784\) 0 0
\(785\) 1611.00 2.05223
\(786\) 0 0
\(787\) −15.5000 26.8468i −0.0196950 0.0341128i 0.856010 0.516959i \(-0.172936\pi\)
−0.875705 + 0.482847i \(0.839603\pi\)
\(788\) 0 0
\(789\) −283.500 163.679i −0.359316 0.207451i
\(790\) 0 0
\(791\) −122.000 845.241i −0.154235 1.06857i
\(792\) 0 0
\(793\) −156.000 + 270.200i −0.196721 + 0.340731i
\(794\) 0 0
\(795\) −238.500 413.094i −0.300000 0.519615i
\(796\) 0 0
\(797\) 595.825i 0.747585i −0.927512 0.373793i \(-0.878057\pi\)
0.927512 0.373793i \(-0.121943\pi\)
\(798\) 0 0
\(799\) 1255.74i 1.57164i
\(800\) 0 0
\(801\) 284.000 + 491.902i 0.354557 + 0.614110i
\(802\) 0 0
\(803\) 1011.50 1751.97i 1.25965 2.18178i
\(804\) 0 0
\(805\) 148.500 116.913i 0.184472 0.145234i
\(806\) 0 0